M

r.S
he
rif
Ab
u
El
ha
ss
an
 1

3
𝒄 = 𝟑𝒏 + 𝟒𝟎
√𝒙 − 𝟕 = 𝟕

an
The equation above gives the cost, in
dollars, of the materials and tools Kyla What value of 𝒙 satisfies the given
used to make 𝒏 toy cars to sell at a craft equation?

ss
fair. If the cost of her materials and tools
was 115$, how many toy cars did Kyla A) 0
make?

ha
A) 40 B) 14

B) 35 C) 42

C) 30 El D) 56

D) 25
u
4
Ab

2 The distance 𝒅 in feet, traveled by a

falling object 𝒕 seconds after the object
is dropped can be modeled by the
equation 𝒅 = 𝟏𝟔𝒕𝟐 , which of the
rif

following expresses the number of

seconds after the object is dropped in
terms of the distance traveled?
he

𝟒
A) 𝒕 =
√𝒅
r.S

√𝒅
B) 𝒕 =
𝟒
The graph of 𝒚 = 𝒇(𝒙) is the parabola
𝟒
shown in the 𝒙𝒚-plane, If 𝒇(𝒂) = 𝟎, C) 𝒕 =
𝒅𝟐
M

what is the value of 𝒂 ?

A) -9 𝒅𝟐
D) 𝒕 =
𝟒

B) −𝟑

C) 𝟑

D) 9
 5 6
A rental-company manager is supplying
chairs and umbrellas for a pool party
that 90 guest will attend the manager

an
𝟐
will provide enough chairs for at least
𝟑
𝟐

ss
of the guests and umbrellas for at most
𝟑

of the guests, where each umbrella

ha
shades 3 guests, which of the following
systems represents the number of chairs, The graph (not shown) of a linear
c, and the number of umbrellas , u , that function , where 𝒚 = 𝒉(𝒙) , is a line
the manger will provide for the party?
El
completely contained in only quadrants
𝑰 𝒂𝒏𝒅 𝑰𝒍 . Which of the following could
A) C ≤ 𝟔𝟎
u
define the function 𝒉?
U≥ 𝟐𝟎
Ab

A) 𝒉(𝒙) = 𝟑𝒙 + 𝟑
B) C ≥ 𝟔𝟎
B) 𝒉(𝒙) = 𝟑𝒙
U≥ 𝟐𝟎
rif

C) 𝒉(𝒙) = 𝟑
C) C ≤ 𝟔𝟎
D) 𝒉(𝒙) = −𝟑
he

U≤ 𝟐𝟎

D) C ≥ 𝟔𝟎
r.S

U≤ 𝟐𝟎
M
 7 9
The function 𝒑 is defined by 𝒑(𝒉) =
𝟐𝒉 + 𝒉𝟐 .If k> −𝟐 𝒂𝒏𝒅 𝒑(𝒌) = 𝒑(−𝟐),
A certain new car depreciates by 20%
what is the value of k ?

an
during each of its first 5 years of
ownership. If V0 represents the value of
A) −𝟏 the car when purchased and 𝒕 represents
the number of years since it was

ss
B) 𝟎 purchased , which of the following
functions , 𝑽(𝒕) , can be used to
C) 1 approximate the value of the car for 𝟎 ≤

ha
𝒕≤𝟓?
D) 2
A) V(t)=V0(0.20)t
8
The total volume of the water in the five
El B) V(t)=V0(1.20)t

C) V(t)=V0(0.80)t
great Lakes is 5,439 cubic miles. The
u
lakes have volumes of 116 cubic miles , D) V(t)=V0(1.80)t
Ab

393 cubic miles , 850cubic miles 𝒙 cubic

10
miles , and y cubic miles , where 𝒙 >
𝒚 .Which of the following equations
rif

In the 𝒙𝒚-plane, a circle has center (0, 0)

represents the relationship between x
and radius 2. Which of the following is
and y ?
he

an equation of this circle?

A) 𝒙 − 𝒚 = 𝟔. 𝟕𝟗𝟖
A) 𝟐𝒙𝟐 + 𝒚𝟐 = 𝟎
r.S

B) 𝒙 − 𝒚 = 𝟒, 𝟎𝟖𝟎
B) 𝒙𝟐 + 𝒚𝟐 = 𝟒
C) 𝒙 + 𝒚 = 𝟔. 𝟕𝟗𝟖
C) (𝒙 + 𝟐)𝟐 + (𝒚 + 𝟐)𝟐 = 𝟎
M

D) 𝒙 + 𝒚 = 𝟒. 𝟎𝟖𝟎
D) (𝒙 + 𝟐)𝟐 + (𝒚 + 𝟐)𝟐 = 𝟎
 12
11

an
ss
Triangle ABC is similar to triangle

ha
WXY (not shown), where ∠𝑪
corresponds to ∠𝒀 , what is the tangent

Line 𝒍 is shown in the 𝒙𝒚-plane above,

which of the following is an equation of
El
of ∠𝒀 ?

A) 3√𝟐
u
line 𝒍 ?
B) 3
Ab

A) 𝟐𝒙 − 𝟑𝒚 = 𝟔
C) 1
B) 𝟐𝒙 + 𝟑𝒚 = 𝟔
𝟑
D)
𝟑√𝟐
rif

C) 𝟑𝒙 − 𝟐𝒚 = 𝟔

D) 𝟑𝒙 + 𝟐𝒚 = 𝟔
he
r.S
M
 13
𝟐𝒙 + 𝟏
−𝟏 15
𝒙+𝟑

an
Which of the following is equivalent to
the given expression?
𝟐𝒙
A)

ss
𝒙+𝟐
𝟐𝒙
B)
𝒙+𝟑

ha
𝒙+𝟒
C)
𝒙+𝟑
𝒙−𝟐
D)
𝒙+𝟑

14
El
u
The figure above represents a right
circular cone with radius 𝒓 and height 𝒉.
Ab

A second right circular cone has 𝟖 times

the volume as the cone shown. Which of
the following could be the dimensions of
rif

the second cone? (The volume of a cone

he

with base radius 𝒓 and height 𝒉

𝟏
is 𝝅𝒓𝟐 𝒉.)
𝟑
r.S

Which of the following is a equation of A) Radius = 2r, height = 2h

the graph shown? B) Radius = 2r, height = 4h
M

A) 𝒚 = 𝟑𝒙 C) Radius = 4r, height = h

B) 𝒚 = 𝟑𝒙 + 𝟏 D) Radius = 4r, height = 4h

C) 𝒚 = 𝟐𝒙
D) 𝒚 = 𝟐𝒙 + 𝟏
M
r.S
he
rif
Ab
u
El
ha
ss
an
 16 19
𝟏
𝒙 − 𝟕𝟎𝟎 = 𝟎
𝟐
𝟐𝒙 − 𝟑𝒚 = 𝟐𝟐

an
What value of 𝒙 satisfies the equation
above? −𝟒𝒙 + 𝟓𝒚 = −𝟔𝟔

ss
If (x, y) is the solution of the system
above, what is the value of 𝒚 ?

ha
20

El 𝟏 𝟏 𝟏
17 + =
u
𝒕 𝟏𝟖 − 𝒕 𝟒
Ab

What is one possible value of 𝒕 that

(𝟐𝒙 − 𝟏)(𝒙 + 𝟓)
satisfies the equation above?
The given expression is equivalent
to 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄 , where 𝒂, 𝒃, 𝒂𝒏𝒅 𝒄 are
rif

constants. What is the value of 𝒃?

he

18
r.S

𝟑𝒙 + 𝟓 + 𝒙 = 𝟐(𝟐𝒙 + 𝒃)
M

In the equation above, 𝒃 is a constant. If

the equation has infinitely many
solutions, what is the value of 𝒃?
M
r.S
he
rif
Ab
u
El
ha
ss
an
 1
3
If 𝟑𝟖 = 𝟏𝟏 + 𝟑𝒙 , what is the value 𝒙?
A messenger delivered 10 packages on
A) 9 Monday before 11 a.m. and 4 packages

an
B) 13 per hour after 11 a.m. In which of the
C) 22 following equations does 𝑷 represent the

ss
D) 27 total number of packages the messenger
had delivered on Monday 𝒉 hours after

ha
11 a.m.?
2
A) 𝑷 = 𝟒𝟎𝒉

A store charges $4.00 per pound for

ElB) 𝑷 = 𝟏𝟒𝒉
C) 𝑷 = 𝟒 + 𝟏𝟎𝒉
apricots. At this rate, what will the store D) 𝑷 = 𝟏𝟎 + 𝟒𝒉
u
charge for 2.5 pounds of apricots?
Ab

A) $6.00
B) $8.00
4
rif

C) $10.00
D) $12.00
he

(𝒙 − 𝟏)(𝒙 − 𝟐)(𝒙 − 𝟑) = 𝟎

Which of the following is NOT a value

r.S

of 𝒙 that satisfies the equation above?

A) 0
M

B) 1
C) 2
D) 3
 5
The line graph below shows the 6

percentage of US workers who walk to

work based on census data collected in

an
the years 1980, 1990, 2000, and 2010.

ss
ha
El
The graph above shows the atmospheric
pressure, in hectopascals (hpa), for a
u
Of the following time periods, which had town in Australia over a 72-hour period.
Ab

the greatest average yearly decrease in Based on the graph. Which of the
the percentage of workers who walk to following statements is (are) true?
work?
I. The minimum atmospheric
rif

A) 1980 to 2010 pressure occurred during the

B) 1980 to 1990
he

first 24 hours of the time period.

C) 1990 to 2000 II. The atmospheric pressure 36
D) 2000 to 2010 hours into the time period was
r.S

greater than the atmospheric

pressure at the end of the time
M

period.
A) Neither I nor II
B) I only
C) II only
D) Both I and II
 7
8
An object moves along a straight path
An equation of a line in the 𝒙𝒚-plane is
from a starting point. The distance 𝒚, in
𝒚 = 𝒎𝒙 + 𝒃 where 𝒎 and 𝒃 are
meters, of the object from its starting
constants. Which of the following
point after 𝒙 seconds is shown in the

an
changes to the equation would
graph below. correspond to a vertical shift of the line
by 3 units up?

ss
A) Increasing the value of 𝒎 by 3
B) Increasing the value of 𝒃 by 3

ha
C) Increasing the values of both 𝒎 and
𝒃 by 3
D) Increasing the values of both 𝒎 and
El𝒃 by 1.5

Which of the following is true?

u
9
An object’s momentum is the product of
Ab

A) The object traveled farther during

the period 𝟎 < 𝒙 < 𝟓 than during its mass and its velocity. What is the
velocity, in meters per second, of an 8-
the period 𝟓 < 𝒙 < 𝟏𝟎.
kilogram object that has a momentum of
rif

B) The object traveled farther during

56 kilogram meters per second?
the period𝟓 < 𝒙 < 𝟏𝟎 than during
he

the period𝟎 < 𝒙 < 𝟓 . A) 7

C) The object traveled the same B) 28
r.S

during the period 𝟎 < 𝒙 < 𝟓 as C) 64

during the period 𝟓 < 𝒙 < 𝟏𝟎. D) 448
D) The distance the object traveled
M

during the periods 𝟎 < 𝒙 < 𝟓 and

𝟓 < 𝒙 < 𝟏𝟎 cannot be determined
from the graph.
Questions 10 and 11 refer to the following
11
information.
The velocity of water is 45 inches per
𝝅 𝟐 second through cylindrical pipe A and
𝑸= 𝒅 𝒗 75 inches per second through cylindrical
𝟒

an
pipe B. If both pipes have the same
The flow 𝑸, in cubic inches per second, diameter, what is the ratio of the flow
of water that flows through a cylindrical rate in pipe A to the flow rate in pipe B?
pipe with diameter𝒅, in inches, and with

ss
A) 9 to 25
velocity𝒗 , in inches per second, can be B) 3 to 5
modeled by the equation above. C) 5 to 3

ha
D) 25 to 9
10
For a certain cylindrical pipe, which of 12
The population of a city was
the following best represents the graph
of the water’s flow rate 𝑸 versus the
El
approximately 300,000 once year and
330,000 the next year. Using these data,
Maia modeled the population of the city
water’s velocity 𝒗?
u
for a 10-yaer period with an exponential
function of the form 𝒚 = 𝒂𝒃𝒕 . Where 𝒂
Ab

and 𝒃 are constants and 𝒕 is the number

of years after the start of 10-year period.
Which of following statements best
characterizes the change in population
rif

that her model predicts?

A) The model predicts an increase of
he

30,000 people every year during

the 10-year period.
B) The model predicts an increase of
330,000 people every year during
r.S

the 10-year period.

C) The model predicts a 10%
increase over the prior year’s
population every year during the
M

10-year period.
D) The model predicts a 100%
increase over the initial population
at the end of the 10-year period.
 13 14
The scatterplot below shows the number
of congressional representatives, 𝒙, and
population 𝒚, in thousands, for 25 of the

an
50 states in the United States.

In triangle 𝑨𝑩𝑪 above, what is the

ss
̅̅̅̅ ?
length of 𝑨𝑩

ha
A) 10
B) 20
C) 10√𝟑

D)
𝟏𝟎√𝟑
𝟑
El
u
Which of the following could be an
Ab

equation of a line of best fit for these

data?
rif

A) 𝒚 = −𝟑𝟏 + 𝟕𝟏𝟔𝒙
B) 𝒚 = −𝟑𝟏 − 𝟕𝟏𝟔𝒙
he

C) 𝒚 = −𝟑𝟏 + 𝟕𝒙
D) 𝒚 = −𝟑𝟏 − 𝟕𝒙
r.S
M
 15 17
A sample of students was selected at 𝟔𝒙 − 𝟖𝒚 = 𝟐𝟒
random from all ninth-grade students in
a large school district. The proportion of 𝟐 𝟖
− 𝒙+ 𝒚=𝒎

an
the students in the sample who were 14 𝟑 𝟗
years old was 80%, with an associated
In the system of equations above, 𝒎 is a
margin of error of 5%. Which of the

ss
following is NOT a plausible number of constant. If the system has more than
14-year-olds in the 3,601 ninth-grade one solution. What is the value of 𝒎?
students in the school district?

ha
𝟖
A) 2,750 A) −
𝟑
B) 2,900 𝟏
B) −
C) 3,050
D) 3,200 El C)
𝟐
𝟑
𝟑

𝟖
D)
u
𝟑
Ab

16
The graph of a polynomial equation in
the 𝒙𝒚-plane contains the points (-1,0),(2,
rif

0), and (3, 0). Which of the following

could be the equation of the graph?
he

A) 𝒚 = −𝒙(𝟐𝒙)(𝟑𝒙)
B) 𝒚 = (𝒙 − 𝟏)(𝒙 + 𝟐)(𝒙 + 𝟑)
r.S

C) 𝒚 = 𝒙(𝒙 − 𝟏)(𝒙 − 𝟐)(𝒙 + 𝟑)

D) 𝒚 = (𝒙 + 𝟏)𝟐 (𝒙 − 𝟐)(𝒙 − 𝟑)
M
Questions 18 and 19 refer to the
19
following information.
The mean of the 1990 data set is 8.0 toe,
and the mean of 2010 data set is 7.5 toe.
What is the percent decrease of the

an
mean from 1990 to 2010?
A) 0.5%

ss
B) 5%
The box plots above show the C) 6.25%
distribution of the average amount of
D) 6.67%
energy used per person, in tons of oil

ha
equivalent (toe). For 25 countries, in
1990 and in 2010.

18
Which of the following correctly
El
20
u
compares the median and range of these
distributions? For the function 𝒇, if 𝒇(𝒛) = 𝟑𝒛, which
Ab

of the following is equivalent to 𝒇(𝒛 − 𝟐)?

A) The median in 2010 is greater
than median in 1990, and the A) −𝟑𝒛
range in 2010 is less than the B) 𝟑𝒛 −2
range in 1990. C) 𝟑𝒛 − 𝟔
rif

B) The median in 2010 is greater

D) −𝟑𝒛 + 𝟔
than median in 1990, and the
range in 2010 is greater than the
he

range in 1990.
C) The median in 2010 is less than
median in 1990, and the range in
r.S

2010 is less than the range in 1990.

D) The median in 2010 is less than
median in 1990, and the range in
2010 is greater than the range in
M

1990.
 21 23
The distribution of the number of days
served in office by the first 43 presidents
of the United States has a mean of

an
approximately 1,900 days. The ninth
president. William Henry Harrison,
served only 31 days, the few number of

ss
days as president. What would be the
effect on the mean of the distribution if
the number of days William Henry

ha
Harrison served from the data?
A) The mean would decrease.
The shaded region shown above
B) The mean would increase.
C) The mean would be unchanged.
El
represents the solution to which of the
following systems of inequalities?
D) The effect on the mean cannot be
u
A) 𝒚 < 𝒙
determined.
Ab

𝒚≤𝟒
B) 𝒚 < 𝒙
22
𝒚≥𝟒
rif

C) 𝒚 > 𝒙
𝒚≤𝟒
he

D) 𝒚 > 𝒙
𝒚≥𝟒
r.S

In the figure above, sides 𝑨𝑩 and 𝑨𝑫 of

tringle 𝑨𝑩𝑫 are extended to points C
M

and E, respectively. If 𝒚 = 𝟕𝟐, what is

the value of 𝒙?
A) 104
B) 108
C) 112
D) 148
 24 25
A polling agency conducted a survey
about public opinion on car-sharing
services. The agency surveyed a random

an
sample of adult residents from three
large cities in the United States and
reported that 73% support car-sharing
services, with an associated margin of

ss
error of 4%. Based on the study design,
what is the largest population to which
these survey results can be generalized?

ha
Miranda jogged home from a friend’s A) All adult residents of the United
house along a straight path without States
making any stops. The graph above B) All adult residents of large cities in
gives Miranda’s distance 𝑫 , in miles,
from home as a function of the time 𝒕, in
minutes, after she left her friend’s house.
El the United States
C) All adult residents who support
car-sharing services
u
Which of the following statements is D) All adult residents of the three
true about Miranda’s jog home?
Ab

large cities in the survey

A) Miranda’s speed in miles per
minute, decreased at a constant
rate. 26
rif

B) After jogging for approximately

2.5 miles, Miranda was 30 minutes
𝟐𝒙 − 𝟔
he

from home.
𝒙𝟐 − 𝒙 − 𝟔
C) Miranda’s distance from home
decreased at a constant rate of 12 Which of the following expressions is
r.S

miles per minutes.

equivalent to the expression above
D) Miranda’s distance from home
decreased at a constant rate of 1 for 𝒙 > 𝟓?
mile per 12 minutes.
M

𝟏
A)
𝒙+𝟏
𝟏
B)
𝒙−𝟐
𝟐
C)
𝒙−𝟏
𝟐
D)
𝒙+𝟐
 27
29
𝟑𝒙 = 𝟔𝒚 + 𝟖
A music artist released a new album.
In the 𝒙𝒚-plane, the graph of which of The function 𝒇 models the weekly sales,
in dollars, of the album𝒙weeks since the

an
the following equations is perpendicular
first week of sales. The model predicts
to the graph of the equation above? that each week the album will have 2%
fewer sales than the previous week.

ss
A) 𝒚 = −𝟐𝒙 + 𝟏𝟎 Which of the following could define𝒇?
𝟏
B) 𝒚 = − 𝒙 + 𝟒 A) 𝒇(𝒙) = 𝟑𝟓𝟎(𝟎. 𝟎𝟐)𝒙
𝟑

ha
𝟏
C) 𝒚 = 𝒙 − 𝟔 B) 𝒇(𝒙) = 𝟑𝟓𝟎(𝟎. 𝟖𝟎)𝒙
𝟐

D) 𝒚 = 𝟐𝒙 − 𝟔 C) 𝒇(𝒙) = 𝟑𝟓𝟎(𝟎. 𝟗𝟖)𝒙

28
A data set consists of 50 positive values,
ElD) 𝒇(𝒙) = 𝟑𝟓𝟎(𝟏. 𝟎𝟐)𝒙
u
and the mean of the data is 𝒎. A new 30
data set is made by increasing each 𝟐
Ab

If 𝒂 = 𝒃 + 𝟒 , which of the following

𝟑
value in the original data set by 8.
Which of the following represents the expresses 𝒃 in terms of 𝒂?
mean of the new data set in terms of 𝒎?
𝟐
A) 𝒃 = 𝒂 + 𝟒
rif

A) 𝒎 + 𝟖 𝟑
𝟐
B) 𝒎 + 𝟓𝟎 B) 𝒃 = 𝒂 − 𝟔
𝟑
he

C) 𝟖𝒎 𝟐
C) 𝒃 = 𝒂 − 𝟒
𝟑
D) 𝟖𝒎 + 𝟓𝟎 𝟐
D) 𝒃 = 𝒂 − 𝟔
r.S

𝟑
M
M
r.S
he
rif
Ab
u
El
ha
ss
an
 31 33

Season Number of
birthdays

an
Spring 5

Summer 4

ss
Autumn 𝒙 in rectangle 𝑨𝑩𝑪𝑫 above, 𝑨𝑩 = 𝟐 and
Winter 7 𝑬𝑫 = 𝟏. 𝟕𝟓 . If a point is selected at

ha
random from inside the rectangle, the
The table above shows the number of probability that the point selected will
birthdays in each of the four seasons for be in the shaded region is 0.25. What is
the students in a class. If 16 of the
students’ birthdays are in the summer
or autumn, what is the value of 𝒙?
El
the value of 𝒙?
u
Ab

32
𝒙+𝒚=𝟕
𝒙−𝒚=𝟏 34
rif

A right circular cylinder has a base area

If (x, y) is the solution to the system of of 110 square inches and a volume of
he

equations above, what is the value of 𝒙? 1650 cubic inches. What is the height, in
inches, of the cylinder?
r.S
M
 35
At 1:00p.m. The population of bacteria
Question 37 and 38 refer to the
in a liquid medium is 80 thousand. The
population doubles every 40 minutes. If following information.

an
the population at 5:00 p.m. Will be 𝒏
Instrument Rented Owned Total
thousand, what is the value of 𝒏?
Violin 8 12 20

ss
Viola 5 5 10
Cello 6 2 8

ha
Bass 5 1 6
Total 24 20 44
36
A class X cargo ship can hold a
maximum of 18,000 standard containers.
El
The table above shows the number of
each type of string instrument played at
a high school orchestra concert and the
u
A class X cargo ship can hold 20% more number of each type owned or rented.
containers than a class Y cargo ship.
Ab

How many more containers can a class 37

X cargo ship hold than a class Y cargo
ship?
What fraction of the violins played at
rif

the concert were rented?

he

38
r.S

An additional 4 cellos and 𝒙 basses were

played at the next concert. If the ratio of
M

cellos to basses was the same for both

concerts. What is the value of 𝒙?
2018 December SAT Int'l
ANSWER KEY

Reading Test Answers Writing and Language Test Answers

1 C 11 B 22 D 33 A 43 B 1 C 12 D 23 B 34 B
2 A 12 D 23 B 34 B 44 C 2 D 13 A 24 C 35 A
3 C 13 B 24 C 35 D 45 C 3 C 14 C 25 A 36 C
4 D 14 D 25 C 36 A 46 D 4 D 15 D 26 A 37 D
5 B 15 C 26 C 37 C 47 A 5 C 16 C 27 B 38 B
6 A 16 B 27 D 38 D 48 A 6 A 17 A 28 C 39 B
7 D 17 D 28 B 39 B 49 B 7 B 18 B 29 B 40 A
8 B 18 B 29 D 40 A 50 C 8 C 19 D 30 C 41 A
9 B 19 C 30 C 41 A 51 B 9 A 20 B 31 B 42 B
10 A 20 C 31 A 42 D 52 D 10 D 21 D 32 C 43 B
21 A 32 C 11 C 22 B 33 A 44 D

Math Test Math Test

No Calculator Answers Calculator Answers
1 D 11 D 1 A 11 B 21 B 31 12
2 B 12 C 2 C 12 C 22 D 32 4
3 D 13 D 3 D 13 C 23 B 33 3.5
4 B 14 B 4 A 14 A 24 D 34 15
5 D 15 A 5 B 15 D 25 D 35 5120
6 C 16 1400 6 A 16 D 26 D 36 3000
7 B 17 9 7 B 17 A 27 A 37 0.4
8 D 18 2.5 8 B 18 A 28 A 38 3
9 C 19 22 9 A 19 C 29 C
10 B 20 6 or 12 10 B 20 C 30 D