SC TEST 3 – MODULE 1

1. If 2x + 6y = 12, then ?

A) 2
B) 3
C) 4
D) 6

2. The Sky Telephone Company charges a cent

for the first 3 minutes of a call and charges at
the rate of r cents for each additional minute.
If Jackson uses t minutes, where t > 3, how
much, in dollars, is his call ?

A) a +rt
B) a + r(t-3)
C) 0.01(a + r(t-3))
D) 0.01(a + rt-3)

3.
2
Which of the following is equivalent to the
expression above ?

A) |x + 6| ≥ 4
B) |x + 6| ≤ 4
C) |x 6| 24
D) |x 6| ≤ 4
4. The graph of ( ) is shown.

Which equation defines the linear function ?

A) ( )
B) ( )
C) ( )
D) ( )

5. Sean was assigned a login password to his

library account. He was told that his password
consists of 3 two-digit numbers that have to
satisfy the following three conditions:
One number is an even number.
One number is a prime number.
One number is a multiple of 5.

If each number can only satisfy one of the

conditions above, then which of the following
could be his login password ?

A) 14 – 29 – 45
B) 20 – 16 – 13
C) 12 – 25 – 49
D) 15 – 21 – 26
6. ( ) ( )( )
The function is defined above, where and
are integer constants. If ( ) ( )
and ( ) , what is one possible value
of ?

7.

The equation of a circle in the -plane is

shown above. What is the radius of the circle
?

8. If 4 more than twice a number is equal to 20.

What is 2 more than 4 times the number ?

A) 12
B) 34
C) 26
D) 32

9. Bob receives a basic weekly salary of $200

plus a 10% commission on his sales. In a
week in which his sales amounted to $4000,
the ratio of his basic salary to his commission
was ?

A) 2:1
B) 1:2
C) 2:3
D) 3:2
10.

In the figure above, BCDE is a square and its

area is 16. The points A, E and D are on the
same line. What is the length of ̅̅̅̅ ?

A) 4
B) √
C) √
D) 6

11. Ashley and Beth drove from city A to city B

in exactly 5 hours, not taking rest stops.
Ashley drove up to the area located halfway
between the two cities at the average speed of
40 miles per hour and then Beth drove the
other half at an average speed of 60 miles per
hour. How many hours did Beth drive on their
trip ?

A) 1
B) 2
C) 3
D) 4
 Questions 12 and 13 refer to the following
information.
Ordered Details
20 Sandwiches
20 Soups
5 Salads
4 Sodas
Delivery Fee: 5%
Total amount: $226.17
Megan ordered lunch for her birthday party
and her bill is shown above. The delivery fee
was calculated as a percent of the cost of
Megan's order. The total amount is the sum of
the cost of Megan's order and the delivery fee.

12. What is the cost of Megan's order ?

A) $200
B) $215.40
C) $225.50
D) $250

13. The total amount Megan paid for sandwiches

and salads was $134. If the combined cost of
one sandwich and one salad is $8.50, what is
the cost of one sandwich ?
A) $5.05
B) $6.10
C) $7.25
D) $7.50

14. If > 0 and u < 0, which of the

following must be true ?
A) rt < 0
B) urt < 0
C) r>0
D) t>0
15. If f(x 1) = 5x + 2, what is f(x + 2) equal
to?

A) 5x 2
B) 5x 13
C) 5x 14
D) 5x² 10x + 2

16. X

65°
A B
x°

Y
In the figure above, XAB and XYA are
inscribed in the circle. If AB is the diameter
of the circle, and the measure of XAB is
65°, what is the value of x ?

17.

1600 .
1400
.. .
1000
. .
. . ..
600
...
200
0 50 150 250 350

The scatter plot shows the relationship

between body mass and test bite force for
lions. The linear model of best fit for the data
 is also shown. For a body mass of 175
pounds, which of the following best
approximates the percent increase from the
test bite force to the force that the model
predicts ?

A) 50%
B) 100%
C) 125%
D) 150%

18. If z = a + bi and = 3, where a and b are

real numbers, which of the following is the
value of a ?

A) -0.5
B) -1.5
C) -2
D) -2.5

19. ( ) ( ) ( )
For what value of x is the function f above
undefined ?

20. 2 + 8x + 10
Which of the following is equivalent to the
expression above ?

A) (2x + 2)(x + 5)
B) (2x – 2)(x – 5)
C) 2( ) +2
D) 2( ) +2
21. In the xy-plane, the equation of line is
. If line is perpendicular to
line , what is a possible equation of line ?

A)
B)
C)
D)

22.
Jackie is driving a car at 10 miles per hour.
The graph above shows the speed of his car
over 8 seconds. During which of the
following time intervals did the speed show
the greatest average rate of change ?

A) 0 to 2 seconds
B) 2 to 4 seconds
C) 4 to 6 seconds
D) 6 to 8 seconds

23. The sum of four numbers is 783. One of the

numbers, a, is 25% more than the sum of the
other three numbers. What is the value of a ?

A) 348
B) 435
C) 520
D) 585
 D 10 C

24.

A 12 B
Find the area of the shaded region within the
trapezoid if AB = 12, BC = 8, CD = 10, and
AB is perpendicular to BC ?

A) 88
B) 40
C) 60
D) 44

25. The state income tax where Alison lives is

levied at the rate of k% of the first $30,000 of
annual income plus (k+4)% of any amount
above $30,000. This year Alison’s income
was $65,000 and she paid $9,850 for the
income tax. What is the value of k ?

26. ( √ )( √ )

If x is positive, which of the following is

equivalent to the expression above ?

A) √

B) √
C)
D) x⁹
 y

27. y = x² - 8x + 16

P Q

x
O R

Figure not drawn to scale.

The graph of y = x² - 8x + 16 is shown in the

xy-plane above. If point P is the y-intercept of
the graph, what is the area of rectangle
OPOR?
 SC TEST 3- MODULE 2

1.
x² - y²=35
x+y=5
In the system of equations above, which of
the following is the value of x ?

A) 5
B) 6
C) 7
D) 8

2. P (x) = (x - 2)Q(x) + R
The equation above shows when P(x) is
divided by (x - 2), the remainder is R, where
Q(x) is the quotient. If P(x)=5 - 3x + 4,
what is the value of R ?

A) 4
B) 6
C) 12
D) 18

3. If is a solution of the equation

= + c where c is a constant, what is
another value of x that satisfies the equation ?

A) 1
B) 2
C) 3
D) 4

4. ( )(a + bi) = 1
 In the equation above, a and b are constants.
If i = √ , what is the value of a ?

A) -

B) -

C)
D)

5. y

x
O

The graph of a quadratic function

f(x) = ax² + bx + c is shown in the xy-plane
above. Which of the following must be true ?

I. a > 0
II. b >0
III. c >0

A) I only
B) I and II only
C) II and III only
D) I, II, and III
6.
y
R(6,k)

x
O P(2, 0)

In the xy-plane above, the slope of PQ is 1

and the slope of QR is . What is the slope of
PR ?

7. 1.313113111311113 …

The decimal number above consists of only Is

and 3s. The first 3 is followed by one I, the
second 3 is followed by two Is, and the third 3
is followed by three Is. If such a pattern goes
on, how many Is are between the 94th 3 and
the 98th 3 ?

8. If w < z, and which of the

following must be true ?

A) None
B) II and III
C) I and II
D) I and III
9. If a, b, and c are consecutive positive integers
such that a < b < c and a+ b + c is a multiple
of 6, then which of the following must be
true?

A) a is an even integer
B) b is an odd integer
C) c is a multiple of 3
D) a is an odd integer

10.

x°

In the regular hexagon shown above, what is

the value of x ?

A) 120
B) 108
C) 72
D) 60

11. If a and b are both positive e integers

and , how many pairs of (a, b) is
possible ?

A) 12
B) 10
C) 8
D) 6
12.

The incomplete table above shows the results

of a survey about subject preference given to
100 students. What is the probability of art
students being females ?

A)
B)
C)
D)

13. A circle with center at coordinates (4,

5) touches the x-axis at only one point. What
is the radius of the circle ?

14. The price of a pizza at the pizza

store includes:
i. The basic charge
ii. An additional charge for
each topping

If the price of a 1-topping pizza is $16 and the

price of a 3-topping pizza is $20,
what is the price of a 5-topping pizza ?

15. If and ( ) ,
what is the value of ?

A) 7
B) 8
C) 11
D) 14
16. If there are 8 points in a plane, no three
of which are collinear, how many distinct
lines can be formed by connecting two
of these points ?
A) 15
B) 21
C) 28
D) 49

17. If a supermarket has brand A juice

smoothie on sale every 7 days and has brand
B juice smoothie on sale every 5 days. Within
a year (365 days), how many times does this
supermarket have both brands of juice
smoothie on sale on the same day ?
A) 9
B) 10
C) 11
D) 12
18. The average (arithmetic mean) of 7,
14, and x is 16. What is the value of x ?
A) 25
B) 26
C) 27
D) 28

19.
In the figure above, l1 // l2, what is the value
of x ?
A) 45
B) 50
C) 60
D) 70
20. In a junior high school with seventh
and eighth graders, there is the same number
of girls as boys. The eighth grade has 220
students, and there are 5 boys for every 6
girls. In the seventh grade there are 5 boys for
every 4 girls. How many girls are in the
seventh grade ?

21.

In the figure above, if the area of

parallelogram OABC is 16, what is the value
of x?
22. The equation
( +3)( )= where and
are constants. If the equation is true for all
values of , what is the value of ?

A) 8
B) 6
C) 4
D) 3
23.
The Venn diagram above shows the
distribution of 35 students at a school who
took biology, chemistry, or both. What
percent of the students who take both
chemistry and biology ?

A) 15%
B) 20%
C) 23%
D) 25%
24. f(x) = + mx + 4

In the function above, f (x) > 0 for all values

of x. Which of the following could be the
value of m ?

A) 8
B) 6
C) 4
D) 2

25. A farmer can plow a field in k days.

How many days will it take two farmers
working at the same rate to plow a field two
times larger ?

A) 2k
B) k
C)
D)
26.
 a
b
In the figure above, four congruent rectangles
and a square are put together to form a larger
square. The perimeter of each rectangle is 24,
and the area of the smaller square is 36. If the
dimensions of each rectangle are a and b as
shown above, what is the value of b ?

27. f(x)=g²(x) -7g(x)+15

In the equation above, if f(2) = 3, what is one

possible value of g(2) ?