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The Redesigned SAT/ACT Diagnostic

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system without written permission of College Planning Partnerships.

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Version 2.3

ii The SAT/ACT Diagnostic

 The Redesigned SAT/ACT Diagnostic

TABLE OF CONTENTS
Welcome To The Redesigned SAT/ACT Diagnostic iv
The SAT/ACT Diagnostic 1
Administering The Diagnostic: 2
Read This Before You Take The Test: 3
ACT English Test 4
SAT Reading Test 12
ACT Mathematics Test 22
SAT Writing and Language Test 35
ACT Reading Test 44
SAT Math Test—No Calculator 50
SAT Math Test—Calculator 56
ACT Science Test 66
Answer Key & Solutions 76
Comparing The SAT & ACT 98
Tip Sheet 100
Tips for the SAT Reading and Writing/Language Sections 101
Tips for the ACT Reading and English Sections 101
Helpful Tips for the SAT Math Section 102
Helpful Tips for the ACT Math Section 102
Helpful Tips for the ACT Science Section 102
60 Facts, Formulas, and Concepts that ALL Students Must Know 103
Returning Your Results 111
Bubblesheets 114

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The Redesigned SAT/ACT Diagnostic

Welcome To The Redesigned SAT/ACT Diagnostic

Thank you for your interest in the SAT/ACT Diagnostic. Standardized testing, though no one’s favorite pastime, is still a critical
part of the college application process. Studying for the right test is critical.

Why The SAT/ACT Diagnostic Is a Good First Step

We have discovered that most students have a natural predisposition towards the SAT or ACT. We designed this test to show
students which exam, if either, they are better suited for - as efficiently as possible.

The Benefits of Focused Efforts

The life of a high school junior or senior is incredibly busy, and their amount of time is limited. A student who prepares for both
tests is using half of their energy and time preparing for an exam whose results admissions officers may not even consider.

We believe that spending your time preparing for the right test is critical.

How To Take the Right First Step

Enclosed, you will find the exam booklet (with proctoring instructions), bubblesheets, and a solution guide. Before you begin, it is
absolutely critical that you:

• Read all of the instructions carefully, especially the paragraph about guessing.

• Find a quiet space that will remain quiet for about 4 hours. The closer you can simulate test conditions, the better. Make sure
you have at least three sharpened pencils, as well as a calculator.

• Have a watch or clock in view of your testing area. It is important that you do not exceed the allotted time on any single
section. If you do so, your results may not be valid.

We wish you the best of luck. Please give us a call at 860-664-9857 if you have any questions.

iv The SAT/ACT Diagnostic

 1 The SAT/ACT
ACT English Test
Diagnostic

www.satactdiagnostic.com 1
The Redesigned SAT/ACT Diagnostic

Directions:
Administering The Diagnostic:

If a proctor is available for the exam, he/she should do the following before conducting the test. If not, the student must do the
following.

• Remove the bubblesheets at the back of the exam. Students should write their name on each bubblesheet and fill in all of
page one.
• Ensure that the student has at least three pencils, an eraser, and a calculator (to be used on sections 3 and 7 ONLY).
• Ensure that any electronic device is turned off for the duration of the exam.
• Remove any earplugs, which may not be worn during testing, any highlighters, rulers, dictionaries or other books, pens
or colored pencils, pamphlets and papers of any kind, including scratch paper.
• Read the student instructions (located on the next page) aloud. Answer any questions.

Before each passage, the proctor should post the start and end time for the section and say:

• This section is [X] minutes long. It will end at [time].

• (Only before section 6): This section contains 12 questions, of which nine are multiple choice, and three require student-
produced responses. Please follow the directions for submitting responses to Questions 10 through 12 carefully. They can
be found immediately before Question 10.
• (Only before section 7): This section contains This section contains 24 questions, of which 19 are multiple choice, and
five require student-produced responses. Please follow the directions for submitting responses to Questions 20 through
24 carefully. They can be found immediately before Question 20.
• If you finish before time is called, you MAY NOT turn to any other section.

(Recommended) With five minutes remaining in the section, say:

• You have five minutes remaining in this section.

Section Time (Minutes) Questions Calculator

ACT English 27 45 No
SAT Reading 42 33 No
ACT Math 40 40 Yes
Break 5 N/A N/A
SAT Writing & Language 26 33 No
ACT Reading Test 27 30 No
SAT Math (No Calculator) 15 12 No
Break 5 N/A N/A
SAT Math (Calculator) 34 24 Yes
ACT Science 26 29 No
Total 247 246

CONTINUE READING ON THE NEXT PAGE

2 The SAT/ACT Diagnostic

 The Redesigned SAT/ACT Diagnostic

Directions:
Read This Before You Take The Test:

This booklet contains tests in English, Writing, Mathematics, Reading, and Science. CALCULATORS MAY BE
USED ON SECTIONS 3 AND 7 ONLY. Use a number 2 pencil and make your marks heavy and dark. Do not use a
pen or any other ink pen.

The questions in each section are numbered, and the suggested answers for each question are lettered. On the
bubblesheet, the rows of circles are numbered to match the questions, and the circles in each row are lettered to
correspond to the answers.

For each multiple-choice question decide which answer is best and fill in the corresponding circle on the
bubblesheet. Make sure to fill in the circle completely. For the grid-ins in Section 6 and 7, eight questions do not
have answer choices. Write your answer choices in the designated areas provided on the bubblesheet. Mark only one
answer for each question.

If you decide to change an answer, erase your answer thoroughly before marking a new answer. Make sure to fill
in the correct answer on the bubblesheet.

Only answers marked on your bubblesheet will be scored. Your score on all sections will be based only on the
number of questions you answer correctly. You will NOT be penalized for guessing on any test sections. IT IS TO
YOUR ADVANTAGE TO ANSWER EVERY QUESTION EVEN IF YOU HAVE TO GUESS.

You may work on a section ONLY when your test supervisor tells you to do so. If you finish a section before
time is called, you may use the remaining time to return to questions you are unsure of. You may NOT go back to a
previous section. You may NOT proceed to another section until you are advised.

You may NOT fill in or alter circles within a section after time is called for that section.

DO NOT TURN THE PAGE UNTIL TOLD TO DO SO.

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ACT ENGLISH TEST

1
45 Questions — 27 Minutes
DIRECTIONS: There are three passages in this sec- Read the entire passage once before you start to an-
tion. In the column next to the text you will find ques- swer. Some questions pertain to a larger portion of the
tions that correspond to the underlined portions in the text, or the passage in its entirety. Make certain that
text. Choose the best answer choice. NO CHANGE is you’ve read enough of the text beyond the question to
the correct answer choice if the underlined portion does derive the right answer. Bubble your answers on the
not need improvement. bubblesheet.

PASSAGE I

Harvesting Strawberries
The guide, my new mentor, handed me a basket

and showing me which row to begin with. 1. A. NO CHANGE

1 B. and showed
C. by showing
D. had shown
“Sparkle Supreme are down here,” he said. “Three rows 2. If the writer wanted to connect the opening paragraph to
2 the setting of the rest of the essay, which of the following
over are Early Glow.” choices – assuming all are true –would best do this?
2
F. NO CHANGE
G. I had spent several days finding the right farm.
H. You can’t always get Early Glow and Sparkle
Supremes.
From afar, the rows looked pleasant and inviting, J. I thanked him for giving me a large basket.

they were clustered with red fruit. The sun shone down, 3. A. NO CHANGE
3 B. all of them were
dissipating the morning chill. It was a perfect June morning C. they’re
D. DELETE the underlined portion

to pick fruit. For example, the paths between rows were 4. F. NO CHANGE
4 G. In the far distance,
littered with sharp rocks, and swarms of gnats hovered H. Up close,
J. Or else,

overhead. The bushy plants formed dense mounds, visual 5. A. NO CHANGE

5 B. visually
C. so visually
D. visual so

appealing. The sky was crystal clear. Dull red berries hid 6. If all of the choices are accurate, which one provides the
6 greatest contrast to the description of the rows in the first
beneath the leaves where previous pickers had missed them. sentence of this paragraph?
F. NO CHANGE
G. Bright berries glowed
H. Ripe berries glistened
J. Sun-soaked berries rested

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4 The SAT/ACT Diagnostic

1
I saw the earlier gatherers far ahead down the row.
Unauthorized copying or reuse of
any part of this page is illegal.

7.
1
Assuming that all choices are true, which most effectively
7 concentrates on one person’s picking the strawberries?
A. NO CHANGE
B. I bent down and searched through the leaves for the
ripest fruit.
C. This farm was well-known throughout the area.
D. We have a tradition in my family of picking straw-
Sparkle Supreme and Early Glow—the words berries every June.
themselves make your mouth water—being cultivated in 8. F. NO CHANGE
8 G. have been cultivated
H. to be cultivated
J. DELETE the underlined portion
New England for decades. Many farmers now grow it 9. A. NO CHANGE
9 B. there own
C. their one
D. them
commercially and in increased quantities. Locals and out- 10. If all of the the choices are true, which one provides
10 information that is most relevant to the topic of the
of-towners can’t seem to get enough of them. Early Glows paragraph?
10
are larger than average and have perfect shape. Sparkle F. NO CHANGE
G. The farm has been in the same family for years.
Supremes are bright red, medium-sized, and loaded with H. The day was already hot, and it wasn’t yet noon.
J. Strawberries are my favorite fruit.
intense, super-sweet flavor.

Usually, the best way to pick a strawberry is to

pinch the stem above the berry and allow it to roll into your

palm. This will minimize bruising of the fruit. Don’t throw

the berries into the basket, and don’t overfill the basket.

Fruit should not be picked during the hottest part of the day

because the berries become soft and damaged.

Early Glow berries set and come into maturity 11. A. NO CHANGE
11 B. become old enough to pick
earlier than any other strawberry. But when the C. ripen
D. grow into ripeness

fruit, which grows on farms, is clustered among the 12. F. NO CHANGE

12 G. that features prominently in supermarket displays
H. which has always been popular
J. DELETE the underlined portion

leaves, so that a picker can have a hard time finding all of 13. A. NO CHANGE
13 B. a picker
the berries. My guide advised me to be sure to push back C. so a picker
D. so that pickers
the leaves in order to find all the berries. Being careful not 14. F. NO CHANGE
14 G. I was careful not to overfill the basket,
to overfill my basket, I walked back to the stand where H. Carefully avoiding the mistake of making the basket
14
overfull,
several baskets rested out of the sunlight. I popped a berry J. The basket being not overfull,

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1 Unauthorized copying or reuse of

into my mouth, spat out the hull, and allowed the sweet
any part of this page is illegal.

15. A. NO CHANGE
1
15 B. would of spit
flavor to make all the work worthwhile. C. have spat
D. spitted

PASSAGE II

Saving the Whooping Cranes

[1]
Each fall a magical event takes place—the annual

migration of whooping cranes from their summer breeding

range to their winter habitat in Florida. Their route includes 16. The writer would like to insert the following accurate
16 information:
croplands, marshes, and submerged sandbars in rivers in the
“In Wisconsin”
eastern United States. [A] Because the cranes fly relatively Should the writer do so?
F. Yes, because it gives a detail than connects the
cranes’ near extinction to a specific region.
G. Yes, because it balances the sentence – winter habitat
in Florida and summer breeding range in Wisconsin.
H. No, because it creates a confusion whether the
cranes summer in Florida or Wisconsin.
J. No, because it gives details that makes the essay less
focused.

lowly when landing or taking off, however, 17. A. NO CHANGE

17 B. lower
C. more lowly
D. low

the risk for them of colliding with wind turbines and 18. F. NO CHANGE
18 G. they are at risk of
transmission towers that are proliferating along the route. H. while risking
J. their risk of
[2]
[1] In the mid-1900’s, whooping cranes were near

extinction (only 21 birds) due to over-hunting and reduction

of habitat. [B] [2] Now the birds have relapsed because of 19. A. NO CHANGE
19 B. recovered
C. rebuild
D. remain

conservation efforts. [3] Private donations has funded this 20. F. NO CHANGE
20 G. been funding
H. have funded
J. is funding

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6 The SAT/ACT Diagnostic

1
program by scientists, from the Whooping Crane Eastern
Unauthorized copying or reuse of
any part of this page is illegal.

21. A. NO CHANGE
1
21 B. scientists from the Whooping Crane Eastern
Partnership. [4] One such effort, Operation Migration, aims Partnership
21
C. scientists, from the Whooping Crane, Eastern
to teach the cranes to avoid the flight corridor in Partnership
D. scientists – from the Whooping Crane Eastern
Partnership
areas where the endangered cranes may fly and 22. F. NO CHANGE
22 G. in areas that have many power lines and turbines
H. in areas where the cranes would like to fly
J. in areas
establishing a new flight path. 24 23. A. NO CHANGE
23 B. they would establish
C. having established
[3] D. establish
The Partnership engages pilots of ultra-light
aircraft to lead the birds on training flights over the White 24. To improve Paragraph 2, Sentence 3 should be placed
F. where it is now.
River Marsh State Wildlife Area in Wisconsin throughout G. before Sentence 1.
H. after Sentence 1.
the summer. This builds the cranes’ stamina for their fall J. after Sentence 4.
migration to their Florida wintering grounds. [C] Each year

since 2001 a class of cranes has been led by the aircraft on 25. A. NO CHANGE
25 B. have
C. are
D. is

their first migration south via a flight path that avoids 26. F. NO CHANGE
26 G. by means of
wind farms and power lines. During these flights H. with
J. as
through the eastern United States pilots lead the birds to rich 27. A. NO CHANGE
27 B. flights, through the eastern United States, pilots
feeding grounds. lead
[4] C. flights through the eastern United States, pilots lead
D. flights through the eastern, United States pilots lead
By avoiding the highly hazardous route over the

Great Plains where wind farms are increasingly plentiful, the

birds are safer because they encounter less power lines and 28. F. NO CHANGE
28 G. fewer than
H. fewer
J. lesser

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1 Unauthorized copying or reuse of
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windmill blades during take-off and landing. Scientists at

1
29. The writer of the essay wants to incorporate the following
sentence:
Operation Migration are optimistic that the new flight path
Normally, the birds fly between 500 and 5000 feet
will alleviate this condition. [D] and are quite safe.
If the writer uses this sentence it should be placed at
which point:
A. A in Paragraph 1
B. B in Paragraph 2
C. C in Paragraph 3
D. D in Paragraph 4

Question 30 asks about the preceding passage as a

whole.

30. If the writer’s primary goal were to explain the rate of

success of a recent project to save whooping cranes from
extinction, would this essay accomplish this goal?
F. Yes, because it contains information about the
number of cranes alive today.
G. Yes, because it describes how the project described
in this essay has led to new ways to protect the
cranes.
H. No, because it only provides an overview of a
project and does not report results.
J. No, because the essay is focused on the use of ultra-
light aircraft.

PASSAGE III

Mark Rothko — Who Painted Color

American painter Mark Rothko (1903-1970) loved

color, in the late 1940’s Rothko abandoned all suggestion of 31. A. NO CHANGE
31 B. color during
figures and instead exploited the expressive power of color C. color, during
D. color. In
by deploying it in large fields of color that surround the

viewer when seen up close. Each viewer will have his own

personal response to a swath of red-purple: from a 32. If the writer omitted the phrase “from a Christian’s…
32 achieved enlightenment” and placed a period after the
Christian’s vision of the supreme sacrifice of Christ’s blood word “purple”, the paragraph would lose:
32
to the Buddhist’s view of the casting off of title and privilege F. a sense of the variety of Rothko’s viewers’ reactions
32 to the colors
by Siddhartha as he achieved enlightenment. G. a hint as to why Rothko painted few people
32 H. an explanation of why Rothko appreciated color
J. examples of how light affected Rothko’s work
Rothko believed that because color affects our

mental state and mood. It is the dramatic element that 33. A. NO CHANGE
33 B. mood, or it
C. mood, it
D. mood that it

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8 The SAT/ACT Diagnostic

1 Unauthorized copying or reuse of
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conveys life and immediacy in a painting. His art is deeply

1
grounded in his spirituality. “Art to me is an anecdote of the

spirit,” he said. Rothko believed that the rectangles of color

in his work, “Four Darks in Red (1958)”, offered a new way 34. F. NO CHANGE
34 G. offer
to represent the presence of the spirits he had tried to capture H. presents
J. offering
in earlier works that employed actual figures. These new

shapes themselves say what the figures once said. The artist 35. A. NO CHANGE
35 B. shapes themself
imagined that the colors and shapes would create a kind of C. shapes; themselves
D. shapes, themselves

direct communication, between himself and the viewer 36. F. NO CHANGE

36 G. communication, with
which might touch the viewer with a higher spirituality. H. communication, with,
J. communication between
His original technique of applying color helped

Rothko achieve the power and spirituality of his work. In

Orange and Yellow (1956) he layered color on color, placing

the bright, rich yellow and orange on a background of duller,

softer orange. The result is a remarkable effect of light: the 37. A. NO CHANGE
37 B. (Do not begin a new paragraph) Nevertheless the
radiance of the yellow interacts with the smoldering orange, C. (Begin a new paragraph) Nevertheless the
D. (Begin a new paragraph) In the
and both are tempered by the gentle orange

which has been placed behind the other two colors. 38. F. NO CHANGE
38 G. in the background.
H. being placed in the background.
J. color.

The entire painting one of Rothko’s most famous, is imbued 39. A. NO CHANGE
39 B. painting, one of Rothko’s most famous
with a luminous quality. C. painting, one of Rothko’s most famous,
D. painting, one of Rothko’s most, famous
Fourteen Rothko paintings can be seen at the

Rothko Chapel at Saint Thomas Catholic University in

Texas. All of these paintings are in hues of dark purple,

maroon, and black. The darkness of the works floods the 40. Which choice best reinforces the feeling that the darkness
40 was intense?
F. NO CHANGE
G. appears to
H. makes aware
J. seeps through to

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www.satactdiagnostic.com 9
1
viewer and expresses Rothko’s mood of melancholy, and
Unauthorized copying or reuse of
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41. A. NO CHANGE
1
41 B. mood of melancholy and, sense of loss
sense of loss in his last years. 42 C. mood of melancholy and sense of loss,
41
D. mood of melancholy and sense of loss

42. Which of the following true statements would draw a

conclusion consistent with the information presented in
the paragraph?
F. Landscapes were other types of work Rothko created
in earlier times.
G. These fourteen paintings stand as a final testament
to Rothko’s belief in the power of color.
H. Color was also an important element in Rothko’s
earlier work.
J. Other examples of Rothko’s use of these colors can
be found in the Yale Art Gallery.
As it turns out, these works, but they would not be 43. A. NO CHANGE
43
B. however they
unveiled until the Chapel’s opening in 1971, are his final
C. which
statement to the world. Rothko committed suicide on D. and

February 25, 1970. The beautiful hues in the works 44. If all the choices are true, which one is most consistent
44
with the tone of the essay?
foreshadowed his tragic death. 45
F. NO CHANGE
G. luminous qualities of his art
H. Chapel’s impressive size
J. melancholic colors of the Chapel

Question 45 asks about the preceding passage as a

whole.

45. If the writer had intended to convey an aspect of Rothko’s

talent, would this essay successfully attain the goal?
A. Yes, because the essay describes the central role of
color in Rothko’s paintings.
B. Yes, because the essay includes biographical infor-
mation on Rothko.
C. No, because the essay gives no examples of Roth-
ko’s portraiture.
D. No, because the essay focuses more on Rothko’s
subjects than on his technique.

STOP. BE CERTAIN NOT TO EXCEED THE

ALLOTTED TIME. YOU MAY PROCEED TO
SECTION 2 WHEN TOLD TO DO SO.

10 The SAT/ACT Diagnostic

No Testing Material On This Page
 2 Unauthorized copying or reuse of
any part of this page is illegal.
2
SAT Reading Test
42 MINUTES, 33 QUESTIONS

Locate Section 2 of your bubblesheet to record the questions in this section.

DIRECTIONS
Read the passages below and then choose the best answer for each question based on
what was written or implied in the passage or passages as well as the accompanying
graphics (such as a table, graph, or diagram).

Question 1–11 are based on the following passage. of misery which was to befall me.
This passage is adapted from Daniel Defoe, Robinson Crusoe, My father, a wise and grave man, gave me serious
originally published in 1719. and excellent counsel against what he foresaw was my
design. He called me one morning into his chamber,
I was born in the year 1632, in the city of York, of 35 where he was confined by the gout, and expostulated
a good family, though not of that country, my father very warmly with me upon this subject. He asked
being a foreigner of Bremen, who settled first at Hull. me what reasons, more than a mere wandering
Line He got a good estate by merchandise, and leaving off inclination, I had for leaving father's house and my
5 his trade, lived afterwards at York, from whence he native country, where I might be well introduced, and
had married my mother, whose relations were named 40 had a prospect of raising my fortune by application
Robinson, a very good family in that country, and and industry, with a life of ease and pleasure. He told
from whom I was called Robinson Kreutznaer; but, me it was men of desperate fortunes on one hand, or
by the usual corruption of words in England, we are of aspiring, superior fortunes on the other, who went
10 now called - nay we call ourselves and write our name abroad upon adventures, to rise by enterprise, and
- Crusoe; and so my companions always called me. 45 make themselves famous in undertakings of a nature
I had two elder brothers, one of whom was out of the common road; that these things were all
lieutenant-colonel to an English regiment of foot either too far above me or too far below me; that
in Flanders, formerly commanded by the famous mine was the middle state, or what might be called
15 Colonel Lockhart, and was killed at the battle near the upper station of low life, which he had found, by
Dunkirk against the Spaniards. What became of 50 long experience, was the best state in the world, the
my second brother I never knew, any more than my most suited to human happiness, not exposed to the
father or mother knew what became of me. miseries and hardships, the labour and sufferings of
Being the third son of the family and not bred to the mechanic part of mankind, and not embarrassed
20 any trade, my head began to be filled very early with with the pride, luxury, ambition, and envy of the
rambling thoughts. My father, who was very ancient, 55 upper part of mankind. He told me I might judge of
had given me a competent share of learning, as far as the happiness of this state by this one thing - viz. that
house-education and a country free school generally this was the state of life which all other people envied;
go, and designed me for the law; but I would be that kings have frequently lamented the miserable
25 satisfied with nothing but going to sea; and my consequence of being born to great things, and
inclination to this led me so strongly against the will, 60 wished they had been placed in the middle of the two
nay, the commands of my father, and against all the extremes, between the mean and the great; that the
entreaties and persuasions of my mother and other wise man gave his testimony to this, as the standard
friends, that there seemed to be something fatal in of felicity, when he prayed to have neither poverty
30 that propensity of nature, tending directly to the life nor riches.

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12 The SAT/ACT Diagnostic

 2 Unauthorized copying or reuse of
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2
65 He bade me observe it, and I should always find 4
that the calamities of life were shared among the
upper and lower part of mankind, but that the middle Which choices provide the best evidence for the
station had the fewest disasters, and was not exposed answer to the previous question?
to so many vicissitudes as the higher or lower part of
70 mankind. A) Lines 12–16 (“I…Spaniards”)
B) Lines 21–31 (“My…me”)

1 C) Lines 38–41 (“I…pleasure”)

D) Lines 65–70 (“He…mankind”)
The main purpose of the passage is to

A) discuss some grave character flaws in Robinson

5
Crusoe.
B) focus on the efforts of a father to convince his As used in line 9, “corruption” most nearly means
son on how best to live his life.
A) evolution.
C) provide an overview of how a family in the early
B) dishonesty.
1600s decided on the best way to live a life of
ease and pleasure. C) crime.
D) explain the relationship between a father and his D) misuse.
son.
6
2 It can most reasonably be inferred that after the
Which best summarizes the third and fourth narrator left home, his parents
paragraphs of the passage (lines 32–64)?
A) missed him enormously.
A) A father, who is deeply concerned about his son’s B) realized he had a propensity to travel and seek
choice to leave home and country, tries to make a adventure.
strong case for him to stay.
C) were greatly pleased with his success after all.
B) A son’s fatal attraction to the sea and why he
D) did not know what happened to him.
misjudges happiness.
C) A wise and grave father convinces his son to 7
pursue what he called “the upper station of low
life.” Which choice provides the best evidence for the
answer to the previous question?
D) A son has to wrestle with his decision to go along
with the wishes of his father and mother. A) Lines 4–11 (“He…me”)
B) Lines 16–18 (“What…me”)
3 C) Lines 41–55 (“He…mankind”)
The narrator indicates that his choice to go to sea led D) Lines 55–64 (“He … riches”)
him to a life of

A) solitude.
B) fortune.
C) misery.
D) self-satisfaction.

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www.satactdiagnostic.com 13
 2 Unauthorized copying or reuse of
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2
8 10
Which situation is most similar to the one described Which choice best summarizes the father’s view on
in lines 1–11 (“I was … me”)? what was most suited to a life of happiness?

A) A son who is born into a well-to-do family A) Seeking neither fortune nor fame, but rather
decides to change his name after being corrupted aiming for the middle state.
by society. B) Resisting a life of ease and pleasure.
B) A sea captain decides to shorten his long, C) Cherishing what one has and not wishing for
foreign-sounding name so that everyone will what one doesn’t have.
remember his name.
D) Seeking true adventure and ignoring a
C) A family placed in the middle of something materialistic life.
larger than itself reluctantly agrees to its name
being shortened. 11
D) A long family name that originated in Germany
The author’s father can best be described as
is shortened when the family moves to France
and the family does not fight to retain the A) wise and unconcerned.
original pronunciation of the name.
B) serious and distrustful.
9 C) caring and inquisitive.
As used in line 28, “entreaties” most nearly means D) trusting and ambitious.

A) peace offerings.
B) pleas.
C) discussions.
D) tears.

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14 The SAT/ACT Diagnostic

 2 Unauthorized copying or reuse of
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2
Question 12–22 are based on the following Russell Feingold, a democrat from Wisconsin, said
passage. the current ruling “may represent the latest step in an
This passage is adapted from news accounts published effort by a majority of the court to dismantle entirely
by The Washington Post, The New York Times and The the long-standing structure of campaign finance
Associated Press during the first few days that followed the 50 law erected to limit the undue influence of special
historic Supreme Court ruling that struck down campaign interests on American politics.”
finance reform in April of 2014. It was almost as if Justice Roberts had anticipated
responses similar to McCain’s. “Money in politics
The Supreme Court’s controversial landmark may at times seem repugnant to some, but so
decision in 2014 to abolish the limits on campaign 55 too does much of what the First Amendment
contributions, struck down the ceilings on the vigorously protects,” Roberts wrote. “If the First
Line maximum amount of money an individual can Amendment protects flag burning, funeral protests
5 contribute to federal candidates in a two-year election and Nazi parades—despite the profound offense
cycle. The justices said that the old campaign finance such spectacles cause—it surely protects political
laws violated free-speech rights. 60 campaign speech despite popular opposition.”
The divisive 5-4 decision put an end to the The decision struck down a law that very few
limit on the amount of money wealthy donors can Americans could afford to violate; the amount of
10 contribute to candidates and political committees. money an individual could contribute over two years
The decision illustrates a deeply divided court: the to candidates and political committees. Under the
liberal justices were in favor of keeping in place 65 old law, individuals could not contribute more than
the current campaign finance restrictions that $48,600 to candidates, plus an additional $74,600 to
they argue are key to ensuring that the rich do not political committees.
15 have undue influence over the electoral process, Republican Party officials cheered the opinion.
while the conservative justices argued that the First The ruling “is an important first step toward restoring
Amendment (freedom of expression) prohibits 70 the voice of candidates and party committees and
Congress from creating laws that restrict the exercise a vindication for all those who support robust,
of First Amendment rights in the form of campaign transparent political discourse,” said Reince Priebus,
20 contributions. chairman of the Republican National Committee.
The justices’ contentious decision drew a Justice Breyer’s dissent, argues that the court’s
distinction between contributions, which the court 75 decision is unconstitutional. “The First Amendment
said could be limited to prevent corruption or the advances not only the individual’s right to engage
appearance of corruption, and expenditures, which in political speech, but also the public’s interest in
25 the court determined were a form of direct personal preserving a democratic order in which collective
expression. speech matters,” Breyer wrote. “Where enough
“There is no right more basic in our democracy 80 money calls the tune, the general public will not be
than the right to participate in electing our political heard . . . And a cynical public can lose interest in
leaders,” wrote Chief Justice John G. Roberts Jr. in political participation altogether.”
30 the court’s main opinion. “We have made clear that Breyer argued that removing the aggregate
Congress may not regulate contributions simply limits on campaign contributions created large
to reduce the amount of money in politics, or to 85 loopholes that will allow the rich to unduly influence
restrict the political participation of some in order to government. An individual he called “Rich Donor”
enhance the relative influence of others.” could write a check for $3.6 million to benefit his
35 The liberal justices represented by Justice political party and its candidates because of the
Stephen G. Breyer sharply disagreed with the court’s loopholes, he said.
ruling. Breyer read his dissent from the bench: 90 Roberts took issue with Breyer’s reasoning.
“Today’s decision, we fear, will open a floodgate,” He Roberts wrote that the counter arguments presented
underscored that the ruling “overturns key precedent, by the dissenters and the government, “are either
40 creates serious loopholes in the law and undermines, illegal under current campaign finance laws or
perhaps devastates, what remains of campaign divorced from reality.”
finance reform.”
U.S. Senator John McCain, a republican from the
state of Arizona, who sponsored the 2002 Bipartisan
45 Campaign Finance Reform ACT with U.S. Senator

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2
12 16
As used in line 3, “ceilings” is closest in meaning to The statements made in paragraph eight (lines 61–67)
indicates that the ruling will most likely help
A) excesses.
B) upper limits. A) the wealthiest Americans.

C) amounts. B) the disenfranchised.

D) glass floors. C) the middle class.

D) the candidates who have little financial support.
13
17
The judges struck down the current campaign law
that limited the amount of money an individual could What is one of the impacts that Justice Breyer
contribute based on the fact that believes “Rich Donor” may ultimately have on voting
in the United States?
A) money in politics is not repugnant.
B) it’s a violation of the Campaign Finance Reform A) It may encourage more people to run for office.
Act. B) It will make more candidates think twice before
C) people are free to elect and support the the run for office.
candidates of their choice. C) It may discourage the public from participating
D) it’s a violation of the First Amendment. in politics.
D) It will prove to be a benefit to the Republican
14 party candidates.
Which choice provides the best evidence for the 18
answer to the previous question?
Which choice provides the best evidence for the
A) Lines 11–20 (“The decision … contributions”) answer to the previous question?
B) Lines 27–34 (“There is … others”)
A) Lines 1–6 (“The Supreme … cycle”)
C) Lines 68–72 (“Republican Party … Committee”)
B) Lines 8–20 (The divisive … contributions”)
D) Lines 90–94 (“Roberts … reality”)
C) Lines 35–42 (“The liberal … reform”)
15 D) Lines 74–82 (“Justice Breyer’s … altogether”)
What is Justice Stephen G. Breyer’s biggest concern 19
(lines 35–42) about the new ruling?
As used in line 83, “aggregate” most nearly means
A) It may put an end to campaign finance reform.
B) It might encourage more unqualified candidates A) most.
to run for office. B) complete.
C) It could jeopardize the First Amendment. C) highest.
D) It will overturn other key precedents that the D) total.
middle class is dependent upon.

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16 The SAT/ACT Diagnostic

 2 Unauthorized copying or reuse of
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2
20 Question 23–33 are based on the following
passage.
Chief Justice Roberts (lines 90–94) counters Breyer’s Passage 1 is adapted from Gurdev S Khush, “Genetically
argument in a manner that could best be categorized modified crops: the fastest adopted crop technology in
as the history of modern agriculture” by Agriculture & Food
Security. Passage 2 is adapted from Charles Benbrook,
A) cold and scholarly “Impacts of genetically engineered crops on pesticide use in
the U.S. – the first sixteen years” by Environmental Sciences
B) respectful but strong
Europe.
C) legal and sarcastic
Passage 1
D) rhetorical but direct Over the last thirty years, many of the crops that
humans eat—corn, soybeans, wheat, for example—
21 have been modified on a genetic level. Like other
Based on the U.S. Supreme Court's decision to Line genetically modified (GM) crops, corn is still corn,
abolish limits on campaign finance, it is reasonable to 5 but the DNA of the corn has been altered to provide
the maximum amount of utility to both the consumer
conclude that
and the farmer.
A) Supreme Court Justices, while they don’t always The continued adoption of GM crops has helped
agree on legal matters, have great admiration for the environment as well as the farmer, opines Clive
one another when they’re off the bench. 10 James, founder of The International Service for the
Acquisition of Agri-biotech Applications. James, who
B) Supreme Court Justice have no issue with writing has published annual reports on the global status of
highly critical and biting remarks about their commercialized GM crops since 1990, cites sources
colleagues’ legal decisions. that estimate the value of increased crop production
C) Supreme Court Justices believe that their legal 15 from planting GM crops between 1996 and 2010 at
actions will come under fierce attack. $78 billion. These plantings, he said, also effected
savings of 443,000,000 kg of pesticides, thereby
D) Supreme Court Justices care deeply about the contributing to environmental sustainability. In 2010
U.S. and work to uphold the Constitution to the alone, GM crops helped reduce CO2 emissions by
letter of the law. 20 19 billion kg, the equivalent to taking approximately
nine million cars off the road.
22 GM crops are beneficial to farmers’ livelihoods.
They produce foods that last longer before perishing
What is the author’s main point about the Supreme than their non-GM counterparts. They produce
Court’s 2014 decision? 25 bigger yields than non-GM crops because farmers
A) Rich people will now have more influence over can more efficiently combat pests, weeds, and
diseases. Because of these multifarious benefits, GM
government.
crops have helped alleviate poverty by increasing
B) Poor people will now have less influence over incomes for 15 million small farmers who are among
government. 30 the poorest in the world.
C) The decision will only limit the wealthiest While opponents of GM farming categorize
Americans. its bounty as unsafe for human consumption,
distinguished international scientific organizations
D) The decision has further ignited a controversial such as the American Association for the
debate over campaign reform. 35 Advancement of Science and U.S. National Academy
of Sciences have offered volumes of compelling
and internationally accepted scientific data that
demonstrate that GM foods are as safe as those
harvested from conventionally raised crops.

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2
Passage 2 into drinking water sources.
40 Genetically engineered crops have not come 65 An estimated 94 percent of the soybean crop
without a cost to the consumer, the farmer and the in the U.S. in 2011 was planted as a GM variety.
environment. A growing number of herbicide- Similarly, 72 percent of maize (corn) and 96 percent
resistant (HR) weeds, a byproduct of the burgeoning of cotton planted in 2011 were planted as GM
genetically modified (GM) agribusiness, are forcing varieties. The frequency of human exposures to
45 farmers to increase herbicide application rates and to 70 toxic herbicides and levels of exposure via food,
apply different herbicides to prevent new, unforeseen drinking water, and the air have risen in the U.S. in
blights before they manifest. recent years. More than two-thirds of air and rainfall
At one time, the notion of applying herbicides samples tested in Mississippi and Iowa in 2007 and
such as glyphosate to commercial crops was 2008 contained glyphosate.
50 unimaginable. Glyphosate, a non-selective herbicide, 75 Heightened risk of public health impacts can be
killed both crops and weeds alike. However, as expected with more intensive herbicide use to protect
early as 1996, scientists created and planted the first GM crops. Stephanie Seneff, a research scientist at
genetically modified soybean and canola to resist the Massachusetts Institute of Technology, noted that
glyphosate. Farmers could now easily combat the when ingested, some common herbicides can slowly
55 weeds that disturbed their crops. 80 disrupt normal body functions and induce diseases
These developments led to a substantial increase such as Parkinson’s and various forms of cancer.
in the use of herbicide per hectare* from 1996 Though they may make the life of a farmer easier, it
through 2011. This increase has had harmful effects is imperative that the use of glyphosate is halted until
on the environment and the actual fruits of its regulators determine whether it is fully safe when
60 efforts. The upward trend in herbicide use on GM 85 ingested by humans.
crops compared to non-GM crops not only led to the
emergence and rapid spread of herbicide-resistant * a metric unit of square measure, equal to 2.471 acres or
10,000 square meters.
weeds, but also resulted in more toxins disseminating

The following table is adapted from Charles Benbrook, “Impacts of genetically engineered crops on pesticide use in the U.S. – the first
sixteen years” by Environmental Sciences Europe.

Projected rates of change in herbicide use, 2005-2011

Corn 2010–2011 2005–2010 (aggregate) 2005–2010 (per year)

Total Herbicides 2% 10.2% 2.0%
Glyphosate 2.5% 12.9% 2.6%
Soybeans 2010–2011 2005–2010 (aggregate) 2005–2010 (per year)
Total Herbicides 3.2% 35.2% 5.9%
Glyphosate 3.3% 53.4% 8.9%
Cotton 2010–2011 2005–2010 (aggregate) 2005–2010 (per year)
Total Herbicides 2.2% 3.1% 0.06%
Glyphosate -1% -10.3% -2.1%

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18 The SAT/ACT Diagnostic

 2 Unauthorized copying or reuse of
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2
23 27
The author of Passage 1 suggests that the usefulness Which choice provides the best evidence for the
of GM crops may benefit answer to the previous question?

A) the environment. A) Lines 50–54 (“Glyphosate … resist glyphosate”)

B) consumer and farmers. B) Lines 56–59 (“These developments … efforts”)
C) research scientists and farmers. C) Lines 65–72 (“An estimated … years”)
D) consumer, farmers and the environment. D) Lines 82–85 (“Though they … humans”)

24 28
Which best describes the evidence for the answer to As used in line 55, “disturbed” most nearly means
the previous question?
A) unbalanced.
A) Lines 1–11 (“Over … Applications”) B) worried.
B) Lines 16–21 (“These plantings … off the road”) C) hindered.
C) Lines 22–24 (“GM crops … non-GM D) interrupted.
counterparts”)
D) Lines 27–30 (“Because of these … world”) 29

25 The reference to the percentages of soybean, maize

and cotton planted in the U.S. in 2011 (lines 65–69)
As used in line 33, “distinguished” most nearly means serves mainly to

A) woefully undermined. A) make the case that due to rainfall alone more
B) easily discerned. than 66 percent of Americans have been exposed
to toxic herbicides.
C) eminently royal.
B) argue that Mississippi and Iowa are two states
D) highly respected. one should avoid due to toxic air and rainfall.

26 C) make the case that a very large percentage of

Americans who eat GM crops are exposed to
The author of Passage 2 indicates that ultimately the toxic herbicides.
use of glyphosate primarily should be seen as the
D) argue that people should avoid eating GM
catalyst that led to
varieties of soybean and maize (corn) based
A) scientists creating and planting genetically products.
modified plants.
B) harmful effects on crops and the environment.
C) unimaginable commercial crops.
D) an overall decrease in the use of herbicide.

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2
30 32
According to the table, which statement is true about How would the author of Passage 2 most likely
the projected change in glyphosate use from the year respond to the assertion made in paragraph three
2010 to the year 2011? (lines 22–30) that GM crops are beneficial to farmers’
livelihoods and alleviating poverty?
A) The rate of change of glyphosate on corn crops
is projected to be wildly out of proportion to the A) With disdain, because a thorough examination of
rate of change in each of the five years previous. farmers’ wages illustrates that GM crops have not
B) The amount of glyphosate used on cotton crops increased their livelihoods.
is projected to decrease for the first time since B) With approval, because GM crops have increased
2005. farmers’ livelihoods and reduced poverty.
C) About 53.4% of all soybean crops planted C) With concern, because while GM crops may be
between 2005 and 2010 received glyphosate beneficial to farmers’ livelihoods and alleviating
applications at some point during their growth. poverty, this type of farming is likely to heighten
D) The rate of increase of glyphosate use on soybean the risk of public health issues.
crops is projected to be smaller between 2010 D) With excitement, because GM crops are the best
and 2011 than it typically was between 2005 and way to rid the world of hunger.
2010.
33
31
Which choice would best support how the author of
Which choice best states the relationship between the Passage 1 would most likely respond to the charge of
two passages? “heightened risk of public impact” (line 75, Passage 2)
due to intensive herbicide use to protect GM crops?
A) Passage 1 states that genetically modified crops
will reduce the cost of food in the marketplace, A) Lines 9–11 (The … applications)
while Passage 2 states that GM crops will B) Lines 11–21 (James … road)
increase the cost of food.
C) Lines 22–30 (GM … world)
B) Passage 1 argues that genetically modified
crops benefit the consumer, the farmers, and D) Lines 31–39 (While … crops)
the environment, while Passage 2 argues that
GM crops pose a risk to the consumer and the
environment.
C) Passage 1 states that genetically modified crops
do not benefit the consumer, while Passage
2 states that genetically modified crops are
unhealthy.
D) Passage 1 argues that genetically modified crops
have increased dramatically since 1990, while
Passage 2 argues that this increase is not as large
as it appears to be.

STOP. BE CERTAIN NOT TO EXCEED THE

ALLOTTED TIME. YOU MAY PROCEED TO
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20 The SAT/ACT Diagnostic

No Testing Material On This Page
3 Unauthorized copying or reuse of
any part of this page is illegal.

ACT MATHEMATICS TEST

3
40 Questions — 40 Minutes
DIRECTIONS: Solve the problems, select the correct easier to solve without the use of a calculator.
answer, and fill the corresponding bubble on your bub- NOTE: Unless stated otherwise, the following may be
blesheet. assumed.
Do not spend too much time on a single problem. Solve 1. Illustrated figures are NOT always drawn to scale.
as many problems as you are able; once finished, re- 2. Geometric figures are in a plane.
turn to any problem in the remaining time.
3. The word line means a straight line.
You are allowed to use a calculator on this section of the 4. The word average means arithmetic mean.
exam, but some problems on the exam may actually be

1. Ashwin purchased 100 shares of stock at $22.50 per share. DO YOUR WORK HERE.
Each share rose $0.40 during his first month of ownership,
dropped $0.25 during the second, and rose $0.05 during the
third. What is the current value of Ashwin’s investment?
A. $2260
B. $2270
C. $2320
D. $2950
E. $3250

5 (x - 3)
2. For what value of x is the equation 4 = 20 true?
F. 13
G. 16
H. 19
J. 22
K. 28

3. A bag of licorice candies contains 28 red licorice pieces

and 32 black licorice pieces. What is the ratio of red pieces
to black pieces?
A. 1:7
B. 1:8
C. 7:8
D. 7:15
E. 8:7

4. In the figure below, AB is congruent to BC and A, C, and

D are collinear. What is the measure of +ABC ?

F. 36º B
G. 63º
H. 117º 153º
A D
J. 126º C
K. 153º

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22 The SAT/ACT Diagnostic

3
5. What is the result of the subtraction problem below?
Unauthorized copying or reuse of
any part of this page is illegal.

DO YOUR WORK HERE.

3
(4x 2 + 3) - (- 3x 2 - x + 5)

A. 7x 2 - x - 2
B. 7x 2 + x - 2
C. 7x 2 + x + 8
D. 7x 2 - x - 2
E. 7x 2 + x - 2

6. A swimming pool in the shape of a right rectangular prism

has length 14 feet and width 18 feet. The volume of the
water in the pool is 3780 cubic feet. To the nearest foot,
what is the depth of the water in the pool?
F. 7
G. 10
H. 15
J. 25
K. 120

7. Which of the following is the least common denominator

a b c
of the fractions 4 , 5 , and 30 ?
A. 30
B. 60
C. 120
D. 240
E. 600

8. The average of x, 2x, 4x and 8x is 67.5. What is the value

of x ?
9
F. 8
9
G. 2
H. 6

J. 9

K. 18

9. In the figure below, lines l and m are parallel and intersect

at line k as shown. Which of the following equations must
be true?
k

xº
A. x = 2y l
B. x=y
C. x = 90 - y yº
D. x = 180 - y m
E. x = 360 - 2y

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3 Unauthorized copying or reuse of

10. Which of the following expressions is equivalent to

any part of this page is illegal.

DO YOUR WORK HERE.

3
^ 4a 3 b 2h^ 5ab 5h ?
F. 19a 3 b 10
G. 19a 4 b 7
H. 20a 3 b 7
J. 20a 3 b 10
K. 20a 4 b 7

11. Which of the following translations shifts all points

graphed in the (x, y) coordinate plane to the left by 3 units?
A. (x, y) " (x, y - 3)
B. (x, y) " (x, y + 3)
C. (x, y) " (- 3x, y)
D. (x, y) " (x - 3, y)
E. (x, y) " (x + 3, y)

12. Carlie flipped a coin 162 times. The coin landed with the
heads side up 52 more times than it landed with the tails
side up. How many times did it land with the heads side
up?
F. 87
G. 93
H. 103
J. 107
K. 110

13. Which of the following number line graphs represents the

solution set of the inequality 6x + 5 $ 7 ?

A.
-2 0 2
B.
-2 0 2
C.
-2 0 2
D.
-2 0 2
E.
-2 0 2

14. In the standard (x,y) coordinate plane, what is the slope of

the line with equation 4x + 5y = 10 ?

F. -2
5
G. -4
4
H. -5
4
J. 5
5
K. 4

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24 The SAT/ACT Diagnostic

3 Unauthorized copying or reuse of
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15. The table below shows the daily noon temperatures for DO YOUR WORK HERE.
3
Minneapolis, Minnesota between Monday, March 9, 1987,
and Sunday, March 15, 1987. If the median noon tempera-
ture for this week was 33 ℉, which of the following could
NOT have been Sunday’s noon temperature?

Noon
Day
Temperature (℉)
Monday 29º
Tuesday 33º
Wednesday 40º
Thursday 22º
Friday 35º
Saturday 36º
Sunday

A. 11º
B. 29º
C. 32º
D. 33º
E. 35º

16. What is the solution set of the equation x 2 - 2x = 15 ?

F. " - 5, 3 ,
G. " - 3, 5 ,
H. " - 3, 2 ,
J. " - 0, 2 ,
K. " - 3, 5 ,

17. Will earns a weekly salary of P dollars, of which Q dollars

is withheld for federal and state taxes and R dollars is
withheld for his retirement savings. The remaining money
represents Will’s take-home pay. What fraction of Will’s
weekly salary is his take-home pay?

Q+R
A. P
P
B. Q+R
P-Q-R
C. P
Q+R-P
D. P
P
E. P+Q+R

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18. The dimensions of the right triangle shown below are given DO YOUR WORK HERE.
3
in feet. What is the area, in square feet of the triangle?

F. 2x 2 - 01x - 3
G. 2x 2 + 15x - 3 4x - 2
H. 4x 2 - 01x - 6
J. 4x 2 + 10x - 3
K. 4x 2 + 10x - 6 x+3

19. Which of the following graphs in the standard (x, y) coor-

dinate plane is the graph of y # ax + b , where a > 0 and
b < 0?

A. y D. y

x
O

x
O

B. y E. y

x x
O O

C. y

x
O

20. If x - 9 = 11 , what are the possible values of x?

F. - 20 and 2
G. - 20 and 20
H. -2 and 2
J. -2 and 20
K. 9 and 20

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26 The SAT/ACT Diagnostic

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21. As shown below, a 24-foot ramp forms an angle of 8c with DO YOUR WORK HERE.
3
the ground, which is horizontal. Which of the following
is an expression for the vertical rise, in feet, of the ramp?

24 ft
?

8º

A. 24 sin 8c
B. 24 cos 8c
C. 24 tan 8c
D. 24 sec 8c
E. 24 csc 8c

22. Rami took a survey of the entire junior class at Highland

Park High School. When he reported his results, he noticed
that 68% of the class preferred weekly homework to daily
homework. If 289 students in the junior class prefer weekly
homework to daily homework, how many students are
there in the junior class?
F. 136
G. 289
H. 351
J. 425
K. 714

23. On October 1, the price of gasoline at Quick Mart was

$2.25 per gallon. On November 1, the price of gasoline
was $2.43. By what percent did the price of gasoline rise
between October 1 and November 1?
A. 7.4%
B. 8.0%
C. 9.0%
D. 12.5%
E. 18.0%

24. If f (x) = 2x + 1 and g (x) = x 2 , what is the value of

f (g (4)) ?
F. 33
G. 51
H. 65
J. 81
K. 144

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www.satactdiagnostic.com 27
3 7
Unauthorized copying or reuse of
any part of this page is illegal.

DO YOUR WORK HERE.

3
25. If the circumference of a circle is 2 r inches, how many
inches long is its radius?

2
A. 7
4
B. 7
7
C. 4
7
D. 2
7
E. 2

26. In the standard (x,y) coordinate plane, the point (6, - 6) is

the midpoint of the line segment with endpoints (4, - 2)
and:
F. (2, - 12)
G. (5, - 14)
H. (5, - 12)
J. (8, - 10)
K. (8, - 12)

27. A toy rocket is launched from the ground. Its height, h ft.
above the ground, t seconds after it is launched, is given by
the function h = - 16t 2 + 64t . How much did the rocket
descend between 2 seconds and 3 seconds after it was
launched?
A. 8 ft.
B. 16 ft.
C. 24 ft.
D. 32 ft.
E. 64 ft.

28. Which of the following value is equal to (- 2i) 4 ?

F. - 16
G. - 2
H. 2i
J. 16i
K. 16

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28 The SAT/ACT Diagnostic

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DO YOUR WORK HERE.

3
Use the following information to answer questions
29–31.

In the diagram below, a ladder is leaned up against a wall. The

top of the ladder reaches 10 feet up the wall. The angle of ele-
vation is shown on the diagram.

Wall

10 feet

Ladder
11 feet

angle of elevation

29. What is the distance, in feet, from the base of the wall to
the bottom of the ladder?
A. 1
B. 21
C. 5
D. 9
E. 221

30. Suppose a 25-foot ladder was placed against the same wall
so that its angle of elevation was congruent to the angle
of elevation of the 11-foot ladder. Which of the following
proportions correctly determines how far up the wall this
ladder would reach?
10 11
F. x = 25
10 11
G. 25 = x
10 25
H. x = 11
21 11
J. x = 25
21 x
K. 10 = 11

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31. Which of the following calculations correctly determines DO YOUR WORK HERE.
3
the angle of elevation labeled in the diagram?

A. arcsin a 11 k
10

B. arccos a 11 k
10

C. arctan a 11 k
10

D. arccot a 11 k
10

E. arccsc a 11 k
10

32. On a map in the standard (x,y) coordinate plane, the cities

of Allentown and Burnham are represented by the points
(- 2, 3) and (7,7), respectively. Each unit on the map rep-
1
resents an actual distance of 2 mile. Which of the fol-
lowing is closest to the distance, in miles, between the two
cities?
F. 4.9
G. 6.5
H. 8.3
J. 9.2
K. 13.0

33. The distance from the Sun to Neptune is approximately

4.503 # 10 9 km. The distance from the Sun to Venus is
approximately 1.08 # 10 8 km. About how much further
away from the Sun than Venus is Neptune?
A. 4.169 # 10 1
B. 4.395 # 10 1
C. 4.169 # 10 8
D. 2.137 # 10 9
E. 4.395 # 10 9

34. In the circle shown below, central angle +MON measures

&
40º and MN is 2r centimeters long. How many centime-
ters long is the radius?

40°
O N
F. 4
G. 6
H. 9
J. 12
K. 18
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30 The SAT/ACT Diagnostic

3 Unauthorized copying or reuse of
any part of this page is illegal.

35. In the standard (x,y) coordinate plane, what are the coordi- DO YOUR WORK HERE.
3
nates of the center and the length of the radius of the circle
with the equation ^ x - 5 h + ^ y + 3h2 = 4 ?
2

Center Radius
A. (- 5 , - 3) 2
B. (- 5 , - 3) 4
C. (- 5 , - 3) 2
D. (- 5 , - 3) 4
E. (- 5 , - 3) 16

36. In 9XYZ shown below, lengths given are in centimeters,

and the measure of +X is 44º. Which of the following is
closest to the length, in centimeters, of YZ ?
(Note: for any triangle with side lengths a, b, and c,
a 2 = b 2 + c 2 - 2bc cos i , where i is the measure of the
angle opposite the side of length a. The value of cos 44c
is approximately 0.72)

17
F. 10.3
G. 12.5
H. 15.0 44º
J. 16.0 X Y
K. 23.4 8

37. After five weeks of his new training regimen, Luke notices
that the number of miles he has run each week forms a
geometric sequence. During the first three weeks, Luke ran
2 3 1
2 7 , 3 7 , and 5 7 miles, respectively. How many miles
did he run during the fifth week?
4
A. 18 7
1
B. 10 7
6
C. 10 7
4
D. 11 7
1
E. 13 7
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38. The system of equations below has multiple solutions all of DO YOUR WORK HERE.
3
5
which satisfy the equation y = 4 x - 2 . What is the value
of b?
15x - 12y = 24
5x + by = - 2b
F. - 6
G. - 4
H. - 2
J. 4
K. 6

39. A parabola with equation y = ax 2 is graphed in the stan-

dard (x,y) coordinate plane below. The value of a is greater
than 1. Which of the following statements must be true?

x
O

A. If (p, q) lies on the parabola, then (- p, q) lies on the

parabola.
B. If (p, q) lies on the parabola, then (- p, - q) lies on
the parabola.
C. The point (10, 100) lies on the this parabola.
D. For all (p, q) on the parabola, q > p .
E. The graph of this parabola lies entirely in the first and
fourth quadrants.

40. In trapezoid ABCD shown below, +C measures 60º and

AD is perpendicular to CD. Which of the following values
is closest to the area, in square units, of ABCD ?

A B
F. 48 8
G. 83
H. 97 60°
J. 111 D C
K. 128 16

STOP. BE CERTAIN NOT TO EXCEED THE

ALLOTTED TIME. YOU MAY PROCEED TO
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32 The SAT/ACT Diagnostic

No Testing Material On This Page
No Testing Material On This Page
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4
SAT Writing and Language Test
26 MINUTES, 33 QUESTIONS

Locate Section 4 of your bubblesheet to record the questions in this section.

DIRECTIONS
Read each passage carefully and then choose the answer choice that either improves the
quality of writing or that conforms to the conventional standards of written English.

Each passage has questions that require you to correct errors in sentence structure, usage
or punctuation. Other questions ask that you revise sentences to improve the expression
of ideas.

There will also be questions that directly refer you to a portion of the passage and other
questions will require you to consider the passage as a whole. This portion of the test also
involves evaluating graphs, tables, and figures.

Choose “NO CHANGE” if you believe that the sentence is grammatically correct and does
not need to be improved.

Questions 1–11 are based on the following passage 1

A) NO CHANGE
Solunar Fishing
B) sits;
In the early hours of dawn, Angelo Agostinelli
C) sat—
1 sat in the cockpit of his fishing boat outside the
D) had sat
Gloucester Harbor, a seascape dotted 2 with other
boats, buoys, and lobster pot markers. Agostinelli 2

fishes for whatever the sea yields, and he does so A) NO CHANGE

according to the relationship of the sun and the moon B) between
relative to each other. He didn’t always fish this way. C) for

When he began, he used methods familiar to most of D) on

his colleagues: sonar, tide tables, weather forecasts; but

as he gained experience, he became convinced that “fish
become more active during solunar periods than at
other times” and that these periods were the best times
to catch the fish.

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4
This type of fishing is based on the belief that a 3
natural day for fish and many other animal species A) NO CHANGE
accords with a diurnal (twice daily) ‘biological clock’ B) however,
that seems to coincide with lunar time. Solunar C) by contrast,
fishermen believe, 3 for instance, that the times of the D) therefore,
new moon (the dark of the moon) and full moon are
the periods of maximum intensity of fish movement 4
and feeding. 4 Although the sun’s position also A) NO CHANGE
influences fish and animal behavior, solunar theory B) Because
posits that the pull of the two celestial objects—sun and C) So
moon—is naturally strongest when the two are aligned, D) DELETE the underlined portion and begin the
as in the new and full phases of the moon. sentence with a capital letter.

5 Nature is nothing new. Pliny the Elder, a

Roman observer of nature in the first century, stated 5

that the moon “replenishes the Earth; when she A) NO CHANGE

approaches it, she fills all bodies, while, when she B) People all over the world fish by the moon.

recedes, she empties them.” Ancient Egyptians and C) Fishing by the moon is not new.
D) Talk of the moon’s influence is far-reaching.
Chinese people performed tasks according to the lunar
calendar, and, to this day, the vaunted Old Farmer’s
6
Almanac includes regional lunar calendars and advice
on 6 fishing and hunting. The 7 almanacs editor, A) NO CHANGE

Jason Booker, says : “This information is of value to our B) actions relevant to fishing.

readers who practice solunar methods — and find great C) points in time at which to undertake certain
tasks.
success.”
D) optimal times to find and catch the most fish.

7
A) NO CHANGE
B) almanacs’s
C) almanac’s
D) almanacs’

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36 The SAT/ACT Diagnostic

 4 Unauthorized copying or reuse of
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4
Solunar fishing has its 8 skeptics, who are not 8
sure of the method’s efficacy. Recalling advice on the A) NO CHANGE
best lunar time to fish for bass, a Florida angler says her B) skeptics, who have yet to be convinced.
first reaction was “in a pig’s eye.” Current mainstream C) skeptics — those who doubt this method.
science does not factor lunar tables into 9 their D) skeptics.
explanation of fish behavior, so using them may seem
quaint or even irrational. Additionally, solunar fishing 9
owes as much to astrology as to astronomy, and few A) NO CHANGE
scientific studies have been conducted to measure B) those
the moon’s overall influence on fish behavior, 10 so C) it’s
supporters continue to wait for their practices to be D) its
verified.
Booker says, “We are of the mind that you accept 10
or reject by choice.” Indeed, despite her doubts, The writer wants to conclude the paragraph
the skeptical Florida angler wound up going after effectively while also reinforcing the point that
doubt still exists about the efficacy of solunar
her bass according to solunar tables and claims her fishing. Which choice accomplishes this goal?
catch was “the best I ever had.” Marine biologist Zoe A) NO CHANGE
Burgard has a similar response to Agostinelli’s bounty B) and therefore no scientific data on the subject
in Massachusetts. 11 “Look at the number of fish, exist at this time.

and the wide variety,” she says. “How can you say his C) yet many continue to practice solunar fishing.
D) leading many to conclude that solunar fishing
methods don’t work?” At this stage, one could only
is unsustainable.
conclude that the evidence must be experienced to be
believed.
11
Which choice gives an additional supporting
example that emphasizes the importance of the
senses in judging the success of the solunar fishing
method?
A) NO CHANGE
B) “Look at the beauty of the seascape here in
Gloucester!”
C) “I’ve taken notes on the size of the catch for the
last three trips out.”
D) “Most of the solunar tables predict that
tomorrow will be an excellent day to fish.”

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4
Questions 12–22 are based on the following passage 12
A) NO CHANGE
Vanishing Forests: A Threat to Global Agriculture
B) fertile soil: this is
Forests play an important role in the agriculture
C) fertile soil,
industry by combating soil erosion and transpiring
D) fertile soil;
precipitation. Most studies indicate that global
agriculture depends on appropriate growing conditions,
13
including 12 fertile soil—to increase crop output.
A) NO CHANGE
The importance of soil 13 highlights the potentially
B) highlights the potentially disastrous effects
disastrous affects of an emerging crisis: loss of forests
C) highlight the potentially disastrous effects
leads to loss of soil and to disruption of the water cycle.
D) highlight the potentially disastrous affects
14 They know it as deforestation, this
phenomenon will have a detrimental impact on global
14
agriculture if its causes and solutions are not quickly
A) NO CHANGE
determined. As forest areas diminish, their ability to
B) Known as deforestation,
keep soil from eroding and precipitation to be regulated
C) It is known as deforestation,
also declines. This loss of forest follows a pattern
D) Deforestation,
suggested by forest transition (FT) theory. Global
population increase and the need for wood products
15
create an expected decline in forest area, but the actual
Which choice offers the most accurate
decline over the last fifty years 15 exceeded 2.5 percent interpretation of the data in the chart?
of the forest area each recorded year. There was one A) NO CHANGE
sign of hope when the actual rate of decline slowed B) was over double what it had been five years
during the 1970’s, yet in the following decades the loss previous.
C) exceeded the acceptable level in all but one of
of forest world-wide has accelerated. Between 2007
the recorded years.
and 2012, the 16 rate of deforestation was an alarming
D) exceeded the 1.5 percent acceptable range each
1 percent, with a loss of 3.6% of the world’s total forest recorded year.
area.
16
Which choice offers an accurate interpretation of
the data in the chart?
A) NO CHANGE
B) rate of deforestation was an alarming 3.2
percent,
C) rate of deforestation rose over 1 percent,
D) number of tree losses grew by 2.5 percent,

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38 The SAT/ACT Diagnostic

 4 Unauthorized copying or reuse of
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4
Worldwide Forest Decline, 1967−2012 17
4% Which choice most smoothly and efficiently
3.5% introduces the writer’s discussion of studies of
Percent Total Forest Loss

3% deforestation in this paragraph?

2.5%
A) NO CHANGE
2%
1.5% B) Trees are vanishing, and according to studies
1% there are numerous possible reasons for this
acceptable range alarming trend.
0.5%
0% C) Several possible reasons, offered by different
studies, may explain why so many trees are
67
72
77
82
87
92
97
02
07
12
vanishing.
19
19
19
19
19
19
19
20
20
20
Year D) DELETE the underlined sentence.
Adapted from Dennis van Engelsdorp et al., “Preliminary Results: Hon-
ey Bee Colony Losses in the United States, Winter 2012-2013.” ©2013
by the Bee Informed Partnership. 18
At this point the writer is considering adding the
following sentence. “Another reason is the damage
17 Studies have offered several possible reasons
caused by insects and diseases introduced to areas
for the loss of forest. One reason that is often cited where no natural protection exists.” Should the
is, paradoxically, the clearing of forest to create areas writer make this addition here?
A) Yes, because it provides another reason to
suitable for farming. 18 Deforestation for lumbering
explain loss of forest.
and to make space for city expansion and highways also
B) Yes, because it introduces a new idea that will
play a role. become important later in the passage.
C) No, because it introduces a new idea that will
not become important later in the passage.
D) No, because it contradicts the main idea of the
passage.

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 4 Unauthorized copying or reuse of
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4
Given the importance of forest cover to agriculture, 19
the impact of this accelerating loss on soil erosion and A) NO CHANGE
water cycle regulation 19 is not to be scoffed at. A B) is a pretty big deal.
reduction in forest area leads to less ability to hold C) can’t be put on the back burner.
soil in place and less rainfall, which in turn leads to D) cannot be ignored.
smaller food production and higher prices for scarce
commodities. Some countries will have to resort to 20
importing food 20 supplies; when there is a loss of A) NO CHANGE
food production, this being an expensive proposition. B) supplies, when there is a loss of food
Other countries will have to ration food supplies for production and this is an expensive
proposition.
21 they’re population or try to change the eating habits
C) supplies, an expensive proposition when there
of people. Furthermore, there may be sociological is a loss of food production.
repercussions. Agroecologist Gilbert Rehbun has D) supplies; an expensive proposition when there
suggested that rising food prices could lead to an is a loss of food production.
increase in obesity as people turn to cheaper, more
filling but less wholesome, fare. 21
Though the causes of deforestation are clear, A) NO CHANGE
political and economic pressures make it difficult to B) there
reverse the process. More stringent control of slash- C) their
and-burn clearing operations, as well as more extensive D) it’s

tree replacement programs, could begin a shift in a

more favorable direction. 22 22
The writer wants a conclusion that addresses the
future of efforts to combat deforestation. Which
choice results in the passage having the most
appropriate concluding sentence?
A) NO CHANGE
B) Still, forests have experienced such devastating
losses that the consequences of the issue have
been felt worldwide.
C) Although deforestation is a relatively new
phenomenon, scientists have been studying all
aspects of the problem for over a century.
D) The political will to address this issue is
lacking, so there seems to be little that can be
done.

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40 The SAT/ACT Diagnostic

 4 Unauthorized copying or reuse of
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4
Questions 23–33 are based on the following passage 23
The writer is considering deleting the underlined
Louis A. Lauder portion (ending the sentence with a period).
In 2013, cosmetics billionaire Louis A. Lauder Should the writer do this?
donated his collection of Cubist masterpieces to New A) Yes, because the underlined portion detracts
from the paragraph’s focus on Cubism.
York City’s Metropolitan Museum of Art. The gift
B) Yes, because the information in the underlined
included 78 Cubist works— 23 including paintings by portion is provided in the previous sentence.
Picasso, Braque, Leger, and Gris. The gift is estimated C) No, because the underlined portion helps
to be worth over a billion dollars. specify what is included in the gift.
24 Because of the astonishing size and value of the D) No, because the underlined portion gives an
example of a particular Cubist work.
25 donation to the Metropolitan Museum, choosing
an area to display the items within the museum 24
was a challenge. Working in conjunction with the A) NO CHANGE
architecture firm of Greenberg and Reichenbach, the B) Regardless of
museum staff developed plans for a new wing to be C) In contrast to
devoted exclusively to the Cubist collection. Soon D) In addition to
viewers will be able to enjoy Picasso’s “Woman in an
25
Armchair (Eva)” and Braque’s “Terrace at the Hotel
A) NO CHANGE
Mistral”, 26 so as of now the collection is unavailable.
B) donation of so many Cubist works,
C) massive donation of art works,
D) donation,

26
A) NO CHANGE
B) for
C) and
D) but

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4
This all is relatively new to the Met, which, 27
surprisingly, acquired 27 their first Cubist work only A) NO CHANGE
in 1996. Although the museum loved Picasso, for B) his/her
example, one critic notes that “while the Museum of C) its
Modern Art was swallowing huge gulps of Cubism, D) it’s
the Met was satisfied with a menu made up primarily
28
of Blue Period, Rose Period, and neo-Classical
A) NO CHANGE
dishes.” The Met, 28 moreover, lacked examples of an
B) therefore,
important movement in art history.
C) however,
The word Cubism was coined in 1908 to describe
D) in short,
the paintings that took familiar shapes and turned them
upside down, transforming traditional views of objects 29

into broken planes. Artists like Picasso and Braque A) NO CHANGE

redefined concepts of space in their work and further B) anachronistic elements like
dismantled tradition by incorporating 29 such esoteric C) everyday objects like
entities as sawdust, rope, and bits of newspaper into D) commonplace, ordinary items as

their paintings, sculptures, and collages. This made 30

viewers uncomfortable; they found 30 access with A) NO CHANGE
the new work difficult. But the new movement took B) access to
hold and paved the way for abstraction, which became C) excess of
dominant for the next fifty years. D) excess to

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42 The SAT/ACT Diagnostic

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4
[1] Mr. Lauder’s gift, consequently, has a historical 31
significance. [2] Braque’s “Trees at L’Estaque” is A) NO CHANGE
thought to be one of the first Cubist pictures, creating B) had studied
a new form of space that the artist arrived at after he C) would be studying
31 study Cezanne’s landscapes. [3] And both artists D) could have studied
introduced new media— 32 Braque with his first
32
collage “Fruit Dish and Glass” and Picasso with his
A) NO CHANGE
sculpture “Head of a Woman”—into Cubism. 33
B) Braque with his first collage “Fruit Dish and
The collection looks both forward to abstraction Glass” and Picasso, with his sculpture “Head of
and backward through Picasso’s embrace of African a Woman”
tribal art in his use of nontraditional forms. It pays C) Braque, with his first collage “Fruit Dish and
Glass” and Picasso with his sculpture “Head of
homage to a movement that not only inspired Western a Woman”
artists but also became significant throughout the D) Braque with his first collage, “Fruit Dish and
world. As Met curator Ethan Lucas said, “We will now Glass”, and Picasso with his sculpture “Head of
a Woman”
be able to tell many different stories that we were never
able to tell before.” 33
The writer plans to add the following sentence to
this paragraph.
Picasso’s “Oil Mill,” also in the Lauder
collection, influenced the Italian Futurist
School.
To make the paragraph most logical, the sentence
should be placed
A) after Sentence 1.
B) before Sentence 1.
C) after Sentence 2.
D) after Sentence 3.

STOP. BE CERTAIN NOT TO EXCEED THE

ALLOTTED TIME. YOU MAY PROCEED TO
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5 Unauthorized copying or reuse of
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ACT READING TEST

5
30 Questions—27 Minutes

DIRECTIONS: There are three passages. Each passage is

followed by ten questions. After reading a passage, choose
the best answer to each question and mark it on the bub-
blesheet. You may refer to the passages as often as you like.

PASSAGE I 40 chance to lose, for father was a poor man and it meant
promotion and increase of salary; but it also meant the
PROSE FICTION: This passage is adapted from the short story
The Story Girl by Lucy Maud Montgomery (© 1911, Grosset &
temporary breaking up of our home. Our mother had
Dunlap, Publishers, n.d.) died before either of us was old enough to remember her;
father could not take us to Rio de Janeiro. In the end he
“I do like a road, because you can be always won- 45 decided to send us to Uncle Alec and Aunt Janet down
dering what is at the end of it.” The Story Girl said that on the homestead; and our housekeeper, who belonged
once upon a time. to the Island and was now returning to it, took charge of
us on the journey. I fear she had an anxious trip of it,
Felix and I, on the May morning when we left Toronto poor woman! She was constantly in a quite justifiable
5 for Prince Edward Island, had not then heard her say it, 50 terror lest we should be lost or killed; she must have felt
and, indeed, were but barely aware of the existence of great relief when she reached Charlottetown and handed
such a person as the Story Girl. We did not know her at all us over to the keeping of Uncle Alec. Indeed, she said as
under that name. We supposed we should get acquainted much.
with her when we reached there, and we had an idea, from
10 Aunt Olivia’s letters to father, that she would be quite a “The fat one isn’t so bad. He isn’t so quick to move
jolly creature. Further than that we did not think about 55 and get out of your sight while you’re winking as the thin
her. We were more interested in Felicity and Cecily and one. But the only safe way to travel with those young
Dan, who lived on the homestead and would therefore be ones would be to have ‘em both tied to you with a short
our roommates for a season. rope—a MIGHTY short rope.”

15 But the spirit of the Story Girl’s yet unuttered remark “The fat one” was Felix, who was very sensitive
was thrilling in our hearts that morning, as the train pulled 60 about his plumpness. He was always taking exercises
out of Toronto. We were faring forth on a long road; and, to make him thin, with the dismal result that he became
though we had some idea what would be at the end of it, fatter all the time. He vowed that he didn’t care; but he
there was enough glamour of the unknown about it to lend DID care terribly, and he glowered at Mrs. MacLaren in a
20 a wonderful charm to our speculations concerning it. most undutiful fashion. He had never liked her since the
65 day she had told him he would soon be as broad as he was
We were delighted at the thought of seeing father’s long.
old home, and living among the haunts of his boyhood.
He had talked so much to us about it, and described its For my own part, I was rather sorry to see her going;
scenes so often and so minutely, that he had inspired us and she cried over us and wished us well; but we had
25 with some of his own deep-seated affection for it—an forgotten all about her by the time we reached the open
affection that had never waned in all his years of exile. We 70 country, driving along, one on either side of Uncle Alec,
had a vague feeling that we, somehow, belonged there, in whom we loved from the moment we saw him. We felt at
that cradle of our family, though we had never seen it. We home with him and became very good friends with him on
had always looked forward eagerly to the promised day that twenty-four mile drive.
30 when father would take us “down home,” to the old house
with the spruces behind it and the famous “King Orchard” Much to our disappointment it was dark when we
before it—when we might ramble in “Uncle Stephen’s 75 reached Carlisle—too dark to see anything very distinctly,
Walk,” drink from the deep well with the Chinese roof as we drove up the lane of the old King homestead on the
over it, stand on “the Pulpit Stone,” and eat apples from hill. Behind us a young moon was hanging over south-
35 our “birthday trees.” western meadows of spring-time peace, but all about us
were the soft, moist shadows of a May night. We peered
The time had come sooner than we had dared to 80 eagerly through the gloom.
hope; but father could not take us after all. His firm
asked him to go to Rio de Janeiro that spring to take “There’s the big willow, Bev,” whispered Felix excit-
charge of their new branch there. It was too good a edly, as we turned in at the gate.

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44 The SAT/ACT Diagnostic

5 Unauthorized copying or reuse of
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There it was, in truth—the tree Grandfather King had 6.

5
The narrator mentions all the following features of her
planted. It had taken root and grown; our father and our father’s old home EXCEPT:
85 uncles and aunts had played in its shadow; and now it was F. the deep well.
a massive thing. G. Aunt Olivia’s Bower.
H. King Orchard.
“I’m going to climb it tomorrow,” I said joyfully. J. the big willow.

1. The passage can best be described as:

A. a dialogue between two people in which both relate
their memories of an event.
B. an account of the narrator’s remembrance of an
important event in her life. 7. The author capitalizes the word in line 58 most likely to
C. a character sketch of two children as related by the emphasize:
narrator. A. Felix’s plumpness.
D. a detailed description of a landscape at a particular B. the children’s hostile nature.
time. C. the children’s ability to get out of sight.
D. Bev’s strong ties to her father.

2. Which of the statements below best describes the rela-

tionship between the narrator of the story and Mrs.
MacLaren?
F. The narrator regards Mrs. MacLaren as her favorite
adult.
G. The narrator has mixed feelings about Mrs. 8. As used in line 22, “haunts” is closest in meaning to:
MacLaren. F. frightening presences in a house.
H. The narrator believes Mrs. MacLaren has to be a G. something difficult to forget.
stern taskmaster. H. spirits that inhabit one’s memories.
J. The narrator is resentful of Mrs. MacLaren for J. places one frequented.
calling her “the fat one.”

3. It can reasonably be inferred from the story that the

narrator’s feelings toward Carlisle are primarily:
A. those of dreading an unfamiliar place.
B. those of joy at recalling a much-loved familiar place. 9. The story indicates that the distance between Charlotte-
C. those of eager anticipation. town and Carlisle is:
D. those of despair over the loss of a loved one. A. a long train ride.
B. twenty-four miles.
C. a three hour ride.
4. The references to the Story Girl most likely suggest that D. more than sixty miles.
the narrator:
F. planned to get to know her.
G. was intimidated by the stories she heard about her.
H. was related to Aunt Olivia.
J. knew her extremely well.

5. Based on the passage, which of the following happened 10. According to the story, Felix and Bev are to live on
to Bev first chronologically? Prince Edward Island:
A. She heard about The Story Girl in a letter. F. permanently.
B. Her mother died. G. for part of a year.
C. She left Toronto to go to Prince Edward Isle. H. with their father.
D. Her father was transferred to Rio de Janeiro. J. in April.

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www.satactdiagnostic.com 45
5
PASSAGE II
Unauthorized copying or reuse of
any part of this page is illegal.

just providing the information in the first place.

5
HUMANITIES: This passage is adapted from the journal article
“Facebook Killed the Reunion Star: How Facebook is Changing
Facebook is not only involved in creating identity; it
Who We Are and What We Do” by Sara Ridenour which appears is plays a major role by displaying your identity to others.
in Fast Capitalism (© 2011 Issue 8.1) Before Facebook, we may not have known as much about
55 our friends as we do now. We have all been told to steer
Do people create or mediate the identity that they clear of two topics with friends, family, and company –
display on Facebook? Of course, at some level, they must; religion and politics; however, Facebook puts these topics
you have to decide what to post on Facebook and what not front and center. When I accept a Facebook friend, he/she
to post. However, I wonder just how much true thought can go to my Info page and obtain far more information
5 goes into this decision process. Before posting a picture 60 about me than I might normally provide (and I am rather
on Facebook, do people really think about the effect the cautious about the information I offer on Facebook). I do
picture will have on their identity? Also, I believe that not have anything on my Facebook profile that I think is
our society is moving towards a more “take me as I am” private, sensitive information, but, at the same time, most
mentality, and if that is the case, can we really argue that people would not come up to me and ask me what religion
10 a Facebook identity is drastically different than one’s true 65 or political party to which I belong. I am not ashamed of
self? either, and was I asked, I would answer honestly, but the
fact of the matter is, before Facebook, it is not likely that
We live in a world that allows us to construct our I would have been asked.
identity in a variety of ways—online via Facebook posts
and statuses, by the clothes we wear, the color of our hair, It is not only friends that are interested in their peers
15 even the brand of our shoes. So, the question begs, are 70 Facebook profiles and the information provided there.
we changing our identity by dyeing our hair or are we Employers look at Facebook to determine the “real”
only becoming a truer version of the person we believe person instead of the best-foot-forward, rehearsed iden-
we really are? Is our constructed identity our true reality? tity that people use during an interview. Recently, there
I am not convinced that people really try to construct have been several news stories about people being rep-
20 the best possible identity, rather than their true identity, 75 rimanded, and even facing termination, for Facebook
online anymore; I think more and more people are putting posts. This brings up all kinds of first amendment and
their flawed selves out there. A quick perusal through my privacy issues, and I am not going to get into that here;
Facebook newsfeed and the recent picture postings by my however, it does make me think about identity. People
friends supports this theory. As aforementioned, people will say and do things on Facebook that they would not
25 overshare; if they were trying to construct a picture-per- 80 do in their daily life, and that makes me think that people
fect version of themselves, would they really post less- are more true to themselves on Facebook – thus creating
than-flattering pictures of themselves or discuss a battle a real identity, not a simulation. They are more willing to
with acne via a public wall post? portray their flaws on Facebook, and our flaws make us
who we are.
People no longer really worry about privacy so I
30 would argue that the self they create online is a true rep- 85 Facebook is not merely a reflection of an identity
resentation of identity. People have the ability to be more that is already established; Facebook is taking part in the
“real” online than off; the shield of the keyboard and establishment of identity. From his Harvard dorm room,
computer monitor provides a sense of security, protec- Mark Zuckerberg created a phenomenon that not only
tion from judgment. Shy people, like me, find it easier to changes the way we act, it is changing who we are.
35 share via email and on Facebook than face-to-face. Face-
book allows us to be ourselves. 90 Facebook is a significant social force. There is so
much information available to sociologists that it is over-
My Facebook profile is not just a copy of who I am; whelming. Jokingly, I told my professor that Facebook
my Facebook profile shapes my identity. Now, I realize ruined my high school reunion. I thought that I did not
that taken out of context that concept may seem rather mean it literally, but I did; Facebook really did ruin my
40 shallow, allowing Facebook to shape who I am; however, 95 high school reunion. But, in ruining my high school
with the proliferation of Facebook in our society, it is not reunion, Facebook may have improved my daily life. I
hard to believe that Facebook could play a role in estab- have more friends now that I have ever had in my entire
lishing identity. Categories of relationship status, political life! And, I know more about them, and myself, than ever
status, and religion make people think about these labels before. I am certain that a plethora of research concerning
45 and assign themselves an identity. Young people who 100 Facebook is in the works as I type, and I look forward to
may have not considered their political affiliation as part it. These are interesting times and I am excited to be a
of their identity are now faced with a dilemma – who am part of it.
I? And, what does it mean? Of course, you can opt not to
provide this information on Facebook, but not providing Chances are I will not see any of my high school
50 certain information can speak louder to your identity than friends until our next reunion (in ten years). That may

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46 The SAT/ACT Diagnostic

 5
105
Unauthorized copying or reuse of
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seem sad, but really, why do I need to see them? I have

5
16. Based on the passage, why might the author share infor-
Facebook to keep me company. mation on Facebook that he would not divulge in a face-
to-face encounter?
F. Facebook allows him to overcome shyness.
G. Facebook creates an identity that presents him in
11. The main idea of this passage is that: better light.
A. Facebook destroys privacy and is therefore dan- H. Facebook makes it unnecessary to attend social
gerous. events.
B. Facebook offers opportunities for people to inform J. Facebook forces people to create a simulated iden-
others about whom they care about. tity.
C. Facebook allows people to create their identity and
display that identity to others. 17. The main purpose of the fifth paragraph is to:
D. Facebook can be used by employers to screen can- A. tell why the author hides sensitive information from
didates for jobs. Facebook.
B. explain why religion and politics are topics people
12. The author mentions each aspect of Facebook EXCEPT: should avoid on Facebook.
F. people are less true to themselves in real life than C. establish that Facebook is instrumental in getting
they are on Facebook. people to share their identity with others.
G. Facebook helps shy people share things about them- D. help friends hide the truth about themselves from
selves. each other.
H. people are willing to share aspects of themselves on
Facebook that are not necessarily flattering.
J. Facebook causes people to present the most perfect 18. The author puts the word “real” in quotation marks in
picture of themselves that they can create. line 32 in order to:
F. suggest that there is no such thing as a person’s real
13. The word “shield” as it is used in line 32 most nearly identity.
means: G. point out that one’s true self can only be recognized
A. a cover over a machine to protect it from damage. on Facebook.
B. a means of keeping others from judging you. H. question the idea that people seek to hide their true
C. a physical barrier to protect you from assault. identities on Facebook.
D. a way of keeping outside elements from bothering J. reinforce the argument that people try to present the
you. best possible picture of themselves on social media.

14. It can reasonably be inferred from the passage that:

F. fewer people attended the author’s high school 19. According to the passage, why does the author believe
reunion than would have before Facebook. it is important for people to share their weaknesses to
G. people at the author’s high school reunion were others on Facebook?
more willing to share information about religion A. Sharing weaknesses brings people closer together.
and politics than they would have been before Face- B. Sharing weaknesses is an example of how people
book. overshare information on social media.
H. Facebook is likely to become less used in the future C. Sharing weaknesses creates a sense of self-worth.
than it is now. D. Sharing weaknesses establishes a person’s honest
J. Facebook will become a means of helping people identity, not an idealized version.
protect their real selves from scrutiny by others.
20. According to the passage, the development of Facebook
15. The passage suggests that the most important aspect of is:
Facebook is that it:
F. a phenomenon that potentially will eliminate all
A. allows people to share their views on politics and face-to-face interaction.
religion. G. likely to provide information for sociologists to use
B. allows employers to screen prospective job appli- in current and future research.
cants. H. significant in that it changes what most people want
C. eliminates the need to attend school reunions. from life.
D. gives people a chance to shape the identity they J. not a matter of first amendment concern.
wish to present to others.

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www.satactdiagnostic.com 47
5
PASSAGE III
Unauthorized copying or reuse of
any part of this page is illegal.

50
5
to be better at finding creative solutions to social, eco-
nomic and academic problems. A recent neuroimaging
NATURAL SCIENCE: This passage is adapted from an article
“Concerning Human Understanding” by Maxwell Lowe (©2013 by
study found that the elevating serotonin levels in the brain
Maxwell Lowe), which appeared in Scientific Inquiries. created more connections to the posterior cingulate cortex
(PCC), which plays a central role in supporting internal-
The known facts about John Locke’s theory of the 55 ly-directed cognition.
tabula rasa have intrigued philosophers and scientists
since the 17th Century. Locke, an English philosopher Other evidence suggests that the PCC region is
and physician who is also known as the father of clas- highly heterogeneous and may play a direct role in reg-
5 sical liberalism, set out the case that the human mind is ulating the focus of attention, which can determine the
devoid of all knowledge or ideas at the time of birth. At ability of a person to gather and parse information. Only
the moment an infant takes his first breath his mind is a 60 after spending several minutes looking at the ocean can a
blank slate (tabula rasa). He argued that all of our ideas person begin to see that the ocean is at once the color blue,
are constructed in the mind via a process of constant com- and bright cerulean, electric indigo, slate blue and royal
10 position and decomposition of the input that we receive blue.
through our senses.
A recent study conducted at Duke University dis-
In his essay Concerning Human Understanding, 65 covered that PCC monitors a person’s performance and
Locke rejected the notion that the human mind was maintains a person’s motivation when learning new mate-
invested with innate ideas and the power of intuition. He rial, particularly when the person is challenged. Although
15 posited that all of our concepts are derived from sense this research is important in and of itself, more knowledge
experience and that we have no basis of knowledge prior about the PCC is critical because this region of the brain
to or independent of sense experience. 70 is also one of the first to deteriorate when a person has
Alzheimer’s disease.
For centuries it was widely accepted that babies at
birth were intellectual equals. No one had a head start; Locke’s tabula rasa theory has given way to an
20 one baby was not born with a better predilection for almost accepted belief in nativism, or what is sometimes
learning, retaining knowledge, finding creative solutions referred to as innativism, the notion that preexisting ideas
to mathematical problems or discovering how DNA deter- 75 are present in the mind at time of birth. Those who share
mines a person’s capabilities. this view make the case that there are two ways in which a
human can gain knowledge: The first is by learning. The
Recent scientific findings in the United States and baby gathers information from his surroundings and then
25 Europe suggest that we are not a blank slate at birth. In uses it. He learns that when he cries long enough he will
fact, it is spiritedly argued that some people are better 80 magically make his mother appear from another room.
intellectually endowed to grasp concepts, retain infor- The second way a baby acquires knowledge is through
mation or solve complex problems. In 2011 Kenneth innate knowledge, that which is genetically inherited. No
Heilman and his team at the Department of Neurology one had to teach the baby to cry when he is hungry or
30 and Neuroscience at Cornell University discovered that uncomfortable in the middle of the night. No one had to
some people are born with a greater capacity for cre- 85 teach the baby to smile to signal when he is pleased.
ativity. The new research suggested that a person’s DNA
determines why some people are better at solving creative While the argument for nativism is compelling (a
problems than others. baby doesn’t need to be taught to look for his mother when
he hears her voice), Locke’s theory of tabula rasa can be
35 “Creativity is related to the connectivity of large argued persuasively as well. While a person’s genetic
scale-brain networks,” said Szabolcs Keri of the National 90 makeup may make him more likely to solve abstract
Institute of Psychiatry and Addictions in Budapest. “How problems quickly, focus longer, and have an inherent
brain areas talk to each other is critical when it comes self-rewarding system to encourage him to stay the course
to originality, fluency and flexibility.” Highly creative when he learns, he still arrives as a blank slate. While the
40 people have widespread connectivity to the different brain interior structure of our brains may be very different, and
networks, and it is believed that genes create these broad 95 allow some to learn more and to solve problems faster
and healthy thoroughfares in the brain. Studies have than others, at birth the mind is blank until it starts to
shown that specific genes can make people less inhibited, process what it perceives. Science has not demonstrated
provide the ground for better memory, and permit people that the newborn who knows to cry when he wants his
45 to become more aware of their surroundings and them- mother’s attention knew this prior to birth.
selves.

People with duplicate DNA strands that contain a

gene that influences the processing of a key neurotrans-
mitter called serotonin have demonstrated themselves

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48 The SAT/ACT Diagnostic

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21. The statement in lines (82–85) “No one had to teach the
5
27. In the last paragraph, which stance does the author take
baby to cry when he is hungry … no one had to teach the on Locke’s tabula rasa theory?
baby to smile to signal when he is pleased” serves as: A. While the counter argument against Locke’s tabula
A. an illustration that innate knowledge exists in the rasa theory is compelling, modern science has not
mind prior to birth. unequivocally disproved it.
B. further support for Locke’s tabula rasa theory. B. Nativism is so compelling that it disproves Locke’s
C. an example of how quickly babies learn to manip- tabula rasa theory.
ulate others. C. Because each person’s genetic makeup cannot be
D. an example that babies acquire knowledge that they completely determined Locke’s tabula rasa theory
can put to use. is accurate.
D. Science has demonstrated that Locke’s tabula rasa
22. It can be reasonably inferred that the PCC region may theory is invalid.
first help a person to:
F. enjoy a tennis match.
G. focus more on a tennis match.
H. gather more information about tennis matches.
J. make better sense of tennis matches. 28. In his essay, Concerning Human Understanding, Locke
made the case that:
23. The main function of the fourth paragraph is to: F. babies know more than they are often credited with
A. demonstrate how robust scientific research is knowing.
making the case for Locke’s 17th century theory. G. it’s not absolutely clear how knowledge is derived.
B. demonstrate how the recent scientific findings in H. knowledge is derived from sense experience.
the United States and Europe differed on the impor- J. babies have thoughts independent of sense experi-
tance of intellectual endowment. ence.
C. highlight the importance of DNA in determining
why some people are better at solving problems.
D. provide scientific evidence that counters Locke’s
belief that the human being is devoid of knowledge
at the time of birth. 29. The Department of Neurology and Neuroscience at
Cornell University and the National Institute of Psychia-
24. As it is used in line 8, the word blank most nearly means: try and Addictions in Budapest would most likely agree
that:
F. expressionless.
G. free. A. the mind is blank at birth.
H. clean. B. some people are born with a poorer capacity for
J. simple. learning.
C. the PCC plays a role in Alzheimer’s disease.
25. The passage mentions that Locke’s theory has led to all D. Locke placed too big an emphasis on nativism.
of the following EXCEPT:
A. nativism.
B. infantillism.
C. how brain areas talk to one another. 30. The scientists who have rejected Locke’s argument
D. innativism. would most likely agree that:

26. The passage indicates the elevated levels of serotonin F. more research on PCC is necessary before the tabula
create more connections to: rasa theory can be proven false.
G. what a person learns is up to that person.
F. discovering why long-term ailments persist. H. people have a unique ability to discover what moti-
G. internally-directed cognition. vates them to learn new material.
H. neuroimaging. J. a person’s ability to learn is based to a large degree
J. the posterior cingulate cortex. on genetic inheritance.

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ALLOTTED TIME. YOU MAY PROCEED TO
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 6 Unauthorized copying or reuse of
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6
SAT Math Test—No Calculator
15 MINUTES, 12 QUESTIONS

Turn to Section 6 of your bubblesheet to answer the questions in this section.

DIRECTIONS
For questions 1–9, solve each problem, select the best answer from the list of choices, and be
sure to mark your selection by filling in the appropriate circles on the bubblesheet. For questions
10–12, solve each problem and record your response by filling in the appropriate circles on the
bubblesheet. Please carefully read the detailed directions before question 10, and then proceed.
You may use blank areas in the test booklet to do any figuring.

NOTES
1. Use of a calculator is not permitted.
2. Unless otherwise indicated, all variables and expressions used represent real numbers.
3. Unless otherwise indicated, figures provided in this test are drawn to scale.
4. Unless otherwise indicated, all figures lie in a plane.
5. The domain of a given function f is the set of all real numbers x for which f (x) is a real
number, unless otherwise indicated.

REFERENCE

l x 2
c 2x 60º x 45º
r h a x
w
30º 45º
b b x
x 3
1
A = rr 2 A = lw A = 2 bh c2 = a2 + b2 Special Right Triangles
C = 2rr

r
h r h h
h
w w
r
l l
4 1 1
V = lwh V = rr 2 h V = 3 rr 3 V = 3 rr 2 h V = 3 lwh

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2r .
The sum of the measures in degrees of the angles of a triangle is 180.

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50 The SAT/ACT Diagnostic

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6
1 3
A girls youth lacrosse coach earns $9.25 an hour for
B C
coaching a team of 12 girls and an additional bonus of
$20 if the team wins the regional championship. If the
team wins the regional championship, what expression G
F
could be used to determine the coach’s total earnings?
A D
A) 9.25x + 20 , where x is the number of hours E

B) 20x + 9.25 , where x is the number of hours Note: Figure not drawn to scale
C) x (9.25 + 12) + 20 , where x is the number of girls
D) 20x + (9.25 + 12) , where x is the number of girls Trapezoid ABCD above is isosceles with AB = CD and
AD = 44 . The ratio of FE to GE is 3: 8 . What is the
length of ED ?

A) 12
B) 22
C) 28
D) 32

5 (x - y) = x

If (x, y) is a solution to the equation above and x ! 0 ,

4
y
what is the ratio x ? 3
If x > 2 , which of the following is equivalent to
5 1
A) - 4 1 1 ?
2x - 3 x + 4
+
4 3x + 1
B) -5 A)
2x 2 + 5x - 12
4 2x 2 + 5x - 12
C) 5 B) 3x + 1
5
D) 4 C) 3x + 1

D) 2x 2 + 5x - 12

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6
5 7
To design a small business’s website Nathan charges an A cyclist turns onto a stretch of highway that descends 8
initial consultation fee of $120 and $50 per hour spent meters in elevation for every 100 meters traveled along
developing a website. Jeremy charges $180 for his initial the length of the highway. The stretch the cyclist turns
consultation fee and $35 per hour spent developing onto begins at an elevation of 2743 meters, and the
a website. If h represents the number of hours spent cyclist travels at a rate of 17 meters per second. What
developing a website, what are all values h for which is the elevation of the highway, in meters, at the point
Jeremy’s total charge is greater than Nathan’s total where the cyclist passes s seconds after turning onto
charge? this stretch of highway?

A) h > 3 A) 2743 - 0.08s

B) 3#h#4 B) 2743 - 1.36s
C) 4 # h # 5 C) 2743 - 8s
D) h < 4 D) 2743 - 17s

6
2
t = 37 + 5 P
Quinn sells t-shirts at lacrosse tournaments. She uses
the function above to model the relationship between
the number of t-shirts, t , sold per tournament and the
number of parents, P , in attendance. According to the
2
model, what is the meaning of the 5 in the function?

A) For every increase of 2 parents in attendance, five

more t-shirts are sold
B) For every decrease of 2 parents in attendance, five
more t-shirts are sold
C) For every increase of 5 parents in attendance, two
more t-shirts are sold
D) For every decrease of 5 parents in attendance, two
more t-shirts are sold

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52 The SAT/ACT Diagnostic

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6
8 9

Which of the following is equivalent to (2a - b) a a k ?

b2 In the xy-plane, the cubic with the equation
y = ax 3 + bx 2 + cx + d , where a , b , c , and d are
constants, passes through the point (- 2, 5) , which of
2b 2 b 3 the following must be true?
A) a - a
A) - 2c + d = 5
B) 2ab 2 - ab
B) - 8a + 4b - 2c = 5
b 3
C) 8a + 4b + 2c + d = 5
C) 2b 2 - a
D) - 8a + 4b - 2c + d = 5
b2
D) 2b - a
2

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6
7 Answer: 2.5
Answer: 12
DIRECTIONS
Write → 7 / 1 2 2 . 5
For questions 10–12: Solve the problem answer

⎧
in boxes. ⊘ ⊘ ← Fraction ⊘ ⊘
and record your answer in the grid on your
⊙ ⊙ ⊙ ⊙ line ⊙ ⊙ ⊙ ⊙ ← Decimal
bubblesheet, as described below.
⓪ ⓪ ⓪ ⓪ ⓪ ⓪ point
① ① ① ① ① ① ① ①

⎨
1. It is suggested, though not required, that
② ② ② ② ② ② ② ②
you write your answers in the boxes at Grid-in ③ ③ ③ ③ ③ ③ ③ ③
the top of the columns to help you mark result. ④ ④ ④ ④ ④ ④ ④ ④
the circles accurately. You will only receive ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤

⎩
credit if the circles are filled in correctly. ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥
2. Only mark one circle in each column. ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦
⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧
3. There are no negative answers. ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨
4. Some problems may have more than one
correct answer. In such cases, please grid
only one answer.
2
Acceptable ways to grid in 3 are:
1
5. Mixed numbers such as 3 2 must be
2 / 3 . 6 6 6 . 6 6 7
gridded as 3.5 or 7/2 . (If 3 1 / 2 is
⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
entered into the grid, it will be interpreted ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪
31 1 ① ① ① ① ① ① ① ① ① ① ① ①
as 2 , not 3 2 .) ② ② ② ② ② ② ② ② ② ② ② ②
③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③
6. Decimal answers: If a solution is a decimal ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④
and the decimal does not terminate after 1 ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤
or 2 places, carry it out to a third place, to ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥
fill the entire grid. ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦
⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧
⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨

Answer: 201 – either position is correct

NOTE: You
2 0 1 2 0 1 may start your
⊘ ⊘ ⊘ ⊘ answers in any
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ columns, space
⓪ ⓪ ⓪ ⓪ ⓪ ⓪ permitting.
① ① ① ① ① ① ① ① Coulmns don't
② ② ② ② ② ② ② ② need to use
③ ③ ③ ③ ③ ③ ③ ③ should be left
④ ④ ④ ④ ④ ④ ④ ④
blank.

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54 The SAT/ACT Diagnostic

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6
10 12
4
For what value of n is - 3 = n - 9 ? If x + 6 is a factor of x 2 + 3kx + 6k , where k is a
constant, what is the value of k ?

11
If i = - 1 , what is the value of i 3 (2 + 2i) 2 ?

STOP. BE CERTAIN NOT TO EXCEED THE

ALLOTTED TIME. YOU MAY PROCEED TO
SECTION 7 WHEN TOLD TO DO SO.

www.satactdiagnostic.com 55
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7
SAT Math Test—Calculator
34 MINUTES, 24 QUESTIONS

Turn to Section 7 of your bubblesheet to answer the questions in this section.

DIRECTIONS
For questions 1–19, solve each problem, select the best answer from the list of choices, and be
sure to mark your selection by filling in the appropriate circles on the bubblesheet. For questions
20–24, solve each problem and record your response by filling in the appropriate circles on the
bubblesheet. Please carefully read the detailed directions before question 20, and then proceed.
You may use blank areas in the test booklet to do any figuring.

NOTES
1. Use of a calculator is permitted.
2. Unless otherwise indicated, all variables and expressions used represent real numbers.
3. Unless otherwise indicated, figures provided in this test are drawn to scale.
4. Unless otherwise indicated, all figures lie in a plane.
5. The domain of a given function f is the set of all real numbers x for which f (x) is a real
number, unless otherwise indicated.

REFERENCE

l x 2
c 2x 60º x 45º
r h a x
w
30º 45º
b b x
x 3
1
A = rr 2 A = lw A = 2 bh c2 = a2 + b2 Special Right Triangles
C = 2rr

r
h r h h
h
w w
r
l l
4 1 1
V = lwh V = rr 2 h V = 3 rr 3 V = 3 rr 2 h V = 3 lwh

The number of degrees of arc in a circle is 360.

The number of radians of arc in a circle is 2r .
The sum of the measures in degrees of the angles of a triangle is 180.

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56 The SAT/ACT Diagnostic

 7 Unauthorized copying or reuse of
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7
1 3

Monthy Car Sales, Dealership X Which ordered pair (x, y) satisfies the system of
equations shown below?
96
84 4x - y = 18
72 x + 3y = - 2
60
Cars Sold

A) (- 2, 2)
48 B) (2, - 2)
36 C) (4, - 2)
24
D) (5, 2)
12
0 Jan Fe M Ap M Jun Ju Au
. b. ar. r. ay. . l. g.
Month

The line graph above shows the number of cars sold

between January and August last year by Dealership X .
According to the graph, what was the greatest change (in
absolute value) in the number of cars sold between two
consecutive months?
4
A) 18 cars
A production plant owned by a company that produces
B) 24 cars energy drinks has the ability to fill 250 milliliter cans
C) 30 cars from a 3000-liter tank. What is the maximum number
D) 36 cars of 250 milliliter cans that can be filled from the tank?
(1 liter = 1, 000 milliliters)

A) 120, 000
B) 12, 000
C) 1, 200
2 D) 12
A circle has circumference C and radius r . Which of
the following represents r in terms of C ?

2C
A) r = r

C
B) r = 2r

C
C) r = r

2r
D) r = C

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7
5 7
Sheila drove at an average speed of 75 miles per hour What is the slope of the line in the xy-plane that passes
for 4 hours. If her car consumed gasoline at a rate of 9 1
23 miles per gallon, approximately how many gallons of through the points a - 2 , 7 k and a - 2 , 2 k ?
fuel did the car use for the entire 4-hour trip?
5
A) 3 A) - 4

B) 4
B) -1
C) 13
D) 14 C) 1

4
D) 5

6
A electronics store sells the Cheetah brand of flash
storage devices as individual drives or in boxes of 4 8
drives. On a busy day, the store sold a total of 346
Cheetah brand flash drives, of which 38 were sold as 0.9x + y = 8.1
individual drives. Which of the following equations The city of Boston was recently hit with a major
gives the number of boxes of 4 drives, b , sold that day? snowstorm. The equation above can be used to model
the depth of the snow, y , in inches, that still covers
346 - 38 the ground x days after the storm began. What does it
A) b = 4 mean that (9,0) is a solution to this equation?
346 + 38
B) b= 4 A) During the days immediately following the
snowfall, 9 inches of snow melt each day.
346
C) b = 4 - 38 B) It takes 9 days for 8.1 inches of snow to fall.
346 C) When snow began to melt, 9 inches of snow
D) b = 4 + 38 covered the ground.
D) It will take 9 days for the ground to be completely
clear of snow.

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58 The SAT/ACT Diagnostic

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7
9 10
Which scatterplot shows a positive association that is
10
not linear? (Note: A positive association between two
variables is one in which higher values of one variable 9
correspond to higher values of the other variable.) 8
7
y 6

Frequencies
A)
5
10 4
3
x
10 2
1
B) y 0
0 12 24 36 48 60 72 84 96 108 120
10 Salary (thousands of dollars)

x The histogram above shows the distribution of salaries,

10 in thousands of dollars, of 22 employees working in
y a specific division of Globex Corporation. Which of
C)
the following could be the median salary of the 22
employees shown in the histogram?
10
x A) $46, 000
10 B) $51, 000
C) $61, 000
D) y
D) $77, 000

10
x
10

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7
13
Questions 11–13 refer to the following information.
Based on the data, how many times more likely is it
A survey of 220 randomly selected registered voters aged for a 25 – 34 year old to prefer Candidate Y than for
25 through 44 in Minnesota was conducted to gather data a 35 – 44 year old to prefer Candidate Y? (Round the
on political preferences across various age groups. The data answer to the nearest hundredth)
are shown in the table below.
A) 0.43 times as likely
Prefer Prefer B) 0.61 times as likely
Total
Candidate X Candidate Y C) 1.65 times as likely
Ages 25 – 34 40 89 129 D) 2.34 times as likely
Ages 35 – 44 53 38 91
Total 93 127 220

11
14
Which of the following is closest to the percent of those
A researcher conducted a survey to determine whether
surveyed who preferred Candidate X?
people in a certain large city prefer Mango brand
A) 31% mobile operating systems to Cyborg brand mobile
operating systems. The researcher asked 186 people who
B) 42%
visited a local coffee shop their opinion, and 8 refused
C) 48% to respond. Which of the following factors makes it least
D) 73% likely that a reliable conclusion can be drawn about the
technological preferences of all the people in the city?

A) Sample size
B) Population size
C) Number of people who refused to respond
D) Where the survey was given
12
In 2015, the total population of individuals in
Minnesota between the ages of 25 and 44 was
approximately 2.2 million. If the survey results are used
to estimate information about political preferences of
voters across the state, which of the following is the best
estimate of the total number of individuals between the
ages of 35 and 44 who prefer Candidate X in 2015?

A) 1, 280, 000
B) 530, 000
C) 400, 000
D) 53, 000

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60 The SAT/ACT Diagnostic

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7
16
Questions 15–16 refer to the following information. Based on the model, what is the petroleum usage, in
A local power company collects the data shown below. gallons, of this neighborhood on a day on which the
The graph plots daily petroleum usage required to power a daily high temperature in Boston was 10°F?
specific neighborhood (consisting of 120 homes) in Boston,
MA against daily local high temperatures throughout the A) 16.0
month of March 2013. B) 14.5
C) 13.0
15 D) 11.5

12
Petroleum (gallons)

9
17
6

B C
3

0
0 30 40 50 60 70 80 90 A
Temperature (° Fahrenheit) E D

The power company's data can be modeled by the In quadrilateral ABCD , AB is parallel to CD and
equation P = 16 - 0.15d , where d is the local daily high BC is parallel to AD . If the length of AD and BC
temperature in Boston, in degrees Fahrenheit, and P is the were each doubled and the length of BE was reduced
amount of petroleum, in gallons, used by the neighborhood by 50 percent, how would the area of ABCD change?
on that day. Assume that relationship is also valid for
temperatures colder than those shown on the graph. A) The area of ABCD would be decreased by 50
percent.

15 B) The area of ABCD would be increased by 50

percent.
There were four days in March 2013 in which the daily C) The area of ABCD would not change.
high temperature in Boston was 71°F. Which of the
following is closest to the range of petroleum used by D) The area of ABCD would be multiplied by 2.
the neighborhood, in gallons, on these days?

A) 0.55
B) 0.75
C) 0.85
D) 1.30

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7
18 19
y Which of the following solids has the greatest volume?
6 A) A right circular cylinder whose radius is 6 cm and
whose height is 3 cm.
4 B) A right circular cylinder whose radius is 3 cm and
whose height is 6 cm.
C) A cone whose radius is 6 cm and whose height is 6
2 cm.
x D) A sphere whose radius is 3 cm.
−4 −2 O 2 4

−2

−4

What is the minimum value of the function graphed in

the xy-plane above, for - 5 # x # 5 ?

A) - 3
B) -2
C) 0
D) 3

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62 The SAT/ACT Diagnostic

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7
7 Answer: 2.5
Answer: 12
DIRECTIONS
Write → 7 / 1 2 2 . 5
For questions 20–24: Solve the problem answer

⎧
in boxes. ⊘ ⊘ ← Fraction ⊘ ⊘
and record your answer in the grid on your
⊙ ⊙ ⊙ ⊙ line ⊙ ⊙ ⊙ ⊙ ← Decimal
bubblesheet, as described below.
⓪ ⓪ ⓪ ⓪ ⓪ ⓪ point
① ① ① ① ① ① ① ①

⎨
1. It is suggested, though not required, that
② ② ② ② ② ② ② ②
you write your answers in the boxes at Grid-in ③ ③ ③ ③ ③ ③ ③ ③
the top of the columns to help you mark result. ④ ④ ④ ④ ④ ④ ④ ④
the circles accurately. You will only receive ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤

⎩
credit if the circles are filled in correctly. ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥
2. Only mark one circle in each column. ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦
⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧
3. There are no negative answers. ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨
4. Some problems may have more than one
correct answer. In such cases, please grid
only one answer.
2
Acceptable ways to grid in 3 are:
1
5. Mixed numbers such as 3 2 must be
2 / 3 . 6 6 6 . 6 6 7
gridded as 3.5 or 7/2 . (If 3 1 / 2 is
⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
entered into the grid, it will be interpreted ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪
31 1 ① ① ① ① ① ① ① ① ① ① ① ①
as 2 , not 3 2 .) ② ② ② ② ② ② ② ② ② ② ② ②
③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③
6. Decimal answers: If a solution is a decimal ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④
and the decimal does not terminate after 1 ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤
or 2 places, carry it out to a third place, to ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥
fill the entire grid. ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦
⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧
⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨

Answer: 201 – either position is correct

NOTE: You
2 0 1 2 0 1 may start your
⊘ ⊘ ⊘ ⊘ answers in any
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ columns, space
⓪ ⓪ ⓪ ⓪ ⓪ ⓪ permitting.
① ① ① ① ① ① ① ① Coulmns don't
② ② ② ② ② ② ② ② need to use
③ ③ ③ ③ ③ ③ ③ ③ should be left
④ ④ ④ ④ ④ ④ ④ ④
blank.

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7
20 22
The maximum seating capacity of a restaurant is 68 Annual Income Tax Rate
patrons. All tables at this restaurant seat either 2 or 4
patrons. If the restaurant has 22 tables, how many of the $0 to $20, 000 10%
tables seat 4 patrons? $20, 000 to $50, 000 16%
$50, 000 to $100, 000 22%
$100, 000 + 25%

Country X uses the progressive tax system summarized

in the chart above. Using this chart, a person making
$35, 000 would be taxed 10% for their first $20, 000
of annual income and 16% for their next $15, 000 .
How much would Bill, who made $53, 000 last year, be
taxed under this system? (Ignore the dollar sign when
bubbling-in in your answer. For example: if your answer
is $21, grid in 21 .)

21

x 2 4 6 8 10
f (x) -1 3 10 2 1

Let f (x) be defined for various values of x . if

3
g (x) = 2 x + 4 , what is the value of f ^g ^4hh ?

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64 The SAT/ACT Diagnostic

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7
24
Questions 23–24 refer to the following information. According to the model, what is the total distance
p (t) = 1.5t - 0.2t
2 3
(position-time) traveled of the train, in kilometers, over the first 2.5
minutes of its journey?
v (t) = 3.0t - 0.6t 2 (velocity-time)

a (t) = 3.0 - 1.2t (acceleration-time)

A bullet train leaving Daegu bound for Seoul accelerates

toward its maximum speed. The equations above describe
the acceleration, a (in km/min2), the velocity, v (in km/
min), and position, p (in km), of the train. The time, t , in
minutes, is measured after the train departs. Assume the
model is valid for 0 # t # 2.5 .

(Note: position is measured in kilometers from Daegu)

23
After how many minutes will the velocity of the train
equal 3.6 kilometers per minute?

STOP. BE CERTAIN NOT TO EXCEED THE

ALLOTTED TIME. YOU MAY PROCEED TO
SECTION 8 WHEN TOLD TO DO SO.

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8 Unauthorized copying or reuse of
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ACT SCIENCE TEST

8
29 Questions — 26 Minutes
DIRECTIONS: There are four passages in this section. Each
of them is followed by either five or six questions. Read the
passage, choose the best answer, and fill in the correspond-
ing letter on your bubblesheet. You may refer to any passage
on the exam as many times as you need.
You may NOT use a calculator on this section.

Passage I Table 1 shows the recorded half-lives for seven different

Radioactive decay is the spontaneous breakdown of isotopes of carbon.
an atomic nucleus resulting in the release of energy and
matter from the nucleus. When radioactive isotopes undergo Table 1
radioactive decay, these atoms transform into different
Isotope Half-life (seconds)
isotopes. An isotope’s half-life is the time required for half of
the radioactive nuclei in a substance to decay in this manner. C-14 1.81 # 10 11
C-11 1.22 # 10 3
C-10 1.99 # 10 1
C-15 2.45
C-20 1.60 # 10 -2
1000 C-21 3.00 # 10 -8
C-8 2.00 # 10 -21
900 Key
Po-210
800
Su- 35
700 Be - 7 1. According to Figure 1, for which isotope, V-48 or Be-7,
V- 48 will the average rate of decay be greater over the first
600
280 days?
500 A. V-48, because at any given time after zero, V-48 will
Nr

400 have the higher N r .

B. V-48, because at any given time after zero, V-48 will
300 have the lower N r .
C. Be-7, because at any given time after zero, Be-7 will
200 have the higher N r .
100 D. Be-7, because at any given time after zero, Be-7 will
have the lower N r .
0 40 80 120 160 200 240 280
Time (days)
2. According to Figure 1, the half-life of Be-7 is approxi-
mately:
Figure 1
F. 15 days.
Figure 1 shows, for four isotopes, the change over time G. 50 days.
of the number of nuclei remaining, N r , in a sample initially H. 140 days.
containing 1,000 of the nuclei. J. 280 days.

3. Based on Table 1 and Figure 1, which of the following

correctly orders the half-lives of C-8, C-15, and Po-210
from least to greatest?
A. C-8, C-15, Po-210
B. C-15, C-8, Po-210
C. Po-210, C-8, C-15
D. Po-210, C-15, C-8

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66 The SAT/ACT Diagnostic

8
4.
Unauthorized copying or reuse of
any part of this page is illegal.

A student observed a sample of 2,000 nuclei of C-10 5.

8
A researcher observed a sample of 1,000 Co-56 nuclei
and a sample of 2,000 nuclei of C-8 over the span of for 120 days. After 40 days, the N r of this sample was
20 seconds. Which of the following statements best approximately 660. Based on Figure 1, the N r of Co-56
describes the results of this observation? after 120 days was most likely:
F. After 20 seconds, there were approximately 1,000 A. greater than 400.
C-10 nuclei remaining in the first sample and B. between 200 and 400.
approximately 1,000 C-8 nuclei remaining in the C. between 80 and 200.
second sample. D. less than 80.
G. After 20 seconds, there were approximately 1,000
C-10 nuclei remaining in the first sample and few or
no C-8 nuclei remaining in the second sample.
H. After 20 seconds, there were approximately 500
C-10 nuclei remaining in the first sample and
approximately 500 C-8 nuclei remaining in the
second sample.
J. After 20 seconds, there were approximately 500
C-10 nuclei remaining in the first sample and few or
no C-8 nuclei remaining in the second sample.

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www.satactdiagnostic.com 67
8
Passage II
Unauthorized copying or reuse of
any part of this page is illegal.

Study 2
8
Caffeine is a stimulant found in energy drinks, coffee, One week later, the experiment in Study 1 was repeated
tea, and most colas. Caffeine begins to take effect within with four new groups. However, during this study, the
five minutes of consumption, and reaches its peak effect researchers waited three hours to retest students.
approximately 30 minutes after consumption. Table 1 lists
the typical caffeine content, in grams per liter, of commonly
Table 3
consumed beverages.
Before After
Consumption Consumption
Table 1
Group Typing Error Beverage Typing Error
Substance Caffeine Content (g/L) Speed Rate Speed Rate
7 Hour Energy 3.384 (wpm) (epm) (wpm) (epm)
Espresso 1.736 E 43.6 2.1 Espresso 48.0 2.8
Hot Coffee 0.688 F 43.4 2.1 Hot Coffee 45.5 2.5
Iced Coffee 0.307 G 44.2 2.2 Green Tea 45.2 2.4
Green Tea 0.217 H 43.1 2.2 Decaf 43.7 2.2
Diet Cola 0.127
Decaf 0.000
6. A student from Study 1 recorded typing speeds of 41.1
Researchers conducted a series of experiments to wpm and 56.9 wpm on the two typing tests given. Which
determine whether caffeine affected students’ typing speed in group was this student most likely a part of?
wpm (the number of words per minute that a person produces
using a standard keyboard) and error rate in epm (the number F. Group A
of errors per minute that a person produces using a standard G. Group B
keyboard). H. Group C
J. Group D

Study 1
7. Which of the groups served as a control in Study 2?
Each student sat at a computer terminal. The researchers
A. Group E
tested each student’s typing speed and error rate by directing
B. Group F
them to type a passage from The Fox and the Grape, one
C. Group G
of Aesop’s Fables. Students then were divided into four
D. Group H
groups. Depending on which group they were assigned to,
each student consumed 8 oz. of one of the beverages listed in
Table 1.
8. A fifth group of students repeated Study 1 using Iced
Coffee. If the initial typing speed of the group was 43.8
Thirty minutes later, student typing speed and error rate
wpm and the initial error rate of the group was 2.1 epm,
were tested again using a similar procedure. The results for
which of the following most likely gives the typing
each group were averaged after each test and the results of
speed and error rate of the group thirty minutes later?
both tests are shown in Table 2.
Typing Speed Error Rate
F. 45.2 2.5
Table 2 G. 47.1 2.7
Before After H. 47.9 3.0
Consumption Consumption J. 55.1 3.8
Group Typing Error Beverage Typing Error
Speed Rate Speed Rate
(wpm) (epm) (wpm) (epm) 9. Suppose the students in Group B were also tested 15
A 43.7 2.1 Espresso 53.3 3.6 minutes after consuming their caffeinated beverages.
B 43.4 2.1 Hot Coffee 47.9 3.0 Based on the results of Study 1, the average typing speed
C 44.1 2.2 Green Tea 46.3 2.5 the researchers recorded for this trial most likely would
D 43.5 2.2 Decaf 44.1 2.3 have been:
A. less than 43.4 wpm
B. between 43.4 wpm and 47.9 wpm
C. between 47.9 wpm and 53.3 wpm
D. greater than 53.3 wpm

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68 The SAT/ACT Diagnostic

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10. Based on the results of Studies 1 and 2, if the students in

8
11. Suppose the data for all of the groups, before and after
Group E had also been retested 30 minutes after consum- drinking the caffeinated beverages, were plotted on a
ing the caffeinated beverage, average student typing graph with typing speed on the x-axis and error rate on
speed most likely would have been: the y-axis. Suppose also that the best-fit line for these
F. greater than the average student typing speed data was determined. Which of the following would
measured three hours after students consumed the most likely characterize the slope of this line?
caffeinated beverage. A. The line would not have a slope, because the line
G. equal to the average student typing speed measured would be vertical.
three hours after students consumed the caffeinated B. The slope of the line would be zero.
beverage. C. The slope of the line would be negative.
H. less than the average student typing speed measured D. The slope of the line would be positive.
three hours after students consumed the caffeinated
beverage.
J. less than the average student typing speed measured
before students consumed the caffeinated beverage

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8
Passage III
Unauthorized copying or reuse of
any part of this page is illegal.

13. Based on Combinations 1 through 4, the relationship

8
An elevated inclined chute makes an angle, θ, with between H and X is best represented by which of the
a table. Points A and B, endpoints of the chute, are 0.75 m following graphs?
apart. Point B is at a height H meters above the floor (see
Diagram 1). A. 1.0

X(m)
A 0.8
B
θ 0.6

0 1.0 1.5 2.0 2.5

H H(m)
C
Floor
X
B. 1.0
Diagram 1

X(m)
A marble is released at Point A and travels down 0.8
the inclined chute to Point B. In some trials, the marble is
released from rest; in others, an initial force, F, is applied to 0.6
the marble. The sphere is in free fall between Points B and C
and first hits the floor at Point C, a horizontal distance X from 0 1.0 1.5 2.0 2.5
the bottom of the inclined plane.
H(m)
The table below shows how X, in meters (m), varies for
different values of H, in meters (m); θ, in degrees; and F, in
newtons (N). C. 1.0

Table 1
X(m)

0.8
H F X
Combination θ°
( )
(m) (N) (m) 0.6
1 1.0 25 0 .70
2 1.5 25 0 .85 0 1.0 1.5 2.0 2.5
3 2.0 25 0 .94 H(m)
4 2.5 25 0 1.01
5 1.5 15 0 0.60
6 1.5 20 0 0.77 D. 1.0
7 1.5 25 0 0.85
8 1.5 30 0 0.90
9 1.5 35 0 0.85
X(m)

0.8
10 1.5 40 0 0.77
11 1.5 25 0 0.85 0.6
12 1.5 25 5 0.93
13 1.5 25 10 0.97 0 1.0 1.5 2.0 2.5
14 1.5 25 15 0.99 H(m)

12. According to Table 1 and Combinations 5 through 10, as

θ increases, X:
F. increases only
G. decreases only
H. increases, then decreases
J. decreases, then increases.

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70 The SAT/ACT Diagnostic

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14. Based on the table, X will be greatest for which of the

8
16. When the ball was released, a transformation of energy
following H, θ, and F? occurred which included the marble’s potential energy
H(m) θ(°) F(N) ( Pe ), kinetic energy ( K e ), and heat (Q). Which of the
following statements best describes this transformation?
F. 1.0 20 5
G. 1.0 30 15 F. Pe and Q were converted to K e
H. 2.0 20 15 G. Ke and Q were converted to Pe .
J. 2.0 30 15 H. Pe was converted to K e and Q.
J. Ke was converted to Pe and Q.
15. If experimental trials were conducted in the same manner
in which Combinations 11 through 14 were tested, what
would be the independent variable and what would be
the dependent variable?
Independent Dependent
A. θ X
B. X θ
C. F X
D. X F

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8
Passage IV
Unauthorized copying or reuse of
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8
17. Based on the information provided, which of these is
Introduction most likely a true statement about the Moon?

During the Hadean Eon (the time period that began A. At some point during any given day the Moon is
with the formation of the Earth approximately 4.5 billion 390,000 km from the Earth.
years ago), Earth’s only satellite, the Moon, was formed. The B. At some point during any given day the Moon is
Moon orbits the Earth approximately once every 24 hours. The 410,000 km from the Earth.
Moon’s apogee (the maximum distance between the center C. At some point during any given day the Moon is
of the Earth and the center of the Moon) is approximately 390,000 km from the Sun.
405,400 kilometers and its perigee (the minimum distance D. At some point during any given day the Moon is
between the center of the Earth and the center of the Moon) 410,000 km from the Sun.
is approximately 362,600 kilometers.

An astronomy class discusses possible scenarios of how 18. It is known that the gravitational pull of the Earth is
the Moon was formed. Below are three separate hypotheses strong enough to force an object with the Moon’s veloc-
that the class came to collectively. ity and mass to orbit the Earth if it is within 900,000 km
of the Earth. Given that this information is true which of
the hypotheses, if any, are weakened?
F. None
G. Hypothesis 1
Hypothesis 1 H. Hypothesis 2 and 3
The Moon was created independently of the Earth J. Hypothesis 1, 2 and 3
during the early stages of our Solar System. The two objects
had their own distinct orbits around the sun. Over time, the
two orbits moved closer together. Eventually, the two objects 19. Supporters of Hypothesis 2 would most likely agree with
were close enough to be influenced by the forces of gravity. which of the following chemical compositions for the
The Earth’s gravitational field, being much stronger than that Moon’s crust?
of the Moon’s due to its size, captured the Moon. A. 43% O, 26% Si , 9% Al, and 22% Other
B. 43% O, 16% Si , 16% Al, and 25% Other
C. 55% O, 26% Si , 9% Al, and 10% Other
D. 55% O, 16% Si , 16% Al, and 13% Other

Hypothesis 2
The outer layers of the Moon bear a striking 20. Which of the following processes is most responsible for
resemblance to that of the Earth. Earth’s crust is made up of the formation of the Moon in Hypothesis 2 and 3?
approximately 47% oxygen, 28% silicon, 8.1% aluminum, F. Electromagnetic Force
5% iron, 3.6% calcium, 2.1% magnesium, and 6.2% other G. Nuclear Force
materials. The Moon was created from excess material that H. Fusion
was spun out from the Earth as it rotated during its early years J. Fission
of development. It gathered in a cloud of debris that orbited
around the Earth and slowly melded together.
21. It is known that one of the moons of Mars, Phobos, is a
captured asteroid (an asteroid that passed close enough
to Mars that it was unable to escape its gravitational
pull). Which of the following statements, if true, under-
Hypothesis 3 mines the claim that Earth’s Moon is a captured asteroid?
The Moon was created from material that was ejected A. The average temperature of the Moon is approxi-
from Earth’s crust after a massive impact occurred. An object mately -5° Celsius, significantly cooler than that of
with the approximate size of Mars collided with Earth during the Earth.
Earth’s early evolutionary stage. The impact was so massive B. The surface of the Moon is heavily cratered.
that it sent a significant amount of Earth’s surface hurtling 1
C. The Moon is approximately 80 times the mass of
into space. However, the materials could not escape Earth’s
gravitational forces and were trapped in orbit. These objects 1
the Earth, where as Phobos is approximately
remained hot after impact and continued to crash into each times the mass of Mars. 10 8

other and bonded together as they orbited Earth. After the D. The chemical compositions of Phobos and the Moon
material cooled the end result was the Moon. are significantly different.

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72 The SAT/ACT Diagnostic

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22. Supporters of Hypothesis 1 would most likely agree that

8
23. If Hypothesis 1 is true, which of the following statements
the materials that compose the Moon came from which must be true about the gravitational pulls of the Earth
of the following places? and the Sun? When the Moon was created, the effect of
F. Materials present during the Hadean Eon the Sun’s gravity on the Moon was:
G. Earth A. at first weaker than but eventually equal to the effect
H. Mars of Earth’s gravity.
J. An asteroid field B. at first weaker than but eventually stronger than the
effect of Earth’s gravity.
C. at first equal to but eventually weaker than the effect
of Earth’s gravity.
D. at first stronger than but eventually weaker than the
effect of Earth’s gravity.

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8
Passage V
Unauthorized copying or reuse of
any part of this page is illegal.

Experiment 2
8
Introduction The researchers selected 16 adolescent male rats for
High Fructose Corn Syrup, or HFCS, is a low-cost the Experiment. The rats were divided into 2 groups each
alternative to sucrose (table sugar) commonly found in containing 8 rats such that each group of rats had roughly
American soft drinks. While sucrose is typically derived the same average bodyweight—300 g—at the beginning of
from sugarcane or beet, HFCS is produced by milling corn the experiment. Both groups were given access to a specific
and then adding enzymes until 42% of the mixture, by weight, brand of dry rat food ad libitum, but no other food. Both
consists of fructose. groups had access to unsweetened water. Only one group had
access to water sweetened with HFCS.
The enzymes involved in converting corn starch into
HFCS are: Alpha-amylase, which produces shorter chains Researchers measured the average daily caloric intake
of sugars called oligosaccharides from raw cornstarch, and of the rats in each group, the average bodyweight of the rats
Glucoamylase, which breaks the oligosaccharides down even in each group after 2 months, and the average triglyceride
further to yield pure glucose, and Xylose Isomerase, which level of the rats in each group after 2 months. The results are
converts glucose into fructose. given in the table below.

Because the increased introduction of HFCS in the Table 1

American diet has coincided with an increase in obesity,
Bodyweight
a team of researchers did two experiments to determine Access Daily
after 2 mo. Triglyceride
whether the rise in obesity may be at least partially explained to Caloric
Group (% of Level
by the use of HFCS. HFCS- Intake
baseline (mg/dL)
Water? (kcal)
weight)
Experiment 1
The researchers selected 24 adolescent male rats for A Yes 84 177 201
the experiment. The rats were divided into 3 groups each B No 86 151 147
containing 8 rats such that each group of rats had roughly the
same average bodyweight—300 g—at the beginning of the Experiments and data adapted from High-fructose corn syrup causes
experiment. All groups were placed on a diet that consisted characteristics of obesity in rats: Increased body weight, body fat and
of a specific brand of dry rat food ad libitum (available at triglyceride levels by Bocarsly, Powell, Avena, and Hoebel. Originally
all times), but no other food. All groups also had access to published in Pharmacology, Biochemistry and Behavior, 2010.
unsweetened water. Only some of the groups had access to
water sweetened with HFCS or sucrose.

The researchers measured the average bodyweight 24. Suppose Experiment 1 had continued for a seventh
within each group at various times, as shown in the figure month. The average bodyweight of rats that had access
below. to sucrose-water after seven months most likely would
have been:
Key
No Sweetened Water Added F. Less than 213% of their baseline weight.
Sucrose-Water G. Between 213% and 237% of their baseline weight.
HFCS-Water H. Between 237% and 250% of their baseline weight.
250 J. Greater than 250% of their baseline weight.
Body Weight (% of baseline weight)

200
25. The researchers hypothesized that the rats with access
150 to HFCS-water for two months would consume more
calories than rats without access to HFCS-water. Do the
100 results of Experiment 2 support this hypothesis?
A. Yes, the rats in Group A consumed more calories
than the rats in Group B.
50
B. Yes, the rats in Group A consumed fewer calories
than the rats in Group B.
0 C. No, the rats in Group A consumed more calories
0 1 2 3 4 5 6 than the rats in Group B.
Months After Diet Began D. No, the rats in Group A consumed fewer calories
Figure 1 than the rats in Group B.

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74 The SAT/ACT Diagnostic

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any part of this page is illegal.

26. Suppose the researchers measure the total amount of 28. Based on the results of Experiment 1, approximately
8
HFCS consumed by rats over the 2 experiments to be how many months after the experiment began did the
1000g. Approximately how much fructose did the rats average weight of the rats in the group that had access to
consume between the experiments? HFCS-water equal 600 g?
F. 42g F. 3 months
G. 58g G. 4 months
H. 420g H. 5 months
J. 580g J. 6 months

27. During which month of Experiment 1 did the rats in each 29. Which of these is a question that can be answered by
group gain the most weight? The rats in all three groups analyzing the results of these experiments?
gained the most weight: A. Does access to HFCS-water cause female rats to
A. between zero and one months after beginning the carry more bodyweight?
diet. B. Does HFCS cause diseases such as pancreatitis and
B. between one and two months after beginning the diabetes in humans?
diet. C. Do triglyceride levels rise in male rats that consume
C. between four and five months after beginning the HFCS?
diet. D. What effect does a higher ratio of glucose to fruc-
D. between five and six months after beginning the tose in HFCS have on bodyweight in male rats who
diet. consume HFCS-water?

STOP. END OF DIAGNOSTIC. MAKE SURE

TO HAND YOUR BUBBLESHEET IN.

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 2 Answer Key &
Solutions

76 The SAT/ACT Diagnostic

 SOLUTION GUIDE

ANSWER KEY

Section 1 8. D 28. K 6. G 15. D

1. B 9. B 29. B 7. C 16. B
2. F 10. A 30. F 8. J 17. C
3. D 11. C 31. A 9. B 18. A
4. H 12. B 32. F 10. G 19. A
5. B 13. D 33. E 11. C 20. 12
6. F 14. A 34. H 12. J 21. 1
7. B 15. A 35. C 13. B 22. 7460
8. G 16. A 36. G 14. F 23. 2
9. D 17. C 37. D 15. D 24. 6.25
10. F 18. D 38. G 16. F
11. C 19. D 39. A 17. C Section 8
12. J 20. C 40. H 18. F 1. B
13. B 21. B 19. D 2. G
14. F 22. D Section 4 20. G 3. A
15. A 23. D 1. A 21. A 4. G
16. G 24. A 2. A 22. G 5. B
17. D 25. D 3. D 23. D 6. A
18. G 26. B 4. B 24. H 7. J
19. B 27. B 5. C 25. B 8. B
20. H 28. C 6. D 26. J 9. G
21. B 29. C 7. C 27. A 10. A
22. G 30. D 8. D 28. H 11. J
23. D 31. B 9. D 29. B 12. H
24. J 32. C 10. A 30. J 13. A
25. A 33. D 11. A 14. J
26. F 12. C Section 6 15. C
27. C Section 3 13. B 1. A 16. H
28. H 1. B 14. B 2. C 17. A
29. A 2. H 15. D 3. D 18. F
30. H 3. C 16. C 4. B 19. A
31. D 4. J 17. A 5. D 20. H
32. H 5. E 18. A 6. C 21. C
33. C 6. H 19. D 7. B 22. F
34. G 7. B 20. C 8. C 23. D
35. A 8. K 21. C 9. D 24. G
36. J 9. D 22. A 10. 2/3 25. D
37. A 10. K 23. C 11. 8 26. H
38. G 11. D 24. A 12. 3 27. A
39. C 12. J 25. D 28. F
40. F 13. A 26. D Section 7 29. C
41. D 14. H 27. C 1. B
42. G 15. E 28. B 2. B
43. C 16. G 29. C 3. C
44. J 17. C 30. B 4. B
45. A 18. G 31. B 5. C
19. B 32. A 6. A
Section 2 20. J 33. C 7. A
1. B 21. A 8. D
2. A 22. J Section 5 9. D
3. C 23. B 1. B 10. B
4. B 24. F 2. G 11. B
5. D 25. C 3. C 12. B
6. D 26. J 4. F 13. C
7. B 27. B 5. B 14. D

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The Redesigned SAT/ACT Diagnostic

SECTION 1 | ACT ENGLISH | SOLUTIONS

Passage I – Harvesting Strawberries

Question 1. The best answer is B because both “handed” and “showed” are in the same verb tense.

Question 2. The best answer is F because it is the only answer choice that mentions details of the farm’s setting.

Question 3. The best answer is D because it avoids creating a run-on sentence.

Question 4. The best answer is H because it provides the best contrast to how “inviting” the rows originally looked.

Question 5. The best answer is B because it is the adverb that modifies the adjective “appealing”.

Question 6. The best answer is F because the strawberries were “dull” and they “hid” rather than looking “pleasant and
inviting”.

Question 7. The best answer is B because it is the only one that shows the narrator doing something.

Question 8. The best answer is G because it is the right tense and voice.

Question 9. The best answer is D because “them” refers back to the two types of strawberries.

Question 10. The best answer is F because the rest of the paragraph discusses two types of strawberry.

Question 11. The best answer is C because it is the least wordy.

Question 12. The best answer is J because it eliminates unnecessary information.

Question 13. The best answer is B because the verb “can have” requires a subject “a picker”.

Question 14. The best answer is F because it avoids a run-on (as in B) and is less wordy that C. Choice D creates a
dangling modifier.

Question 15. The best answer is A because it is the right past tense of “to spit”.

Passage II – Saving the Whooping Cranes

Question 16. The best answer is G because the addition does create such balance.

Question 17. The best answer is D because the birds fly low.

Question 18. The best answer is G because it is the only answer which provides a subject and a verb to the independent
clause that follows the comma.

Question 19. The best answer is B because the birds are recovering as their numbers increase.

Question 20. The best answer is H because the subject “donations” requires a plural auxiliary -- “have” rather than “has”.

Question 21. The best answer is B because there is no need to separate the noun “scientists” from the prepositional phrase
that modifies it.

Question 22. The best answer is G because it makes clear that the birds need to avoid specific dangers.

Question 23. The best answer is D because it is parallel in construction with the verb “teach”.

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SECTION 1 | ACT ENGLISH | SOLUTIONS

Question 24. The best answer is J because placed after sentence 4, “this program” refers to “Operation Migration”, which
must be mentioned before “this program”. Also, the following paragraph begins with “The Partnership”.

Question 25. The best answer is A because the subject of the sentence is “A class”, which requires a singular auxiliary —
“has”, not “have”.

Question 26. The best answer is F because “Via” means “by means of” and says it in fewer words.

Question 27. The best answer is C because the introductory phrase “During these flights through the eastern United States”
must be separated from the main clause by a comma.

Question 28. The best answer is H because “power lines” and “windmill blades” are count nouns and therefore require
“fewer” rather than “less”.

Question 29. The best answer is A because placed here, the sentence provides a contrast with the following sentence that
describes the dangers of low flying.

Question 30. The best answer is H because the essay does not report a “rate of success”.

Passage III – Mark Rothko — Who Painted Color

Question 31. The best answer is D because these are two separate sentences and must be punctuated as such.

Question 32. The best answer is H because the contrast between the two viewers’ reactions indicates how various they
were.

Question 33. The best answer is C because the use of “because” makes an independent clause necessary to complete the
sentence.

Question 34. The best answer is G because “rectangles” is plural, so the verb must also be plural.

Question 35. The best answer is A because “shapes” is plural, so they must be “themselves”.

Question 36. The best answer is J because there is no comma needed between the noun “communication” and the phrase
that modifies it.

Question 37. The best answer is A because no transitional word is necessary.

Question 38. The best answer is G because it identifies where the color is in the fewest words.

Question 39. The best answer is C because the appositive “one of Rothko’s most famous” must be surrounded by commas.

Question 40. The best answer is F because “floods” accurately gives a sense of how strong and numerous these feelings are.

Question 41. The best answer is D because the compound direct object of the verb “expresses” requires no comma
separation.

Question 42. The best answer is G because it is the only one that focuses on the works in the Chapel.

Question 43. The best answer is C because the entire clause modifies “works” and must be introduced by “which”

Question 44. The best answer is J because it mentions” colors”, the central theme of the essay, and uses “melancholy” to
emphasize the mood.

Question 45. The best answer is A because color is central to the essay and is clearly an aspect of Rothko’s talent/genius.

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The Redesigned SAT/ACT Diagnostic

SECTION 2 | SAT CRITICAL READING | SOLUTIONS

Passage I – Robinson Crusoe

Question 1. The best answer is B because the author states in (lines 26–27) that his plan to go to sea was against his father’s
commands. In the fourth and fifth paragraphs (lines 32–70) the father gives many examples of a lifestyle he believes would
bring his son more happiness than a life at sea.

Question 2. The best answer is A because throughout the fourth and fifth paragraphs of the passage (lines 32–70) the father
expresses grave misgivings about his son’s plans to go to sea, and offers various reasons why (lines 48–51) living in “the
middle state…, was the best state in the world, the most suited to human happiness.”

Question 3. The best answer is C because the author states in (lines 24–31) that “I would be satisfied with nothing but going
to sea…tending directly to the life of misery which was to befall me.”

Question 4. The best answer is B because lines 21–31 end with statement “tending directly to the life of misery which was
to befall me.”

Question 5. The best answer is D because “misuse” most accurately describes the way the name Kreutznaer was changed to
“Crusoe” upon the family’s move from Bremen to England, and that the family chose to call itself by that name even though it
was not its name. Had this change evolved over a long period of time, “evolution” would have been the correct answer.

Question 6. The best answer is D because in lines 16–18 the author states “…any more than my father or mother knew what
became of me.”

Question 7. The best answer is B. Choice B is the best answer because in lines 16–18 the author states “What became of
my second brother I never knew, any more than my father or mother knew what became of me.”

Question 8. The best answer is D because in lines 2–11 we learn that the author’s name, Robinson Kreutznaer, originated in
Bremen and was changed in England. That the family did not object to this is implied in (lines 9–11) “…we are now called—
nay we call ourselves and write our name—Crusoe…”

Question 9. The best answer is B because an “entreaty” is a plea. The use of the word “persuasions” right after the word
entreaties in the text (line 28) helps the reader to see that the word in context is a plea, not an outburst, a discussion or tears.

Question 10. The best answer is A because the author recounts his father’s advice that neither fortunes (lines 42–43), “…
desperate fortunes on one hand, or of aspiring, superior fortunes on the other…”, nor fame (line 45), “…make themselves
famous”, are as suitable for happiness as the “middle state”, which was (lines 50–51), “the best state in the world, the most
suited to human happiness”.

Question 11. The best answer is C because that the author’s father cares is demonstrated in lines 35–36 and that he is
inquisitive is demonstrated in lines 36–41.

Passage II – Supreme Court

Question 12. The best answer is B because the sentence in lines 8–9 wants to convey that the Supreme Court struck down
the “upper limits” on the maximum amount of money an individual can contribute. Plug your answer choice in and then to
reread the sentence. That will show you why maximum doesn’t work.

Question 13. The best answer is D because the text notes (lines16–20) that “the conservative justices argued that the first
Amendment (freedom of expression) prohibits Congress from creating laws that restrict the exercise of the First Amendment
rights in the form of campaign contributions.

Question 14. The best answer is A because lines 16–20 state “that the conservative justices argued that the First Amendment
(freedom of expression) prohibits Congress from creating laws that restrict the exercise of First Amendment rights in the form
of campaign contributions.”

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Question 15. The best answer is A because lines 32–35 state that the new decision might devastate (ruin, end) “what
remains of campaign finance reform.”

Question 16. The best answer is A because lines 61–67 state that the law pertains to very few Americans since it limits
political contributions to no more than $48,600 to candidates, plus an additional $74,600 to political committees.

Question 17. The best answer is C because in lines 74–82 Breyer noted that “Where enough money calls the tune, the
general public will not be heard … And a cynical public can lose interest in political participation altogether.”

Question 18. The best answer is D because in lines 74–82, Breyer noted that “where enough money calls the tune, the
general public will not be heard … And a cynical public can lose interest in political participation altogether.”

Question 19. The best answer is D because the sentence in question (line 83–86) conveys the following: “Breyer argued
that removing the aggregate limits (the total limits) on campaign contributions created large loopholes to unduly influence
government. lines 61–67 note the new law struck down the amount of money an individual could contribute to candidates and
political committees.

Question 20. The best answer is C because on lines 91–94 Roberts counters that the arguments are “either illegal under
current campaign finance laws,” or made by people who are “divorced from reality.”

Question 21. The best answer is B because both Justice Roberts (lines 91–94) and Justice Breyer (lines 74–82) have written
highly critical and biting remarks about the justices whose rulings differed from theirs. Breyer wrote that the justices’ decision
was unconstitutional. He added the decision could well drive citizens from voting. Justice Roberts wrote that the dissenting
justices’ position was “either illegal” or that the justices were “divorced from reality.”

Question 22. The best answer is D because in the first three paragraphs the author notes in the topic sentence that the
decision is controversial; divisive; contentious. The article goes on to present opposing points of view on the decision from
Senator McCain, Justice Roberts and Justice Breyer.

Passage III – GM Crops

Question 23. The best answer is D because lines 6–7 state that the crops “have been altered to provide maximum amount of
benefit to the both the consumer and the farmhands. The first sentence in the next paragraph (line 8–11) notes the benefit to the
environment.

Question 24. The best answer is A because lines 1–7 state that the crops “have been altered to provide maximum amount of
benefit to the both the consumer and the farmhands. The first sentence in the next paragraph (line 8–11) notes the benefit to the
environment.

Question 25. The best answer is D because the organizations’ data are accepted internationally, which is why they are
highly respected. Lines 35–37 note that the scientific organizations have offered reams of compelling and internationally
accepted scientific data.

Question 26. The best answer is B because the authors states (lines 56–59) the use of glyphosate led to the substantial
increase in the use of herbicides that had harmful effects on the environments and the actual fruits of its efforts.

Question 27. The best answer is B because harmful effects on crops and the environment can be found on lines 56–59.
“This increase has had harmful effects on the environment and the actual fruits of its efforts”

Question 28. The best answer is C because the text states (lines 54–55) that “Farmers could now easily combat the weeds
that disturbed their crops.” The word combat imples that the weeds hindered the growth of the crops.

Question 29. The best answer is C because a very large percentage of Americans who eat GM varieties of soybean (94
percent) and maize (72 percent) are exposed to toxic herbicides (lines 65–69)

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SECTION 2 | SAT CRITICAL READING | SOLUTIONS

Question 30. The best answer is D because the rate of increase of glyphosate use on soybean crops is projected to be 3.3%
between 2010 and 2011, which is smaller than the typical growth of 8.9% between 2005 and 2010. (Table 1).

Question 31. The best answer is B because Passage 1 (lines 1–11) makes the case the modified crops benefit the consumer,
the farmer, and the environment. On the other hand, Passage 2 argues (lines 40–42) that GM crops propose a risk to the
consumer and the environment.

Question 32. The best answer is C because Passage 2 expresses concern that (lines 75–81) “Heightened risk of public
health impacts can be impacted with more intensive herbicide use to protect GM crops. ”

Question 33. The best answer is D because the author of passage 1, who disagrees with this statement in Passage 2,
recognizes it and then goes on to refute it in (lines 31–39).

SECTION 3 | ACT MATHEMATICS | SOLUTIONS

Multiple Choice
Question 1. The correct answer is B. One share of Ashwin’s stock was worth $22.90 after the first month, $22.65 after the
second, and $22.70 after the third. Therefore, 100 shares of stock is worth $100 $ $22.70 = $2, 270 .

Question 2. The correct answer is H. If we multiply both sides of the original equation by 4, we are left with
5 (x - 3) = 80 . Therefore, we divide both sides by 5 to obtain the results x - 3 = 16 . Add 3 to both sides and find that
x = 19 .
28
Question 3. The correct answer is C. We are asked for the ratio of red pieces to black pieces, so we must simplify 32 to
7
8.
Question 4. The correct answer is J. Because +ACB and +BCD are supplementary, +ACB = 27c . Because AB = BC ,
9ABC is isosceles and +BAC = 27c . Therefore, +ABC = (180 - 27 - 27)c = 126c .

Question 5. The correct answer is E. We must distribute the minus sign through the second parentheses so that the
expression becomes 4x 3 + 3 + 3x 2 + x - 5 . Now combine like terms: 7x 2 + x - 2 .

Question 6. The correct answer is H. The volume of a right rectangular prism is calculated using the formula V = lwh .
The problem tells us that l = 14 and w = 18 . Therefore, 3780 = 14 $ 18 $ h . Solve, and h = 15 .

Question 7. The correct answer is B. The least common denominator is the smallest number that divides by 4, 5, and 30
evenly. The number 30 does not divide 4 evenly, but 60 works.
x + 2x + 4x + 8x
Question 8. The correct answer is K. The average of x , 2x , 4x , and 8x is 4 . Therefore,
x + 2x + 4x + 8x 15x
67.5 = 4 . Thus, combining like terms, 67.5 = 4 . Multiply 4 by both sides and obtain 270 = 15x . Thus,
x = 18 .

Question 9. The correct answer is D. The angle vertical to the angle marked with xc (which also is xc ) and the angle
marked yc are consecutive interior angles. Therefore, x + y = 180 , and x = 180 - y .

Question 10. The correct answer is K. The additive rule of exponents says that the product of a 3 and a is a 4 . Similarly,
the product of b 2 and b 5 is b 7 . Additionally, choices F and G are wrong because 4 $ 5 = 20 .

Question 11. The correct answer is D. A shift to the left by three units indicates that x must decrease by 3.

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SECTION 3 | ACT MATHEMATICS | SOLUTIONS

Question 12. The correct answer is J. If x of the flips landed with the heads side up, then x - 52 landed with the tails side
up. Therefore, x + (x - 52) = 162 . Therefore, 2x = 214 , so x = 107 .
2
Question 13. The correct answer is A. Subtract 5 from the initial inequality to obtain 6x $ 2 . Therefore, x $ 6 , which
1
can be simplified as x $ 3 .

Question 14. The correct answer is H. We can isolate y and put the equation into slope-intercept form. Subtract 4x from
4
each side to obtain 5y = - 4x + 10 . Divide both sides by 5 to obtain y = - 5 x + 2 . The slope of this line is the coefficient of
4
x , which is - 5 .
a
Alternatively, we can use the property that the slope of a line in standard form ^ax + by = ch is - b .

Question 15. The correct answer is E. In order for the median temperature for the seven days to be 33c , there must be one
data point equal to 33c in our data set, three other values that are at most 33c in the data set, and three other values that are at
least 33c in the data set.

An inspection of our data set reveals that there are currently three values greater than 33c , so the remaining value must be at
most 33c . Therefore, Sunday’s temperature cannot be 35c .

Question 16. The correct answer is G. The equation is quadratic, so we set it equal to zero (so that we can factor and use
the zero product rule in our next step). If we subtract 15 from both sides, the equation becomes (x - 5) (x + 3) = 0 . Therefore,
the possible values of x are the numbers that make the equations x - 5 = 0 and x + 3 = 0 true, which are x = 5 and x = - 3 .

Question 17. The correct answer is C. Once $Q and $R are both deducted from P , the remaining $P - Q - R represents
P-Q-R
Will’s take home pay. The fraction of his weekly salary is therefore $ P .
1
Question 18. The correct answer is G. The area of a triangle is calculated using the formula A = 2 bh . The problem tells
1
us that b = x + 3 and h = 4x - 2 . Therefore, A = 2 (x + 3) (4x - 2) . Expand, and A = 2x 2 + 5x - 3 .

Question 19. The correct answer is B. The line must have a positive slope (which rules out options C, D, and E). Because
y is less than or equal to the other side of the equation, the shading must be below the line (which rules out option A).

Question 20. The correct answer is J. If x - 9 = 11 , then x - 9 = 11 or x - 9 = - 11 . Add 9 to both sides of both
equations and x = - 2 or x = 20 .

Question 21. The correct answer is A. The sine of an angle in a right triangle is equal to the side opposite it divided by the
x
hypotenuse of the triangle. Therefore, if we label the side that we are solving for x , it is true that sin 8c = 24 . Multiply both

sides by 24 and we get 24 sin 8c = x .

Question 22. The correct answer is J. If x represents the number of students in the junior class, then 68% of x equals
289.Therefore, 0.68x = 289 . Divide both sides by 0.68 and we obtain x = 425 .

Question 23. The correct answer is B. The formula for percentage change is
New Value - Original Value $2.43 - $2.25
Percent Change = Original Value $ 100 . Therefore, we must calculate $2.43 $ 100 , which is equal to
9% .

Question 24. The correct answer is F. The value of g (4) is 16, so the value of f (g (4)) is equal to f (16) , which is 33.

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Question 25. The correct answer is C. The circumference of a circle is calculated using the formula C = 2rr . The
7 7 7
problem tells us that C = 2 r Therefore, 2 r = 2rr . Divide both sides by 2r . We are left with 4 = r .

Question 26. The correct answer is J. The formulas for the midpoint of two coordinates on the (x, y) coordinate plane are
x +x y1 + y2
x m = 1 2 2 and y m = 2 , where the values with m subscripts are the coordinates of the midpoint and all other values
4 + x2 - 2 + y2
are coordinates of the endpoints. Therefore, 2 = 6 and 2 = - 6 Multiply both fractions by two and isolate the

variable to obtain x 2 = 8 and y 2 = - 10 .

Question 27. The correct answer is B. Plug in t = 2 and t = 3 to the function and solve for h . The height at t = 2 is 64
ft., the height at t = 3 is 48 ft. Therefore, the rocket descended 16 ft. between t = 2 and t = 3 .

Question 28. The correct answer is K. The expression (- 2i) 4 is equivalent to (- 2) 4 i 4 . Because i = - 1 , i 2 = - 1 and
i 4 = 1 . Therefore, (- 2) 4 i 4 = 16 $ 1 = 16 .

Question 29. The correct answer is B. We can calculate the third side of the right triangle formed by the ladder, wall, and
ground using Pythagorean theorem. Since the ladder is opposite the right angle, 11 is the hypotenuse, and 11 2 = 10 2 + x 2 ,
where x is the distance from the base of the wall to the bottom of the ladder. Therefore, 21 = x 2 , and 21 = x .

Question 30. The correct answer is F. A correct proportion must align 11 and 25 (as they both correspond to the ladder), 10
and x (as they both correspond to the wall), 10 and 11 (as they both correspond to the triangle in the figure), and x and 25 (as
they both correspond to the similar figure described in the problem). Only Choice A does this.

Question 31. The correct answer is A. To calculate the angle, we must use the correct inverse trig function. Because 10 is
the side opposite the angle of elevation and 11 is the hypotenuse, we must use sine.

Question 32. The correct answer is F. The distance between 2 points in the (x, y) coordinate plane is calculated using

the formula d = (x 1 - x 2) 2 + (y 1 - y 2) 2 . If we plug in (- 2, 3) and (7, 7) for (x 1, y 1) and (x 2, y 2) , respectively, we get

1
that d = (- 2 - 7) 2 + (3 - 7) 2 = 9.8 coordinate units. However each coordinate unit is equal to 2 mile. Therefore,
1
2 $ 9.8 = 4.9 miles.
Question 33. The correct answer is E. The distance from the Sun to Neptune is approximately 4503000000 miles, and
the distance from the Sun to Venus is approximately 108000000 miles. The difference of these numbers is 4395000000 miles,
which can be expressed as 4.395 # 10 9 miles.
& 40 1
Question 34. The correct answer is H. A central angle of 40c means that the arc MN is 360 = 9 of the circumference.

Therefore, the total circumference is 9 $ 2pi centimeters, or 18r centimeters.

The circumference of a circle is calculated using the formula C = 2rr , so 18r = 2rr . Divide both sides by 2r and obtain
r = 9.

Question 35. The correct answer is C. The standard form of a circle in the (x, y) coordinate plane is
(x - h) 2 + (y - k) 2 = r 2 , where (h, k) is the center of the circle and r is the radius. Therefore, according to the equation given
in the problem, h = 5 , k = - 3 , and r = 2 .

Question 36. The correct answer is G. Use the formula given in the note, where b = 8 , c = 17 , and cosi = .72 . We
obtain a 2 = 64 + 289 - 252 (0.72) , so a 2 = 157.16 and therefore a = 12.5 .

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3 2
Question 37. The correct answer is D. We can obtain the common ratio of the sequence by dividing 3 7 by 2 7 .Thus, the
3 1 3
common ratio of the sequence is 2 . We can obtain Luke’s mileage during week 5 by multiplying 5 7 by 2 and multiplying
3 4
the result by 2 again, which results in 11 7 .

Question 38. The correct answer is G. The fact that a linear system of equations has multiple solutions implies that each
equation is a linear multiple of each other equation in the system. Since the x -coefficient in the first equation (15) is three
times the x -coefficient in the second equation (5), the y -coefficient in the first equation (- 12) must also be three times the y
-coefficient in the second equation. Therefore, b = - 4 .

Question 39. The correct answer is A. If (p, q) is on the parabola, then q = ap 2 . Therefore, q = a (- p) 2 , and the point
(- p, q) must also be on the parabola.

Question 40. The correct answer is H. Draw a line from point B to DC . Label the intersection point E . The line BE
must be the height of the trapezoid.

Because +BEC is a right angle, 9BEC is a 30c - 60c - 90c right triangle. Therefore, the height of the trapezoid must be
4 3 units. Additionally, CE is 4 units long. Because CE is 4, AB is 12 units long.
1
The area of a trapezoid is calculated using the formula A = 2 (b 1 + b 2) h where b 1 and b 2 are bases and h is the height of the
1
trapezoid. We know that b 1 = 16 , b 2 = 12 , and h = 4 3 . Therefore, A = 2 (28) 4 3 , which is approximately equal to 97

square units.

SECTION 4 | SAT WRITING | SOLUTIONS

Passage I – Solunar Fishing

Question 1. The best answer is A because it creates a grammatically complete sentence with the right verb tense.

Choices B and C are incorrect because each inserts unnecessary punctuation that disrupts the meaning of the sentence. Choice
D is incorrect because it is the wrong verb tense.

Question 2. The best answer is A because the preposition “with” correctly reflects the relationship between the verbal
adjective “dotted” and the nouns “ boats, buoys, and lobster pot markers.”

Choices B, C, and D are incorrect because each provides a preposition that does not appropriately represent the relationship
between “dotted” and the following nouns. A seascape can be dotted “with” boats and buoys; it cannot be dotted “between,”
“for,” or “on” boats and buoys.

Question 3. The best answer is D because the information in the sentence elaborates on and follows from the claim in the
previous sentence: animal species respond to a diurnal clock.

Choices A, B, and C are incorrect because they do not appropriately signal that the information in the sentence follows from the
claim in the previous sentence. Rather, Choice A suggests the writer is offering an example, and Choices B and C suggest that
the writer is drawing a contrast.

Question 4. The best answer is B because it creates a grammatically complete and standard sentence. It also correctly
reflects the relationship specified in the passage between lunar phases and strength of influence.

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Choice A is incorrect because “Although” suggests that the second clause will contradict the first. Choices C and D are
incorrect because each results in a grammatically incomplete or run-on sentence.

Question 5. The best answer is C because it acts effectively as a transition between the previous paragraph and this one. It
also reflects the content of the new paragraph.

Choices A, B, and D are incorrect because none of them introduces the main idea of the paragraph: the long history of solunar
fishing.

Question 6. The best answer is D because it contains “the most specific” actions which the lunar calendar advises.

Choices A, B, and C are incorrect because each is vague. “Actions,” “certain tasks,” and “fishing and hunting” are all nebulous
terms.

Question 7. The best answer is C because it provides the grammatically correct option for a possessive singular noun. The
editor belongs to, or is affiliated with, the almanac.

Choices A is incorrect because it does not indicate possession. Choices B, and D are incorrect because they suggest there is
more than one almanac.

Question 8. The best answer is D because it does not repeat information. If one is a skeptic, one is not sure of the truth of
something.

Choices A, B, and C are incorrect because they all provide redundant information about skeptics.

Question 9. The best answer is D because it provides the possessive pronoun that grammatically corresponds to the singular
noun “science.”

Choices A, B, and C are incorrect because: A provides a plural pronoun for a singular antecedent; B’s “those” is too vague; and
C confuses “it is” with the possessive pronoun “its.”

Question 10. The best answer is A because it satisfies the directions of the question by reinforcing the point that skepticism
about solunar fishing still exists.

Choice B is incorrect because it concludes the paragraph on too neutral a note. Choice C does nothing to suggest there is still
doubt. Choice D addresses a different problem: that of sustainability.

Question 11. The best answer is A because it focuses on the size and variety of the catch as seen by the biologist and
displayed to the viewer.

Choice B is incorrect because, even though it appeals to the sense of sight, it fails to focus on the fish. Choices C and D are
incorrect because they lack sensory details.

Passage II – Deforestation
Question 12. The best answer is C because it provides the appropriate punctuation for the nonrestrictive modifying phrase
“including fertile soil.” Because the phrase is not essential to the sentence, it should be offset with commas (or other matching
punctuation). Since a comma is used before the phrase, a comma must be used after it as well.

Choices A and D are incorrect because the punctuation does not match t he comma that sets off the nonrestrictive modifying
phrase “including fertile soil.”

Choice B is incorrect because “this is” is unnecessarily wordy.

Question 13. The best answer is B because the verb “highlights” grammatically corresponds with the singular noun

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“importance.” Additionally, “effects” is the correct noun to describe outcomes.

Choices A and D are incorrect because “affects” is the incorrect word in this context. Choice C is incorrect because there is no
subject-verb agreement between the noun “importance” and the verb “highlight.”

Question 14. The best answer is B because it provides an introductory phrase that adequately modifies the sentence subject
“this phenomenon.”

Choices A and C are incorrect because they create run-on sentences. Choice D is incorrect because it creates a redundancy
with the following noun “this phenomenon.”

Question 15. The best answer is D because it accurately represents the information in the chart.

Choices A and C are incorrect because eight of the ten recorded years exceeded 2.5 percent. Choice B is incorrect because there
is no recorded year in which losses were double five years previous.

Question 16. The best answer is C because the percent of forest loss rose from about 2.5 percent in the 2007 period to about
3.5 percent in 2012.

Choice A is incorrect because the rate of 1 percent forest loss is too low. Choice B is also incorrect because the rate of tree loss
was not 3.2 percent in either five-year period. Choice D is incorrect because it overstates the growth in the tree loss percentage.

Question 17. The best answer is A because it adequately introduces the main idea of the paragraph, it is grammatically
correct, and it is in the passive voice, as will the following sentence be.

Choices B and C are incorrect because each is redundant. In B there is no need to refer to trees vanishing and “this alarming
trend” in the same sentence. In C there is no need to specify that “reasons….may explain” in the same sentence. Choice D is
incorrect because if the paragraph were to begin with the sentence”One reason that is often cited…”,the writer’s discussion of
reasons for deforestation would not be introduced smoothly and effectively.

Question 18. The best answer is A because it provides another reason to account for deforestation. The previous sentence
notes “One reason” why forests are disappearing, and this proposed sentence supplies another.

Choices B,C, and D are incorrect because the information does not introduce a new idea that will become important later in the
passage, nor does it contradict the main idea of the passage.

Question 19. The best answer is D because the diction is consistent with the article’s tone and style.

Choices A, B, and C are incorrect because the casual tone and style of “is not to be scoffed at,” “ is a pretty big deal,” and “can’t
be put on the back burner” deviate from the more formal tone of the passage.

Question 20. The best answer is C because it creates a grammatically correct relationship between an independent clause
and a dependent one.

Choices A and D are incorrect because a semicolon should be used to link two independent clauses, but in these cases the
second clause is dependent. Choice B is incorrect because it creates a comma splice.

Question 21. The best answer is C because it provides the correct possessive form of a plural pronoun, referring to the noun
“countries.”

Choice A is incorrect because it is a contraction of “they are,” while choice B is an adverb that refers to a place or a particular
point of time. Choice D is incorrect t because it is the contraction of “it is.”

Question 22. The best answer is A because the passage already has an appropriate concluding sentence that addresses the
future of efforts to combat deforestation.

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Choices B and C fail to address the futures and are therefore incorrect. Choice D fails to preserve the tone of cautious
optimism.

Passage III – Louis A. Lauder

Question 23. The best Answer C because the underlined portion provides specific information that helps clarify the nature
of the gift.

Choice A is incorrect because it does not detract from the focus on Cubism. Choice B is incorrect because it does not repeat
information from the previous sentence. Choice D is incorrect because it mentions only one specific example rather than the
ones actually included in the underlined portion.

Question 24. The best Answer A because “Because of” supports the cause-effect relationship between the two clauses in the
sentence, which state that the size of the donation caused the “challenge.”

Choices B, C, and D are incorrect because they do not support the cause-effect relationship.

Question 25. The best Answer D because it does not contain information which has already been stated in the previous
sentences.

Choices A, B, and C are incorrect because they do contain information that was already stated.

Question 23. The best Answer D because it provides a conjunction “but” that accurately reflect the relationship between the
two clauses. This relationship contrasts the ability to view the paintings with the fact that such availability does not currently
exist.

Choices A, B, and C are not correct because each provides a conjunction that does not reflect the relationship between the two
clauses.

Question 27. The best Answer C because it provides the possessive pronoun ”its” that agrees with the noun “the Met” in
number.

Choice A is incorrect because “their” is plural and therefore not in agreement with “the Met.” Choice B is incorrect because
“the Met” would normally not be referred to as “he or she.” Choice D is incorrect because it is the contracted form of “it is.”

Question 28. The best Answer B because it provides a conjunction “therefore” which captures the cause-effect relationship
between the two sentences. Since the Met had not bought Cubist works, it therefore lacked examples of such work.

Choices A, C, and D are incorrect because each fails to capture the relationship between the sentences. A is incorrect because
it suggests that the second sentence is building on information in the first. C is incorrect because it suggests a contrast
between not acquiring and not possessing Cubist works. Choice D is incorrect because it suggests that the second sentence is a
shortened version of the previous one.

Question 29. The best Answer C because it succinctly labels the items as all belonging to the category “everyday objects.”

Choices A, B, and D are all either incorrect descriptions of the items or wordier versions of the same idea and are therefore
incorrect.

Question 30. The best Answer B because “to” always patterns with “access.”

Choices A and C incorrectly use “with” and “of” as words that pattern with “access.” Choice D is incorrect because it confuses
“excess” with “access.”

Question 31. The best Answer B because it presents the appropriate time indication. He “had studied” Cezanne then
“created” a new form of space.

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Choice A is not correct because without an auxiliary or an ending that denotes time, there is no specific verb tense. Choices C
and D are incorrect because they do not indicate that the study of Cezanne pre-dated the creation of a new form.

Question 32. The best Answer A because it presents two items - the collage and the sculpture - as nonrestrictive elements of
the sentence. It does not add unnecessary punctuation.

Choices B, C, and D are all incorrect because of misplacing commas within the nonrestrictive phrase.

Question 33. The best Answer C because the proposed sentence logically follows information about how the Cubist works
were influential. The word “also” in the proposed sentence precludes the sentence from being placed earlier than after sentence
2. The term “both artists” in sentence 3 demands that the proposed sentence appear before sentence 3

Choices A and B are incorrect because “also” in the proposed sentence requires the sentence to be placed after mention of the
Braque work. Choice D is incorrect because there would be no sensible way that “both artists” in sentence 3 could refer only to
the Braque painting mentioned.

SECTION 5 | ACT READING | SOLUTIONS

Passage I – Prose Fiction

Question 1. The best answer is B because the whole story is told from the narrator’s point of view (not a dialogue) and
focuses on events as well as characters and landscapes.

Question 2. The best answer is G because the narrator refers to Mrs. MacLaren as “poor woman” in line 49, but she also
recognizes that the housekeeper is thoughtlessly cruel in referring to Felix as “the fat one.”

Question 3. The best answer is C because the narrator states in line 29 that she and Felix had “always looked forward
eagerly” to visiting their father’s old home.

Question 4. The best answer is F because the narrator states in lines 8–9 “We supposed we should get acquainted with her
when we reached there”.

Question 5. The best answer is B because the narrator says in lines 42–43 that her mother had died before either she or her
brother could remember her.

Question 6. The best answer is G because the deep well is mentioned in line 33, the King Orchard in line 31, and the willow
in line 81.

Question 7. The best answer is C because the housekeeper states in lines 56–58 “ … the only safe way to travel with those
young ones is have ‘em both tied to you with a short rope.”

Question 8. The best answer is J because the narrator’s father had described the boyhood home in such a way as to “
inspire…some of his deep-seated affection for it”.

Question 9. The best answer is B because the evidence can be seen in lines 71–73, “We felt at home with him and became
very good friends with him on that twenty-four mile drive”.

Question 10. The best answer is G because the narrator notes in line 14 that her relatives on the old homestead would be her
roommates “for a season”. Line 79 notes they were there in April.

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Passage II – Humanities
Question 11. The best answer is C because answer choices A and D are mentioned in only one paragraph each, and B is not
mentioned at all.
Question 12. The best answer is J because nowhere in the passage is it suggested that “Facebook causes people to present
the most perfect picture of themselves that they can create.”

Question 13. The best answer is B because as used in the passage, “shield” is not a physical thing as A and C suggest, and it
cannot prevent attacks, only ward them off.

Question 14. The best answer is F because the author’s high school reunion was spoiled thanks to Facebook’s making it
unnecessary for people to meet face to face.

Question 15. The best answer is D because although the other answer choices are mentioned one time each, Facebook’s
power as identity-shaper is evident throughout the passage.

Question 16. The best answer is F because line 32, “Shy people, like me, find it easier to share via email and on Facebook
than face-to-face. Facebook allows us to be ourselves” shows the author as shy.

Question 17. The best answer is C because Facebook’s ability to get individuals to share their identity with others can be
seen in the first sentence of the fifth paragraph (line 52–53), “Facebook is not only involved in creating identity; it is plays a
major role by displaying your identity to others.”

Question 18. The best answer is F because the rest of the passage makes the case that identity is created and changeable,
not something permanent. For example lines 81–85 state, “Facebook is not merely a reflection of an identity that is already
established; Facebook is taking part in the establishment of identity. From his Harvard dorm room, Mark Zuckerberg created a
phenomenon that not only changes that way we act, it is changing who we are.”

Question 19. The best answer is D because as the author states in lines 79–80 “our flaws make us who we are.”

Question 20. The best answer is G because lines 90–91 state that “there is so much information available to sociologists”
and lines 99–101 state that “a plethora of research is in the works.”

Passage III – Natural Science

Question 21. The best answer is A because in the preceding sentence the author states, “The second way a baby acquires
knowledge is through innate knowledge, that which is genetically inherited.” If the knowledge is inherited it existed before
birth. This statement is in direct opposition to Locke’s tabula rasa theory, which argues that the mind at first is a blank slate.

Question 22. The best answer is G because the text states, “… the PCC may play a direct role in regulating the focus of
attention, which can determine the ability of a person to gather and parse information. Note that focus of attention occurs first.

Question 23. The best answer is D because the first sentence of the paragraph states, “Recent scientific findings in the
United States and Europe suggest that we are not a blank slate (devoid of knowledge) at time of birth.”

Question 24. The best answer is H because if the human mind is devoid of all knowledge or ideas, it is a clean slate (not
expressionless, free, or simple).

Question 25. The best answer is B because nativism can be found on line 73; how the brain areas link to one another can be
found on lines 37–39; innativism can be found on lines 74–75.

Question 26. The best answer is J because lines 51–54 state: “A recent neuroimaging study found that the elevating
serotonin levels in the brain created more connections to the posterior cingulate cortex (PCC).”

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Question 27. The best answer is A because the first sentence of the paragraph introduces the position that while the counter
argument against Locke’s tabula rasa theory is strong, modern science has not disproved it. The paragraph concludes with the
author stating: “Science has not demonstrated that the newborn who knows to cry when he wants his mother’s attention knew
this prior to birth.”

Question 28. The best answer is H because in lines 15–16 it’s stated that “all of our concepts are derived from sense
experience.”

Question 29. The best answer is B because in lines 31–34 it’s stated: “The new research suggested that a person’s DNA
determines why some people are better at solving creative problems than others.” If that is the case we can then deduce that
some people are born with a poorer capacity for learning.

Question 30. The best answer is J because of what’s stated in the fifth paragraph, lines 35–46, and the sixth paragraph, lines
47–55.

SECTION 6 | SAT MATHEMATICS (NO CALCULATOR) | SOLUTIONS

Multiple Choice
Question 1. The correct answer is A. The coach is paid $9.25 per hour, so we must multiply $9.25 by the number of hours
and then add the bonus for winning the regional championship.

Question 2. The correct answer is C. Distribute the 5 through the left side of the equation and obtain 5x - 5y = x .
4
Subtract 5x on both sides of the equation and obtain - 5y = - 4x . Divide both sides by - 5 to obtain y = - 5 x . If we divide
y 4
both sides by x , we obtain x = 5 .
Question 3. The correct answer is D. Because the trapezoid is isosceles, +FAE = +GDE . This fact combined with the

fact that +EFA and +EGD are both right angles implies that 9AFE and 9DGE are similar.
8
Because the ratio of FE to GE is 3:8, the ratio of AE to ED is also 3:8. Therefore, ED is 11 of AD . Because AD is 44,
8
ED is 11 $ 44 = 32 .

Question 4. The correct answer is B. The denominator of the expression can be rewritten as
x+4 2x - 3 3x + 1
(2x - 3) (x + 4) + (2x - 3) (x + 4) = (2x - 3) (x + 4) . Because the numerator of the expression is 1, the end result is the
(2x - 3) (x + 4) 2x 2 + 5x + 12
reciprocal: 3x + 1 . Simplify the top to obtain 3x + 1 .

Question 5. The correct answer is D. Nathan’s fee can be expressed as 120 + 50h . Jeremy’s fee can be expressed
180 + 35h . Therefore, the values for which Jeremy’s total charge is greater than Nathan’s total charge are all those for which
the inequality 180 + 35h > 120 + 50h is true. Subtract 35h from both sides to obtain 180 > 120 + 15h . Subtract 120 from
both sides to obtain 60 > 15h . Divide both sides by 15 and we learn that 4 > h .
2
Question 6. The correct answer is C. A slope of 5 indicates that increasing P by 5 will cause an increase of t by
2
5 $ 5 = 2 . Therefore, an increase of 5 parents will result in an increase of 2 t-shirts.
Question 7. The correct answer is B. The highway descends 8 meters for each 100 meters traveled along the highway.
8
Therefore, the slope of the highway is - 100 = - .08

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SECTION 6 | SAT MATHEMATICS (NO CALCULATOR) | SOLUTIONS

If the cyclist travels 17 meters per second along the highway, then we can calculate his change in elevation per second, x , by
x
solving - .08 = 17 . Therefore, the change in elevation per second is - 1.36 meters. Therefore, after s seconds, the cyclist

has descended 1.36s meters from his initial elevation of 2943 meters, and his elevation is therefore expressed as 2943 - 1.36s .
b2
Question 8. The correct answer is C. We must distribute a to each term in the first parentheses, using the additive rule of

exponents for the second term.

Question 9. The correct answer is D. The cubic passes through the point (- 2, 5) , so plug in x = - 2 and y = 5 to obtain
5 = a (- 2) 3 + b (- 2) 2 + c (- 2) + d . Therefore, - 5 = - 8a + 4b - 2c + d .

Grid-Ins
2 4
Question 10. The correct answer is 3 . Add 9 to both sides to obtain 6 = n . Multiply both sides by n to move the
4 2
variable to the numerator, so 6n = 4 . Now divide both sides by 6 and obtain n = 6 = 3 .

Question 11. The correct answer is 8. First expand (2 + 2i) 2 to obtain 4 + 8i + 4i 2 . Because i 2 = - 1 ,
4 + 8i + 4i 2 = 4 + 8i - 4 = 8i . Now multiply by i 3 to obtain 8i 4 . Because i 4 = i 2 $ i 2 = (- 1) (- 1) = 1 , the value of 8i 4 is 8.

Question 12. The correct answer is 3. If x + 6 is a factor, then the value of the x 2 + 3kx + 6k must equal 0 when we plug
in x = - 6 . Doing so yields 36 - 18k + 6k . Therefore, 36 - 12k = 0 , so 36 = 12k and 3 = k .

SECTION 7 (CALCULATOR) | SAT MATHEMATICS | SOLUTIONS

Multiple Choice
Question 1. The correct answer is B. The greatest change in car sales was between July (60 cars sold) and August (36 cars
sold).

Question 2. The correct answer is B. The circumference of a circle is calculated using the formula C = 2rr We are asked
C
to solve for r , so divide both sides by 2r and obtain r = 2r .

Question 3. The correct answer is C. Rearrange the first equation to isolate y and obtain y = 4x - 18 . Substitute into the
second equation: x + 3 (4x - 18) = - 2 . Therefore, 13x - 54 = - 2 , so 13x = 52 and x = 4 .

Plug x = 4 into the first equation to obtain 16 - y = 18 . Therefore, - y = 2 and y = - 2 .

Question 4. The correct answer is B. The tank holds 3000 $ 1000 = 3000000 milliliters of liquid. Therefore, the tank can
3000000
fill 250 = 12000 cans.
Question 5. The correct answer is C. Over 4 hours, Sheila travels 75 $ 4 = 300 miles. At the rate of 23 miles per gallon,
300
Sheila’s car consumes 23 = 13.04 gallons throughout the trip.

Question 6. The correct answer is A. The number of flash drives sold in boxes of 4 is 346 - 38 . Therefore, the number of
346 - 38
boxes of four sold is equal to 4 .

Question 7. The correct answer is A. The slope of a line passing through (x 1, y 1) and (x 2, y 2) is calculated using the
y2 - y1 2-7 5
equation m = x 2 - x 1 . Therefore, the slope of this line is - 1/2 - (- 9/2) = - 4 .

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SECTION 7 (CALCULATOR) | SAT MATHEMATICS | SOLUTIONS

Question 8. The correct answer is D. Because y means the depth of the snow and x means the number of days after the
storm began, the point (9,0) means that the depth of the snow reaches zero inches 9 days after the storm began.

Question 9. The correct answer is D. Only choices A and D show positive associations. The correct answer is the choice
that does not appear to show a relationship that forms a line, which is D.

Question 10. The correct answer is B. There are 22 employee salaries represented in the histogram. Therefore, the median
salary must be greater than or equal to 11 salaries and less than or equal to 11 salaries. Because 5 of the salaries are less than
$48,000 and 14 of the salaries are less than $60,000, the median salary must be between $48,000 and $60,000. The only option
possible is B.
93
Question 11. The correct answer is B. Of the 220 people surveyed, 93 prefer Candidate X. Because 220 = .4227 , the
percentage of those surveyed who preferred Candidate X is closest to 42%.

Question 12. The correct answer is B. Of the 220 people surveyed, 53 both were aged 35 to 44 and supported Candidate
53 x
X. Therefore, we can estimate the total population of these individuals by solving the proportion 220 = 2200000 . Therefore,

x = 530000 .

Question 13. The correct answer is C. The percentage of survey respondents between the ages of 25 and 34 who preferred
89
Candidate Y is 129 $ 100 = 68.99% . The percentage of survey respondents between the ages of 35 and 44 who preferred
38 .6899
Candidate Y is 91 $ 100 = 41.76% . Therefore, a 25-34 year old is .4176 = 1.65 times as likely to support Candidate Y.

Question 14. The correct answer is D. By obtaining his data at a local coffee shop, the researcher failed to collect a random
sample of the population (i.e., the city) that he was attempting to draw conclusions about.

Question 15. The correct answer is D. The smallest petroleum usage for the four days whose temperature-values are 71 is
about 6.2 and the largest is about 7.5, so the range of these values is 7.5 - 6.2 = 1.3 .

Question 16. The correct answer is B. We can plug in 10 into the model for d and solve for P: P = 16 - .15 (10) , so
P = 14.5 .

Question 17. The correct answer is C. The area of a parallelogram is calculated using the formula A = bh . The problem
asks us to double b and reduce h by 50 percent. Thus, the new area is A = (2b) (0.5h) = bh .

Question 18. The correct answer is A. The function reaches a minimum at approximately (- 2, - 3) , so the minimum
value of the function (aka the smallest y-value) is - 3 .

Question 19. The correct answer is A. The volumes of the four solids can be calculated using the three formulas: the
1
volume of a cylinder is calculated using V = rr 2 h , the volume of a cone is calculated using V = 3 rr 2 h , and the volume of a
4
sphere is calculated using V = 3 rr 3 .

The volume of the cylinder in Choice A is V = r $ 6 2 (3) = 108r .

The volume of the cylinder in Choice B is V = r $ 3 2 (6) = 54r .

1
The volume of the cone in Choice C is V = 3 r $ 6 2 (6) = 72r .
4
The volume of the sphere in Choice D is V = 3 r $ 3 3 = 36r .

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SECTION 7 (CALCULATOR) | SAT MATHEMATICS | SOLUTIONS

Grid-Ins
Question 20. The correct answer is 12. Let x be the number of tables that seat 4 patrons. Because there are a total of
22 tables, there must be 22 - x tables that seat 2 people. Therefore, 2 (22 - x) + 4x = 68 . Simplify the left side and obtain
44 - 2x + 4x = 68 . Therefore, 2x = 24 and x = 12 .
3
Question 21. The correct answer is 1. The value of g (4) is 2 (4) + 4 , or 10. The value of f (10) is determined using the
table to be - 7 .

Question 22. The correct answer is 7460. Bill must pay 10%on his first $20,000 – a total of 0.10 $ $20, 000 = $2, 000.
He must pay 16%on his next $30,000, a total of 0.16 $ $30, 000 = $4, 800 . He must pay 22% on his next $3,000, a total of
0.22 $ $3, 000 = $660 . Bill’s total tax bill is therefore $2, 000 + $4, 800 + $660 = $7, 460 .

Question 23. The correct answer is 2. The train reaches a velocity of 3.6 when v (t) = 3.6 . Therefore, 3.6 = 3t - 0.6t 2 .
Set the equation equal to zero: 0.6t 2 - 3t + 3.6 = 0 . Divide both sides by 0.6 so that the coefficient on t 2 is equal to 1, and we
obtain t 2 - 5t + 6 = 0 , which factors to (t - 3) (t - 2) = 0 . Therefore, the possible answers are t = 2 and t = 3 . However, the
model is only valid for 0 # t # 2.5 , so t = 3 is extraneous.

Question 24. The correct answer is 6.25. The total distance traveled over 2.5 minutes is equal to p (2.5) . Thus,
p (2.5) = 1.5 (2.5) 2 - 0.2 (2.5) 3 = 6.25 .

SECTION 8 | ACT SCIENCE | SOLUTIONS

Passage I – Chemistry
Question 1. The best answer is B because according to Figure 1 N r , the number of nuclei remaining in a given sample, for
V-48 achieves the lowest value over the 280 days. The passage defines radioactive decay as the spontaneous breakdown of an
atomic nucleus resulting in the release of energy and matter from the nucleus so because V-48 is losing the largest amount of
nuclei over the 280 days it must have the greatest average rate of decay in comparison to Be-7

Question 2. The best answer is G because an isotope’s half-life is defined as the time required for half of the radioactive
nuclei in a substance to decay and according to Figure 1 it takes Be-7 somewhere between 40 and 80 days to reach an N r of
500, half of the starting 1,000 nuclei. Because 50 is the only answer choice between the range of 40 and 80 it is reasonable to
infer that 50 days must be the half-life of Be-7.

Question 3. The best answer is A because according to Table 1 C-8 has the lowest half-life of 2.00 # 10 -21 seconds, the
next largest half-life is that of C-15 which is 2.45 seconds, and the largest half-life, according to Figure 1, is Po-210 which is
between 120 and 160 days.

Question 4. The best answer is G because according to Table 1 the half-life of C-10 is approximately 1.99 # 10 1 seconds,
so in a time period of 20 seconds approximately one half of the starting 2,000 nuclei will decay leaving approximately 1,000
nuclei remaining. According to Table 1 the half-life of C-8 is 2.0 # 10 -21 seconds so in a time period of 20 seconds a very
large number of half-lives occur leaving a negligible number of nuclei remaining.

Question 5. The best answer is B because when the N r of 660 is charted on Figure 1 the data point lies between the N r for
Su-35 and Be-7. It is reasonable to infer that trend for Co-56 will mimic those of Po-210, Su-35, Be-7, and V-48. Because the
N r for Su-35 and Be-7 at 120 days is approximately 400 and 200 respectively the N r for Co-56 would most likely lie between
those two values.

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SECTION 8 | ACT SCIENCE | SOLUTIONS

Passage II – Chemistry
Question 6. The best answer is A because typing speed in Group A before consumption was 43.7 words per minute (wpm)
and a typing speed of 53.3 wpm after consumption. Of all of the groups, Group A demonstrated the greatest change in typing
speed over the thirty minute period, with an increase of 9.6 words per minute. The change described in the question from 41.1
wpm to 56.9 wpm is a change of 15.8 wpm, so the best answer would be to choose the group with the greatest change, which is
Group A.

Question 7. The best answer is J because Group H exhibited the smallest amount of change and was given Decaf coffee
as the beverage, which has a caffeine content of 0.000 according to Table 1. The purpose of the experiment was to study how
caffeinated beverages affected students’ typing speeds and error rates. The control would be the group that consumed the least
amount of caffeine so that changes in typing speed and error rate could be measured against that group’s results.

Question 8. The best answer is B because Iced Coffee has a measured caffeine content of 0.307 g/L, which is in between the
caffeine contents of Hot Coffee and Green Tea as seen in Table 1. In Study 1 both Hot Coffee and Green Tea are administered
to the students in Groups B and C producing typing speeds and error rates of 47.9 wpm / 3.0 epm and 46.3 wpm / 2.5 epm,
respectively. Because the caffeine content of Iced Coffee is between that of Hot Coffee and Green Tea it is reasonable to infer
that the wpm and epm of a student who consumed Iced coffee thirty minutes after consumption should be between the recorded
values of Group B and C. The only values that fit into this range are those found in answer choice B, 47.1 wpm and 2.7 epm.

Question 9. The best answer is G because according to the passage, “Caffeine begins to take effect within five minutes, and
reaches its peak effect in about 30 minutes.” This means that if Group B was tested at 15 minutes the average typing speeds
must be between 43.4wpm, the average typing speed measured before the administration of the caffeinated beverage, and
47.9wpm, the average typing speed measured 30 minutes after the administration of the caffeinated beverage.

Question 10. The best answer is A because by comparing the results of Group E after consumption in Table 3 (recorded
three hours after consumption) to the results of Group A, who also consumed Espresso, in Table 2 (recorded thirty minutes after
consumption), the greatest increase in wpm occurred after thirty minutes. Compare 48.0 wpm to 53.3 wpm. It is then correct
to assume that if the students in Group E were tested again after thirty minutes their typing speeds, on average, would be greater
than those measured three hours after consuming the caffeinated beverage.

Question 11. The best answer is J because wpm values are, for the most part, directly proportional to epm values in both
Tables 2 and 3 before and after consumption. If charted on an (x-y) coordinate plane, the slope of the line of best fit would be
positive.

Passage III – Physics

Question 12. The best answer is H because from i = 15 to i = 30 (Combinations 5–8) on Table 1 X increases from 0.60
to 0.90. From i = 30 to i = 40 (Combinations 8–10) on Table 1 X decreases from 0.90 to 0.77, hence as i increases, X
increases and then decreases.

Question 13. The best answer is A because the graph represented in answer choice A has the correct X values for H values
1.0, 1.5, 2.0, and 2.5 as written for Combinations 1–4. Choice B is incorrect because at H = 1.5 X ! 0.90 . Choice C is
incorrect because the relationship described in Table 1 for Combinations 1–4 is directly proportional. Choice D is incorrect
because at H = 1.0 X ! 0.60 .

Question 14. The best answer is J because Table 1 outlines in Combinations 1–4 that the values of H and X are directly
proportional. Table 1 outlines in Combinations 5–10 that the largest value of X occurs when i = 30 . Lastly, Table 1 outlines
in Combinations 11–14 that F is directly proportional to X. So it is reasonable to infer that the best answer will have the largest
H and F values with a i value of 30.

Question 15. The best answer is C because the force, F, is being manipulated by the experimenter and would be described
as the input or cause of the experiment. The horizontal distance, X, from the bottom of the inclined plane to where the marble
ultimately lands is what is being measured and would be described as the output or the effect of the experiment.

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SECTION 8 | ACT SCIENCE | SOLUTIONS

Question 16. The best answer is H because potential energy depends on an object or body’s position in space so before
the ball starts rolling down the inclined plane it has potential energy stored. That energy is then converted into kinetic energy,
which is the energy the ball possesses due to its motion of rolling down the inclined plane. Lastly, due to friction, the marble’s
kinetic energy is converted into thermal energy, or heat.

Passage IV – Astronomy
Question 17. The best answer is A because the introduction states, “The Moon’s apogee (the maximum distance between
the center of the Earth and the center of the Moon) is approximately 405,400 kilometers and its perigee (the minimum distance
between the center of the Earth and the center of the Moon) is approximately 362,600 kilometers.” This means that distance
from Earth to the Moon at some point during the day should be between these two values.

Question 18. The best answer is F because all of the hypotheses rely on the gravitational forces of earth to explain how the
Moon came into existence. Hypothesis 1 states, “The Earth’s gravitational field, being much stronger than that of the Moon’s
due to its size, captured the Moon.” Hypothesis 2 states, “The Moon was created from excess material that was spun out from
the Earth as it rotated during its early years of development. It gathered in a cloud of debris that orbited around the Earth and
slowly melded together.” Lastly, Hypothesis 3 states, “The impact was so massive that it sent a significant amount of Earth’s
surface hurtling into space. However, the materials could not escape Earth’s gravitational forces and were trapped in orbit.”
Hence, none of the Hypotheses are weakened by the given information.

Question 19. The best answer is A because Hypothesis 2 states, “Earth’s crust is made up of approximately 47% oxygen,
28% silicon, 8.1% aluminum, 5% iron, 3.6% calcium, 2.1% magnesium, and 6.2% other materials. The Moon was created from
excess material that was spun out from the Earth as it rotated during its early years of development.” Supporters of Hypothesis
2 would then agree that the Moon should have a similar chemical composition. Answer Choice A is the most similar.
Question 20. The best answer is H because Hypothesis 2 states, “It (excess material) gathered in a cloud of debris that
orbited around the Earth and slowly melded together.” The words ‘melded together’ point toward fusion which is the process
of combining two or more distinct entities into a new whole. Hypothesis 3 states, “These objects remained hot after impact
and continued to crash into each other and bonded together as they orbited Earth.” The words ‘bonded together’ point toward
fusion as well.

Question 21. The best answer is C because the question defines a captured asteroid as “an asteroid that passed close
enough to Mars that it was unable to escape its gravitational pull”, and if the claim in answer choice C that “The Moon is
1 1
approximately 80 times the mass of the Earth, where as Phobos is approximately times the mass of Mars” was correct
10 8
it would undermine the claim that the Moon is a captured asteroid because Phobos is considerably smaller than the Moon in
relation to it’s planet so it is reasonable to infer that the gravitational pull of Earth may not be able to capture an object as large
as the Moon. Answer choices A, B, and D would not have any effect or influence on how the gravitational forces of two objects
would interact with one another.

Question 22. The best answer is F because Hypothesis 1 states, “The Moon was created independently of the Earth during
the early stages of our Solar System.” and the Introduction states, “During the Hadean Eon (the time period that began with the
formation of the Earth approximately 4.5 billion years ago), Earth’s only satellite, the Moon, was formed.” It is reasonable to
infer that the Moon must have been created by material present during the Hadean Eon.

Question 23. The best answer is D because Hypothesis 1 states, “The two objects had their own distinct orbits around the
sun. Over time, the two orbits moved closer together. Eventually, the two objects were close enough to be influenced by the
forces of gravity”, which means that the effect of the Sun’s gravity must have originally been stronger than that of Earth, but
then weaker because Earth was able to capture the moon from the gravitational force of the Sun once it orbited close enough.

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SECTION 8 | ACT SCIENCE | SOLUTIONS

Passage V – Biology
Question 24. The best answer is G because according to Figure 1 the average bodyweight of rats that had access to
sucrose-water after five months is approximately 205% of the baseline weight and after six months is approximately 213%
of the baseline weight. It is also true that the average bodyweight of the rats in this group increased each month and that the
magnitude of change between each month decreased as time progressed. Therefore, it is reasonable to infer that the seventh
month should be between 213% and 237%.

Question 25. The best answer is D because according to Table 1 the rats in Group A consumed 84 calories per day in
comparison to Group B, which consumed 86 calories per day. This evidence does not support the hypothesis that rats with
access to HFCS-water for two months would consume more calories than rats without access to HFCS-water.

Question 26. The best answer is H because according to the Introduction, “…HFCS is produced by milling corn and then
adding enzymes until 42% of the mixture, by weight, consists of fructose.” Because the researchers measured the amount of
HFCS consumed by the rats over the two experiments to be 1000g, 42% of that must be fructose.

Question 27. The best answer is A because according to Figure 1, from month zero to one rats who had access to water with
no sweetener increased their weight by approximately 35%, rats who had access to Sucrose-water increased their weight by
approximately 40%, and rats who had access to HFCS-water increased their weight by approximately 50%. There is no other
one-month-periods where the gains are as high as these.

Question 28. The best answer is F because according to Experiment 1 the rats being tested in the experiment started with an
approximate average body weight of 300g. The rats who had access to HFCS-water reached 600g in weight when, according to
Figure 1, the rats reach a Body Weight 200% of its baseline weight of 300g. This occurs 3 months after the diet began.

Question 29. The best answer is C because in Table 1 triglyceride levels of rats who had access to HFCS-water were
201mg/dL compared to 147mg/dL in rats who did not have access to HFCS-water. This shows a concrete rise in triglyceride
levels. Answer choice A is incorrect because only male rats were used in the experiments. Answer choice B is incorrect
because nowhere in the passage is pancreatitis mentioned. Choice D is incorrect because the passage only depicts HFCS with
42% fructose so there is nothing to compare it with.

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 3 Comparing The
SAT & ACT

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 COMPARISON SHEET

Comparing The ACT & Redesigned SAT

The ACT requires students to do more work in a shorter period of time than does the SAT.
The SAT is based more on reasoning than content. The ACT is based more on content than reasoning.

The Basics of The ACT The Basics of The SAT

• More of a content-based exam
• Favors faster students as there is more work to do in less • More of a reasoning-based exam
time • Favors students who are better in mathematics as it
• Favors students who are better at math and science comprises one-half of the score
because those subjects comprise half of the score
• Favors students who are better at reasoning and deduction
• Favors students who are good at synthesizing a lot of
information in a short time as there is more reading on the • No penalty for incorrect responses
ACT than the SAT

ACT Reading SAT Critical Reading

40 questions in 35 minutes 53 questions in 65 minutes
• Single Passages • Single Passages
• Occasional Dual Passages • Dual Passages
• Does not include graphs, figures, and diagrams • Includes graphs, figures, and diagrams

ACT English (grammar) SAT Writing & Language (grammar)

75 questions in 45 minutes 44 questions in 35 minutes
• Edit and answer questions for 5 different essays
• Edit and answer questions for five different essays
• Will emphasize student command of evidence, both verbal
• No graphs or charts included
and graphical.

ACT Mathematics SAT Mathematics

38 problems to solve in 55 minutes (Calculator Section)
60 problems to solve in 60 minutes
20 problems to solve in 25 minutes (No Calculator Section)
• Can always use a calculator • Has a no calculator section
• Provides no reference formulas • Provides some geometric formulas for reference
• Includes questions about equation of a circle & ellipse • Does not include formula of a circle or ellipse
• Includes logarithms • Does not include logarithms
• Includes imaginary numbers • Does not include imaginary numbers

ACT Essay SAT Essay

1 essay topic in 30 minutes 1 essay topic in 50 minutes
• The Essay section is optional • The Essay section is optional
• Is not part of composite score • Optional and given at the end.
• If taken, schools see essay score listed separately • Students produce a written analysis of a provided source
• Scored by two graders, max score is 12 text.

ACT Science
40 questions in 35 minutes
• Includes a science section

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 TIP SHEET

Tips for the SAT Reading and Writing/Language Sections

1. It’s an open book test: The SAT Critical Reading exam is an open book test. You can always put your finger on the
correct answers. It’s never what you think the text is saying, it’s what the text is saying.

2. Dual passages: Do only the questions pertaining to the first passage, skipping comparisons. Then do only questions
pertaining to the second passage, skipping comparisons. Once you’ve completed both passages then do the comparison
questions.

3. Writing/Language: Read the first paragraph in its entirety, looking for grammar mistakes and to fully understand what
the author is trying to convey, because you will be asked both content and content and grammar questions. After you
complete the paragraph go back and answer the questions. After you answer each question, plug it back into the text and
read it to make sure it’s the best answer choice.

4. Prepare while doing your homework: Each night when you do your homework, spend 25 minutes reading the
homework you’re least interested in as if it were SAT text. It boils down to understanding what you’re reading and that
takes focus. It also helped to remember that the SAT is not as easy as the exams in school and that you have to gear up
for the test.

Tips for the ACT Reading and English Sections

1. Test the three Reading approaches: You are likely to find one that works for you.

• Start with line reference questions then go into the text to find the answers

• Read entire passage then answer the questions

• Preview questions then read the text and answer the questions

2. Practice your timing: The reading portion of the ACT is a speed exam. You have 8 minutes and 45 seconds to read each
passage and answer 10 questions.

3. English: Read the first paragraph in its entirety, looking for grammar mistakes and to fully understand what the author
is trying to convey, because you will be asked both content and content and grammar questions. After you complete
the paragraph go back and answer the questions. After you answer each question, plug it back into the text and read it to
make sure it’s the best answer choice.

4. Prepare while doing your homework: Each night when you do your homework, spend 25 minutes reading the
homework you’re least interested in as if it were ACT text. It boils down to understanding what you’re reading and that
takes focus. It also helped to remember that the ACT is not as easy as the exams in school and that you have to gear up
for the test.

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Helpful Tips for the SAT Math Section

1. Know what you’re solving for: Be sure to underline the question and glance at the answer choices. Always keep in
mind what the question is asking for.

2. You’ve done this before: While some are in a different format, these are still the same concepts as you learned in class.

3. The answers are all on the page: As a last resort, you can plug-in answer choices until one satisfies the conditions of
the problem.

4. No Calculator: From this point forward start to do your homework without a calculator when possible. Any practice
without a calculator will be beneficial come test day.

Helpful Tips for the ACT Math Section

1. It’s a speed test: There are more problems and less time to do them then on the SAT. Work quickly, but do not rush.
Going too fast can lead to careless errors. There is no partial credit! Make sure you use all of the time you are allotted.

2. Don’t be intimidated: Problems that contain a large amount of text are generally simpler than they appear, and are
designed to look intimidating. Read and interpret each sentence before proceeding to the next one, and then piece the
puzzle together when you get to the end.

3. Tips #3 on the SAT also apply here: Use the answer choices to your advantage - all of the answers are already on the
page.

4. Questions 1 through 30 are generally easier, and questions 31 through 60 are generally harder: All questions
are worth the same amount. Because of the time constraints, be aware of where you are in the exam and strategize
accordingly.

Helpful Tips for the ACT Science Section

1. It’s an open book: The ACT Science exam, like the reading exam, is an open book test. You can always put your finger
on the correct answer.

2. Figures, Tables, Charts: The science test on the ACT is not testing how well you remember biology, chemistry, natural
science, or physics. It’s testing how well you can read graphs, read tables, predict trends, and extract information
efficiently. Spend less time reading for understanding and more time attacking the data directly.

3. The test will let you know where to look: If a problem begins In Experiment 1, that should tell you where to look!
Keywords and units can also give you hints when it is still unclear.

4. Identify the one passage worth reading: There is one passage that will have seven questions and very few figures and
tables. That is the only passage you need to read for information. Treat this just like an ACT Reading passage, and note
that it will probably take you an extra two minutes than the other passages. Budget your time accordingly!

5. There’s no substitute for (timed) practice: Given three hours to complete the exam, any student could score in the
30s. The trick is to learn how the exam asks questions and recognize its patterns so you can do it in the time allotted.
Practice, timing upward, and analyze why you spent a long time on passages where you went over the allotted time.

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 TIP SHEET

60 Facts, Formulas, and Concepts that ALL Students Must Know

Arithmetic Concepts
1. Integers are all whole numbers- positive, negative, and zero. Decimals, fractions, and imaginaries are not integers.

2. Real Numbers can be thought of as points on an infinitely long line called, you guessed it, the number line. The real
numbers include:
a
• All the rational numbers which are numbers that can be expressed as the ratio of any two integers b and include:

• All the integers, which are all whole numbers, both positive and negative.

• All the wholes, which are non-negative integers including 0.

• All the natural numbers. Do not worry about naturals. These are positive integers used for counting, ordering,
and naming only. This will not come up on the test. They DO NOT include 0. Irrational numbers, are numbers
a
that CANNOT be expressed as the ratio of any two integers b and include numbers such as r and 2

3. Prime Numbers are numbers that have exactly two factors. The number 1 only has one factor, so it is not prime. The
smallest primes are 2, 3, 5, 7, 11, 13, 17, and 19. The only even prime is 2.
4. Perfect Squares are the product of some integer and itself. For example, 25 is a perfect square, since it can be written as
5 # 5 . Perfect squares include: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169...

5. Perfect Cubes are numbers that are the result of the number multiplied by itself twice: For example, 27 is a perfect cube
because it can be written as 3 # 3 # 3 . Perfect cubes include: 1, 8, 27, 64, 125, 216...

6. Consecutive Numbers are numbers that come one after the next in a sequence, like 3, 4, 5... etc. Can be written as x ,
x + 1 , x + 2 ... etc.

• Consecutive Odd (3, 5, 7...) and Consecutive Even (4, 6, 8...) can both be written as x, x + 2 , x + 4 ... etc.

7. Evens and Odds: Remember: Even + Even = Even, Even + Odd = Odd, Odd + Odd = Even. Even $ Even = Even,
Even $ Odd = Even, Odd $ Odd = Odd. If you forget the rules, test an example.

8. Remainders:
26
• The remainder is the whole number left over after division. For example, 10 is equal to 2 with a remainder of 6.
6
Note that if you express the result as a mixed, unreduced fraction, (in this example, 2 10 ,) the numerator is always

equal to the remainder.

a b a+b
• Remainders are additive: if 7 has remainder 3 and 7 has remainder 2, then 7 has remainder 5.

a b a+b
• Remainders cannot be larger than the divisor. If 4 has remainder 3 and 4 has remainder 2, then 4 has

remainder 1, because there are 5 leftover, but 4 of the leftover form another “group”.

9. Rules of Fractions.

• The number on top is the numerator and on bottom is the denominator

6 3
• Fractions can be reduced by dividing both the top and the bottom by the same number. For example, 8 = 4 . You

can also multiply the top and bottom by the same number.

• To multiply fractions, just multiply the numerators and denominators straight across. For example,
2 5 2$5 10
3 $ 7 = 3 $ 7 = 21 .
2 5 2 7 2$7 14
• To divide fractions, flip the divisor and multiply. For example, 3 ' 7 = 3 $ 5 = 3 $ 5 = 15 .

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The Redesigned SAT/ACT Diagnostic
1 1 3 2 5
• To add or subtract fractions, you need a common denominator. 2 + 3 = 6 + 6 = 6 .

• Fractions that are less than one behave just the opposite of integers when exponents or roots are applied. The square of
1 1 1 1 1
is 16 , less than 4 . The square root of 4 is 2 , more than 4 .

10. Ratios, Fractions, Percentages: Identify the Whole. The key to solving most story problems involving ratios,
fractions, and percents is to identify the whole. Very frequently, the “whole” comes immediately after the word “of” - for
example, “one-half of the students are boys” indicates that the whole group in this problem are the students.
13 k
11. Percentages. Percent means “out of 100”. You can write 13% as .13 or 100 . You can write k percent as 100 or
.01k . The word “of” ALWAYS means multiplication.
12. Percent Change. When dealing with percent change, you are going to have a new value and an original value. Here is
New Value - Original Value
the formula used to calculate the change: Percent Change = Original Value
13. Mean, Median, Mode & Range:
• Mean: Add the numbers up and divide by the amount. Same as Average.
• Median: List lowest to highest, pick the one in the middle. If there are two, add those and divide by 2.

• Mode: The one that occurs most often.

• Range: The difference between the highest and the lowest values in a set.

14. Probability. The probability of an event happening at random if each possible event is equally likely is:
Number of Possible Successes
Probability = Number of Possibilities
15. Counting Possibilities. If event 1 can happen a ways and event 2 can happen b ways, the two events can happen ab
ways. Remember that they are sometimes dependent- if you are filling four actors for four roles, event a (filling the first
role) can happen four ways and event b (filling the second) can happen three since one of the actors is now ineligible.

16. Sequences. Look for sequences that repeat and group terms. When faced with arithmetic sequences (where the
difference between consecutive terms is always the same), label that difference x, and rewrite all of the other values in
terms of x. For example, if the first term is 11, the second term must be 11 + x , the third term must be 11 + 2x … etc.

17. Arithmetic Sequence can be defined as a sequence of numbers where the difference between consecutive terms is
constant. For example, the sequence 6, 10, 14, 18, 22 … is an arithmetic sequence with a common difference of 4.

18. Finding a specific term in an Arithmetic Sequence: the formula you will need to remember is a 1 + (n - 1) d = the
term you are looking for, where a 1 equals the first term, n equals the term you are looking for, and d equals the
common difference.
n
19. Summing an Arithmetic Sequence: ^a first + a last h` 2 j where a first equals the relative first term in the sequence, a last
equals the relative last term in the sequence, and n equals the total number of terms in the sequence.

20. Geometric Sequence can be defined as a sequence of numbers where each term after the first is found by multiplying
the previous one by a non-zero constant called the common ratio. For example, the sequence 4, 12, 36, 108, … is a
1
geometric progression with common ratio 3. Similarly 20, 10, 5, 2.5, … is a geometric sequence with common ratio 2 .

Algebra I Concepts
21. PEMDAS. Parentheses, Exponents, Multiplication, Division, Addition, Subtraction, always left to right. Absolute value
bars function like parentheses. Wrong answer choices very frequently involve PEMDAS mistakes, so always be aware.

22. Inequalities: Flip the inequality signs when multiplying or dividing the entire inequality by - 1 . Combine inequalities
by testing all four pairs of endpoints.

23. Nonlinear Inequalities: Solve the inequality as an equation and plot the answers on a number line. Test one point from
each segment to determine which portions of the number line are parts of your solution set.

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24. Systems of Equations. Two ways to solve multiple equations and multiple variables: substitute, or stack and add/
subtract. Substitute when you have an equation with an isolated variable and stack when you have coefficients that
match in each equation.

• Infinite Solutions occur when the two lines, represented graphically are identical. This means the lines have the same
slope and same y-intercept.

• No Solutions occur when the two lines, represented graphically, are parallel (see tip #45). This means the lines have
the same slope but different y-intercept.

25. Rules of Exponents. You must ALWAYS have the same base before working with exponents.
xa 1
• xa $ xb = xa + b • b = xa - b • (x a) b = x ab • x -n = n
x x
1 m
• x2 = x • xn = n m • (xy) n = x n y n

26. Square Root Simplification & Rules of Roots:

n n 2
• 32 = 16 $ 2 = 4 2 • a b = ab • a+ b ! a+b • = 2
2
27. Made-Up Functions. When dealing with made-up functions, identify the guide given in the problem and simply
plug-in. For example, if told that xVy = xy + y 2 , then 3V5 = 5 (3) + 5 2 = 15 + 25 = 40 .

Plane Geometry Concepts

28. Complementary Angles are angles that sum to 90 degrees.

29. Supplementary Angles are angles that sum to 180 degrees.

30. Vertical Angles occur when two lines intersect each other creating two pairs of congruent angles. For example, x = x ,
y = y , and x + y = 180 .
y°
x° x°
y°

31. Degrees Around a Single Point will always sum to 360 degrees. For example, a + b + c + d + e + f = 360

b°
c°
a° d°
f° e°

32. Parallel lines. When parallel lines are crossed by anther line, you get two types of angles. All angles labeled a° are the
same and all labeled b° are the same, and a + b = 180 . When you see parallel lines on the test, ALWAYS extend them.

a°
b°
b°
a°

a°
b°
b°
a°

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33. Angles of a Triangle will always sum to 180 degrees. The exterior angle of a triangle will always be equal to the sum of
the two opposite interior angles.

E C B

• A + B + C = 180 • E + C = 180 • E = A+B

34. Isosceles Triangles are triangles that have two sides of equal length and the two angles opposite the equal sides are equal
as well.

a° a°

35. Equilateral Triangle is a triangle in which all three sides are equal and all angles are equal to 60 degrees.

60°

60° 60°

36. Any angle inscribed in a semi-circle is a right angle.

B

A C

37. Area, Circumference/Perimeter, Volume Formulas are given to you on the SAT, but not on the ACT. Here are the
ones that will (generally) be tested without being provided to you in the problem:

• Area of a Circle: A = rr 2
x
• Area of a Sector of a Circle with central angle measuring xc : A = 360 rr 2

• Area of a Rectangle: A = lw
1
• Area of a Triangle: A = 2 bh

• Area of a Parallelogram: A = bh
1
• Area of a Trapezoid: A = 2 (b 1 + b 2) h

• Surface Area of a Box: A = 2lw + 2hl + 2hw

• Surface Area of a Cube: A = 6s 2

• Circumference of a Circle: C = 2rr

x
• Arc Length of a sector of a circle with central angle measuring xc : arc length = 360 2rr

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• Perimeter of a Rectangle: P = 2 (l + w)

• Volume of a Box: V = lwh

• Volume of a Cube: V = s 3

• Volume of a Right Circular Cylinder: V = rr 2 h

4
• Volume of a Sphere: V = 3 rr 3
1
• Volume of a Cone: V = 3 rr 2 h
1
• Volume of a Pyramid: V = 3 lwh

38. Pythagorean Theorem states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
It can be written as a 2 + b 2 = c 2 where c is the hypotenuse.

• Pythagorean Triples and Multiples: 3-4-5, 6-8-10, 9-12-15, 12-16-20. 5-12-13, 10-24-26, 7-24-25.

39. Special Right Triangles. Students should be familiar with the side lengths of 45-45-90 and 30-60-90 right triangles as
displayed below. A tip off to when these concepts are being tested are if students see 2 or 3 in your answer choices.

2x 60º
x 45º x 2
x
30º
45º
x 3 x

40. Triangle Side Lengths. The lengths of any two sides of a triangle must sum to greater than the length of the third side.

Coordinate Geometry Concepts

41. Midpoint Formula. If you want to find the midpoint (x m, y m) where the endpoints are (x 1, y 1) and (x 2, y 2) , then
x +x y1 + y2
x m = 1 2 2 , and y m = 2 .
42. Distance Formula. To calculate the distance between (x 1, y 1) and (x 2, y 2) , use the distance formula:
d = (x 1 - x 2) 2 + (y 1 - y 2) 2 . Note that you can often also draw a right triangle and use the Pythagorean Theorem.

43. Vectors represent physical quantities that have both magnitude and direction. Let u = u 1, u 2 and v = v 1, v 2 .
The sum of u and v is the vector u + v = u 1 + v 1, u 2 + v 2 and the difference of u and v is the vector
u - v = u 1 - v 1, u 2 - v 2 .
44. Norm (or Magnitude). The norm or magnitude of a vector is the distance from zero. The norm can be calculated using
u, v = ^u 2 + v 2h , for example, the norm of - 3, - 4 = (- 3) 2 + (- 4) 2 = 9 + 16 = 25 = 5 .

45. Slope and Slope-Intercept Form.

• When you are given a linear function or graph, often the test will refer to slope-intercept form. Slope-intercept form
is when the equation of a line is expressed as y = mx + b , where m is the slope and b is the y-intercept (the value at
which the line crosses the y-axis). You can then plug in coordinate pairs (x, y) .
y2 - y1 Ty Rise
• You can calculate the slope by the formula m = x 2 - x 1 = Tx = Run

• Finally, it is important to know that two parallel lines have the same slope and never intersect, while two
perpendicular lines have slopes that are the negative reciprocals of one another.

46. Functions. When we see function notation such as f (x) = 2x + 7 , we are simply giving the function a name (f) so that
we can refer to it, and indicating that the output of the function is dependent on the variable x.

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The Redesigned SAT/ACT Diagnostic

• When we’re told that f (x) = y , that simply means that (x,y) lies on the graph of f (x) . When we’re asked for f (3) ,
plug in (3) for x to the initial equation and simplify. DON’T forget to substitute the parentheses.

47. General Form of a Parabola + Shifts. The general form of a parabola is y = a (x - h) 2 + k , where (h, k) is the vertex
of the parabola. If a > 0 , the vertex is the lowest point on the parabola it opens upward. If a < 0 , the vertex is the
highest point on the parabola and it opens downward.

• When k is positive you must shift the graph up that many units. If k is negative (subtraction), shift down.

• When h is positive the parabola must shift right that many units. If h is negative (addition inside the parentheses), the
parabola shifts left.

• When a is greater than one the parabola becomes skinnier. If a is a number between zero and one, it becomes wider.

• Finally, remember that if a is negative, the graph is flipped upside down.

• These shifts also apply generally to absolute value functions, for example, f (x) = a x - h + k .

48. General Form of a Circle: The general form of a circle is (x - h) 2 + (y - k) 2 = r 2 , where (h, k) is the center of the
circle, and r is the radius of the circle.
(x - h) 2 (y - k) 2
49. General Form of an Ellipse: The general form of an ellipse is + = 1 , where (h, k) is the center of
a2 b2
the ellipse and a and b are the semi-major and semi-minor axes, you can think of these values as the radii of the x- and
y-axes respectively.

Algebra II Concepts
50. Absolute Value: When x is set equal to something else, remove the absolute value sign and set the other side equal to
its current value OR the current value’s additive inverse.

• Example 1: x = 4 & x = - 4, 4

• Example 2: - x = 8 & x = - 8, 8

This applies basically the same way if something besides x is inside the absolute value. You’ll just have to do a step
or two afterwards.

• Example 3: 4x - 2 = 6 & 4x - 2 = 6 OR 4x - 2 = - 6 & x = - 1, 2 .

However, if you have stuff OUTSIDE the absolute value sign on the same side, you need to isolate the absolute value
before proceeding.

• Example. 4: 2 x + 2 + 1 = 9 & 2 x + 2 = 8 & x + 2 = 4 & x + 2 = 4 OR x + 2 = - 4 & x = - 6, 2 .

51. Absolute Value Inequalities: You can identify a conjunction by a less than ^<h sign: conjunctions are AND statements.

• Example 5: 2 x + 3 # 10 & x + 3 # 5 & - 5 # x + 3 # 5 & - 8 # x # 2

You can identify a disjunction by a greater sign ^>h : disjunctions are OR statements.

• Example 6: 2 x + 3 $ 10 & x + 3 $ 5 & x + 3 $ 5 OR x + 3 # - 5 & x $ 2 OR x #- 8

52. Direct and Inverse Proportions. Remember, if x is directly proportional to y, then y = kx where k is a constant. If
k
y is INVERSELY proportionate to x, then y = x where k is a constant. Sometimes you’ll run into y is directly or
k
inversely proportional to x 2 . Then y = kx 2 or y = 2 .
x
53. Factoring, FOIL and the Quadratic Identities:
• (x + y) 2 = x 2 + 2xy + y 2 • (x - y) 2 = x 2 - 2xy + y 2 • (x + y) (x - y) = x 2 - y 2

108 The SAT/ACT Diagnostic

 TIP SHEET

54. Quadratics and Factoring when a ! 1. To factor a quadratic in the form ax 2 + bx + c = 0 , find two numbers whose
product is ac and sum is b , and use that to fill in the gaps. For example:

• 2x 2 - 17x + 30 & What’re two numbers that multiply to 60 and add to - 17 ? (Answer: - 5 and - 12 ) &
2x 2 - 12x - 5x + 30 & 2x (x - 6) - 5 (x - 6) & so the factors are (2x - 5) (x - 6) .
55. Quadratics and the Discriminant. The discriminant of a quadratic in the form ax 2 + bx + c = 0 is defined as b 2 - 4ac .

• If the discriminant is positive, the quadratic has two distinct roots.

• If the discriminant is negative, the quadratic has two imaginary roots.

• If the discriminant is zero, the quadratic has one double real root.

56. Quadratic Formula, Sum/Product of Roots. The roots of a quadratic of the form ax 2 + bx + c = 0 are
- b ! b 2 - 4ac
2a .
b
• The sum of roots of this quadratic is - a .
c
• The product of roots of this quadratic is a .

57. Imaginary Numbers: When you see i, it means - 1 . Don’t be intimidated! Treat it like any other variable, but
always remember:

• i2 = - 1 $ - 1 = - 1 • i3 = i2 $ i = - 1 $ i = - i • i4 = i2 $ i2 = - 1 $ - 1 = 1 • ...and so on.

58. Logarithms: Remember the three rules of logs and you will be good to go:
b
• log a b + log a c = log a bc log a b - log a c = log a c log a b n = n log a b

59. Matrices:

• When adding matrices, add each respective term (ie, adding the second row and third column of matrix A with the
second and third column of matrix B will give the second row and third column of AB. For example:

1 3 2 0 1 1 1+0 3+1 2+1 1 4 3

• ; E+; E=; E=; E
3 0 4 6 9 2 3+6 0+9 4+2 9 9 6

• When multiplying matrices, multiply the elements of each row of the first matrix by the elements of each column
in the second matrix, and then add the products (ie, multiplying each term in the second row of matrix A with its
respective term in the third column of matrix B and then adding these values will give the second row and third
column of matrix AB).

1 3 2 2#1 2#3 2#2 2 6 4

• Scalar Multiplication: 2 ; E=; E=; E
3 0 4 2#3 2#0 2#4 6 0 8
0 1
1 2 5 (1 $ 0) + (2 $ 5) + (5 $ 8) (1 $ 1) + (2 $ 6) + (5 $ 2) 50 23
• Matrix # Matrix (‘Dot Product’): ; E # >5 6H = < F=; E
3 0 4 (3 $ 0) + (0 $ 5) + (4 $ 8) (3 $ 1) + (0 $ 6) + (4 $ 2) 32 11
8 2
a b
• Determinant of a 2 # 2 Matrix: = ad - bc
c d

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60. Trigonometry:
Opp Adj Opp
• You should remember SOH CAH TOA: Sine = Hyp , Cosine = Hyp , Tangent = Adj .

1 1 1
• You should also know that Sine = cosecant , Cosine = secant , Tangent = cotangent .

• You should be familiar with the mnemonic “All Students Take Calculus” that tells you where each of the three major
trigonometric functions is positive - All in the 1st quadrant,Sine in the 2nd, Tangent in the 3rd, and Cosine in the 4th

• Finally, you should be relatively familiar with the unit circle below. If you draw a right triangle such that one side is
along the x-axis and the hypotenuse forms the angle whose trig value you are looking to calculate, the x value of the
point on the circle (in the figure below, A) will be the value of Cosine and the y-value will be the value of sine.

^ 0, 1h
c- 3 , 1 m r 90c c 1, 3 m
2 2 2 2 2
2r r
3
c- 2 , 2 m 3
c 2, 2 m
2 2 3r r 2 2
4 4
120c 60c
c- 1 , 3 m 5r 135c 45c
r
6 c 3,1m
2 2 6 2 2
150c 30c

^ - 1, 0h 180c 0c 0 x
r 360c 2r
^1, 0 h

210c
7r 330c
6 225c
11r c 3,- 1m
c- 3 , - 1 m 5r 240c 315c 6 2 2
2 2 4 300c 7r
4r 4 c 2,- 2 m
c- 2 , - 2 m 3 5r
2 2
2 2 3r 3
270c 2 c 1, - 3 m
c- 1 , - 3 m 2 2
2 2 ^ 0, - 1h

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 15 Returning Your
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Bubblesheets

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The DSHAPES 2024 BUBBLESHEETS

Marking Directions:
Use only a #2 pencil.
Read and follow directions on exam page.
Select on answer for each question.
Fill in the answer circles completely.
Be sure to erase marks completely to change your answer.
Write only inside the specified boxes.

A First Name Last Name

⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝ ⃝
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Section 1 | English - Bubble in your responses to the multiple choice questions

1 ⒶⒷⒸⒹ 10 ⒻⒼⒽⒿ 19 ⒶⒷⒸⒹ 28 ⒻⒼⒽⒿ 37 ⒶⒷⒸⒹ
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4 ⒻⒼⒽⒿ 13 ⒶⒷⒸⒹ 22 ⒻⒼⒽⒿ 31 ⒶⒷⒸⒹ 40 ⒻⒼⒽⒿ
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6 ⒻⒼⒽⒿ 15 ⒶⒷⒸⒹ 24 ⒻⒼⒽⒿ 33 ⒶⒷⒸⒹ 42 ⒻⒼⒽⒿ
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8 ⒻⒼⒽⒿ 17 ⒶⒷⒸⒹ 26 ⒻⒼⒽⒿ 35 ⒶⒷⒸⒹ 44 ⒻⒼⒽⒿ
9 ⒶⒷⒸⒹ 18 ⒻⒼⒽⒿ 27 ⒶⒷⒸⒹ 36 ⒻⒼⒽⒿ 45 ⒶⒷⒸⒹ

Section 2 | Reading - Bubble in your responses to the multiple choice questions

1 ⒶⒷⒸⒹ 8 ⒶⒷⒸⒹ 15 ⒶⒷⒸⒹ 22 ⒶⒷⒸⒹ 29 ⒶⒷⒸⒹ
2 ⒶⒷⒸⒹ 9 ⒶⒷⒸⒹ 16 ⒶⒷⒸⒹ 23 ⒶⒷⒸⒹ 30 ⒶⒷⒸⒹ
3 ⒶⒷⒸⒹ 10 ⒶⒷⒸⒹ 17 ⒶⒷⒸⒹ 24 ⒶⒷⒸⒹ 31 ⒶⒷⒸⒹ
4 ⒶⒷⒸⒹ 11 ⒶⒷⒸⒹ 18 ⒶⒷⒸⒹ 25 ⒶⒷⒸⒹ 32 ⒶⒷⒸⒹ
5 ⒶⒷⒸⒹ 12 ⒶⒷⒸⒹ 19 ⒶⒷⒸⒹ 26 ⒶⒷⒸⒹ 33 ⒶⒷⒸⒹ
6 ⒶⒷⒸⒹ 13 ⒶⒷⒸⒹ 20 ⒶⒷⒸⒹ 27 ⒶⒷⒸⒹ
7 ⒶⒷⒸⒹ 14 ⒶⒷⒸⒹ 21 ⒶⒷⒸⒹ 28 ⒶⒷⒸⒹ

Section 3 | Math - Bubble in your responses to the multiple choice questions

1 ⒶⒷⒸⒹⒺ 9 ⒶⒷⒸⒹⒺ 17 ⒶⒷⒸⒹⒺ 25 ⒶⒷⒸⒹⒺ 33 ⒶⒷⒸⒹⒺ
2 ⒻⒼⒽⒿⓀ 10 ⒻⒼⒽⒿⓀ 18 ⒻⒼⒽⒿⓀ 26 ⒻⒼⒽⒿⓀ 34 ⒻⒼⒽⒿⓀ
3 ⒶⒷⒸⒹⒺ 11 ⒶⒷⒸⒹⒺ 19 ⒶⒷⒸⒹⒺ 27 ⒶⒷⒸⒹⒺ 35 ⒶⒷⒸⒹⒺ
4 ⒻⒼⒽⒿⓀ 12 ⒻⒼⒽⒿⓀ 20 ⒻⒼⒽⒿⓀ 28 ⒻⒼⒽⒿⓀ 36 ⒻⒼⒽⒿⓀ
5 ⒶⒷⒸⒹⒺ 13 ⒶⒷⒸⒹⒺ 21 ⒶⒷⒸⒹⒺ 29 ⒶⒷⒸⒹⒺ 37 ⒶⒷⒸⒹⒺ
6 ⒻⒼⒽⒿⓀ 14 ⒻⒼⒽⒿⓀ 22 ⒻⒼⒽⒿⓀ 30 ⒻⒼⒽⒿⓀ 38 ⒻⒼⒽⒿⓀ
7 ⒶⒷⒸⒹⒺ 15 ⒶⒷⒸⒹⒺ 23 ⒶⒷⒸⒹⒺ 31 ⒶⒷⒸⒹⒺ 39 ⒶⒷⒸⒹⒺ
8 ⒻⒼⒽⒿⓀ 16 ⒻⒼⒽⒿⓀ 24 ⒻⒼⒽⒿⓀ 32 ⒻⒼⒽⒿⓀ 40 ⒻⒼⒽⒿⓀ
The DSHAPES 2024 BUBBLESHEETS

Marking Directions: Mark only one circle for each question.

Fill in response completely. Erase errors cleanly without smudging.

Correct mark: ⒶⒷⒸⒹⒺ

Do NOT use these incorrect or bad marks.

Incorrect marks: ⒶⒷⒸⒹⒺ
Overlapping mark: ⒶⒷⒸⒹⒺ
Cross-out mark: ⒶⒷⒸⒹⒺ D Student Name:
Smudged erasure: ⒶⒷⒸⒹⒺ
Ⓓ
Mark is too light: ⒶⒷⒸⒹⒺ
Ⓐ

Section 4 | Language / Writing - Bubble in your responses to the multiple choice questions
1 ⒶⒷⒸⒹ 8 ⒶⒷⒸⒹ 15 ⒶⒷⒸⒹ 22 ⒶⒷⒸⒹ 29 ⒶⒷⒸⒹ
2 ⒶⒷⒸⒹ 9 ⒶⒷⒸⒹ 16 ⒶⒷⒸⒹ 23 ⒶⒷⒸⒹ 30 ⒶⒷⒸⒹ
3 ⒶⒷⒸⒹ 10 ⒶⒷⒸⒹ 17 ⒶⒷⒸⒹ 24 ⒶⒷⒸⒹ 31 ⒶⒷⒸⒹ
4 ⒶⒷⒸⒹ 11 ⒶⒷⒸⒹ 18 ⒶⒷⒸⒹ 25 ⒶⒷⒸⒹ 32 ⒶⒷⒸⒹ
5 ⒶⒷⒸⒹ 12 ⒶⒷⒸⒹ 19 ⒶⒷⒸⒹ 26 ⒶⒷⒸⒹ 33 ⒶⒷⒸⒹ
6 ⒶⒷⒸⒹ 13 ⒶⒷⒸⒹ 20 ⒶⒷⒸⒹ 27 ⒶⒷⒸⒹ
7 ⒶⒷⒸⒹ 14 ⒶⒷⒸⒹ 21 ⒶⒷⒸⒹ 28 ⒶⒷⒸⒹ

Section 5 | Reading - Bubble in your responses to the multiple choice questions

1 ⒶⒷⒸⒹ 7 ⒶⒷⒸⒹ 13 ⒶⒷⒸⒹ 19 ⒶⒷⒸⒹ 25 ⒶⒷⒸⒹ
2 ⒻⒼⒽⒿ 8 ⒻⒼⒽⒿ 14 ⒻⒼⒽⒿ 20 ⒻⒼⒽⒿ 26 ⒻⒼⒽⒿ
3 ⒶⒷⒸⒹ 9 ⒶⒷⒸⒹ 15 ⒶⒷⒸⒹ 21 ⒶⒷⒸⒹ 27 ⒶⒷⒸⒹ
4 ⒻⒼⒽⒿ 10 ⒻⒼⒽⒿ 16 ⒻⒼⒽⒿ 22 ⒻⒼⒽⒿ 28 ⒻⒼⒽⒿ
5 ⒶⒷⒸⒹ 11 ⒶⒷⒸⒹ 17 ⒶⒷⒸⒹ 23 ⒶⒷⒸⒹ 29 ⒶⒷⒸⒹ
6 ⒻⒼⒽⒿ 12 ⒻⒼⒽⒿ 18 ⒻⒼⒽⒿ 24 ⒻⒼⒽⒿ 30 ⒻⒼⒽⒿ

Section 6 | Math (No Calculator) - Bubble in your responses to the multiple choice questions
1 ⒶⒷⒸⒹ 3 ⒶⒷⒸⒹ 5 ⒶⒷⒸⒹ 7 ⒶⒷⒸⒹ 9 ⒶⒷⒸⒹ
2 ⒶⒷⒸⒹ 4 ⒶⒷⒸⒹ 6 ⒶⒷⒸⒹ 8 ⒶⒷⒸⒹ

Q. 10 Q. 11 Q. 12

⊘ ⊘ ⊘ ⊘ ⊘ ⊘
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪
① ① ① ① ① ① ① ① ① ① ① ①
② ② ② ② ② ② ② ② ② ② ② ②
③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③
④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④
⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤
⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥
⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦
⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧
⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨
The DSHAPES 2024 BUBBLESHEETS

Marking Directions: Mark only one circle for each question.

Fill in response completely. Erase errors cleanly without smudging.

Correct mark: ⒶⒷⒸⒹⒺ

Do NOT use these incorrect or bad marks.

Incorrect marks: ⒶⒷⒸⒹⒺ
Overlapping mark: ⒶⒷⒸⒹⒺ
Cross-out mark: ⒶⒷⒸⒹⒺ D Student Name:
Smudged erasure: ⒶⒷⒸⒹⒺ
Ⓓ
Mark is too light: ⒶⒷⒸⒹⒺ
Ⓐ

Section 7 | Math (With Calculator) - Bubble in your responses to the multiple choice questions
1 ⒶⒷⒸⒹ 5 ⒶⒷⒸⒹ 9 ⒶⒷⒸⒹ 13 ⒶⒷⒸⒹ 17 ⒶⒷⒸⒹ
2 ⒶⒷⒸⒹ 6 ⒶⒷⒸⒹ 10 ⒶⒷⒸⒹ 14 ⒶⒷⒸⒹ 18 ⒶⒷⒸⒹ
3 ⒶⒷⒸⒹ 7 ⒶⒷⒸⒹ 11 ⒶⒷⒸⒹ 15 ⒶⒷⒸⒹ 19 ⒶⒷⒸⒹ
4 ⒶⒷⒸⒹ 8 ⒶⒷⒸⒹ 12 ⒶⒷⒸⒹ 16 ⒶⒷⒸⒹ

Q. 20 Q. 21 Q. 22 Q. 23 Q. 24

⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘ ⊘
⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙ ⊙
⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪ ⓪
① ① ① ① ① ① ① ① ① ① ① ① ① ① ① ① ① ① ① ①
② ② ② ② ② ② ② ② ② ② ② ② ② ② ② ② ② ② ② ②
③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③ ③
④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④ ④
⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤ ⑤
⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥ ⑥
⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦ ⑦
⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧ ⑧
⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨ ⑨

Section 8 | Science - Bubble in your responses to the multiple choice questions

1 ⒶⒷⒸⒹ 7 ⒶⒷⒸⒹ 13 ⒶⒷⒸⒹ 19 ⒶⒷⒸⒹ 25 ⒶⒷⒸⒹ
2 ⒻⒼⒽⒿ 8 ⒻⒼⒽⒿ 14 ⒻⒼⒽⒿ 20 ⒻⒼⒽⒿ 26 ⒻⒼⒽⒿ
3 ⒶⒷⒸⒹ 9 ⒶⒷⒸⒹ 15 ⒶⒷⒸⒹ 21 ⒶⒷⒸⒹ 27 ⒶⒷⒸⒹ
4 ⒻⒼⒽⒿ 10 ⒻⒼⒽⒿ 16 ⒻⒼⒽⒿ 22 ⒻⒼⒽⒿ 28 ⒻⒼⒽⒿ
5 ⒶⒷⒸⒹ 11 ⒶⒷⒸⒹ 17 ⒶⒷⒸⒹ 23 ⒶⒷⒸⒹ 29 ⒶⒷⒸⒹ
6 ⒻⒼⒽⒿ 12 ⒻⒼⒽⒿ 18 ⒻⒼⒽⒿ 24 ⒻⒼⒽⒿ
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