y =4x + 12

y = (x + 2)2
21. A solution to the given system of equations is (x, y). What is the value of
x2 ?

(x + 2)2 = 4x + 12
x2 + 4x + 4 = 4x + 12
x2 = 8

1
22. A chemist mixed x liters of a 2% saline solution with y liters of a 5% saline
solution to produce a 3% saline solution. Which equation best represents this
situation? (Assume the volumes of the solutions are additive.)
(A) 0.02x + 0.05y = 3(x + y)
(B) 0.02x + 0.05y = 0.03(x + y)
(C) 0.2x + 0.5y = 3(x + y)
(D) 0.2x + 0.5y = 0.3(x + y)

Answer is B.

2
23. The table gives the perimeters of similar triangles T U V and XY Z, where
T U corresponds to XY . The length of T U is 16 .
Perimeter
Triangle TUV 44
Triangle XY Z 352
What is the length of XY ?
A) 2
B) 16
C) 60
D) 128

The answer is D.

3
24. The area of a triangle is 270 square centimeters. The length of the base of
the triangle is 12 centimeters greater than the height of the triangle. What is
the height, in centimeters, of the triangle?

bh h(h + 12)
270 = =
2 2
h (h + 12) = 540 = 18 × 30
h = 18

4
25. An employee earns $30 per hour for the first 40 hours worked in a week.
For each hour worked over 40 hours, the employee earns $45 per hour. What is
the least number of whole hours that the employee must work in a week to earn
at least $1, 610 ?
(A) 50
(B) 49
(C) 10
(D) 9

The answer is 50.

5
 22x − 21y = 43
5x + 14y = 59

26. The solution to the given system of equations is (x, y) = p w

, where p


59 , 826
and w are integers, what is the value of p ?

p w
22 − 21 = 43
59 826
p w
5 + 14 = 59
59 826
Multiply Eq 1 by 2 and Eq 2 by 3 and add them up:
44p 15p
+ = 86 + 177 = 263
59 59
p = 263

6
 x y
2 − 183
10
4 − 171
10
7 − 153
10

27. The table shows three values of x and their corresponding values of y.
There is a linear relationship between x and y. What is the x-coordinate of the
x-intercept of the graph that represents this linear relationship in the xy-plane?

− 171 183


10 − − 10 3
m= =
4−2 5
y − y1 = m(x − x1 )
183 3
y+ = (x − 2)
10 5
183 3
= (x − 2)
10 5
305
+2=x
10
65
x=
2

7
28. In the figure, LQ intersects M P atpoint R, and LM is parallel to P Q. The
lengths of M R, LR, and RP are 9,10, and 19, respectively. What is the length
of LQ ?
(A) 280
19

(B) 190
9

(C) 271
9

(D) 280
9

10 9 190 190 280

= =⇒ QR = =⇒ LQ = 10 + =
QR 19 9 9 9

8
29. The values in data sets X and Y are shown in the table.
X 13 13 14 14 15 16 16 17 17
Y 2 2 3 3 4 5 5 6 6

The standard deviation of data set X is q, and the standard deviation of data
set Y is s. Which of the following statements about the standard deviation of
the data sets is true?
A) q < s
B) q > s
C) q = s
D) The relationship between q and s cannot be determined.

9
30. For an online trivia game, 490 points are awarded for a correct answer if a
question is answered in less than 5 seconds from the time the question is asked.
Each 5 seconds after the question is asked, the number of points awarded for a
correct answer decreases by 20% of the number of points awarded for a correct
answer in the previous 5 seconds, Which function gives the number of points
awarded for a correct answer x seconds from the time the question is asked,
where x is a multiple of 5?
x
(A) f (x) = 490(0.80) 5
(B) f (x) = 490(0.80)5x
x
(C) f (x) = 490(0.20) 5
(D) f (x) = 490(0.20)5x

10
31. A machine makes 9-inch, 8-inch, and 3-inch parts. During a certain day,
the number of 9-inch parts that the machine makes is 4 times the number n of
8-inch parts, and the number of 3-inch parts is 15. During this day, the machine
makes 100 parts total. Which equation represents this situation?
(A) 9(4n) + 8n + 3(15) = 100
(B) 9n + 8n + 3n = 100
(C) 4n + 15 = 100
(D) 5n + 15 = 100

m: #9-inch, n: #8-inch, k: #3-in

m = 4n

k = 15
m + n + k = 100
4n + n + 15 = 100
5n + 15 = 100

11
32. A circle in the xy-plane has its center at (3, 7). Line t is tangent to this
circle at the point (a, −4), where a is a constant. The slope of line t is 45 . What
is the value of a ?
A) − 43
4

B) − 29
5

C) 59
5

D) 67
4

7 − (−4) 11
mAB = =
3−a 3−a
11 5
· = −1
3−a 4
55
= −1 =⇒ 4a − 12 = 55
12 − 4a
67
a=
4

12
33. In triangle ABC and triangle DEF , AB and DE are each equal to 5
centimeters, and angles A and D each have measure 35°. Which additional
piece of information is sufficient to prove that triangle ABC is congruent to
triangle DEF ?
(A) The lengths of sides BC and EF are equal.
(B) The lengths of sides AC and DF are equal.
(C) The measures of angles B and C are equal.
(D) No additional information is necessary to prove that the two triangles are
congruent.

B) SAS

13
34. The graph of the linear function y = f (x) − 19 is shown. If c and d are
positive constants, which equation could define f ?
(A) f (x) = d − cx
(B) f (x) = −d + cx
(C) f (x) = d + cx
(D) f (x) = −d − cx

14
35. For 100 neurons, the table summarizes the distribution of classification and
cell body diameter:
Cell body diameter (micrometers)
Classification Less than 20 20 to 30 Greater than 30
Sensory neuron 13 7 3
Motor neuron 0 15 18
Interneuron 10 34 0
One of these neurons will be selected at random. What is the probability of
selecting a neuron with a cell body diameter that is less than or equal to 30
micrometers, given that it is not classified as a motor neuron? (Express your
answer as a decimal or fraction, not as a percent.)

64/67

15
 √
k − x = 32 − x

36. In the given equation, k is a constant. The equation has exactly one real
solution. What is the minimum possible value of 4k?

2
k − x = (32 − x)
k − x = 322 − 64x + x2
x2 − 63x + 322 − k = 0
has exactly one solution:
∆=0
63 − 4 322 − k = 0
2

632 − 22 322 + 4k = 0
632 − 642 + 4k = 0
4k = 642 − 632 = (64 − 64) (64 + 63) = 127

16
37. Which of the following expressions has a factor of x+2b, where b is a positive
integer constant?
(A) 3x2 + 7x + 14b
(B) 3x2 + 16x + 14b
(C) 3x2 + 18x + 14b
(D) 3x2 + 25x + 14b

3(−2b)2 + 7(−2b) + 14b = 12b2 = 0

12b2 − 18b = 6b (2b − 3) = 0
12b2 − 22b = 2b (6b − 11) = 0
12b2 − 36b = 12b (b − 3) = 0

17
 x(kx − 40) = −8

38. In the given equation, k is an integer constant. If the equation has two
distinct real solutions, what is the greatest possible value of k?

kx2 − 40x + 8 = 0
∆ = 1600 − 32k > 0
1600 > 32k
50 > k
k = 49

18
39. The mass of object A is 416% of the mass of object B, and the mass of
object A is 0.064% of the mass of object C. If the mass of object C is p% of the
mass of object B, what is the value of 1,000
p
?

416
A= B
100
0.064 100A
A= C =⇒ C =
100 0.064
100 416 650000
=⇒ C = B = 6500B = B
0.064 100 100
p = 650000
p 650000
= = 650
1000 1000

19
 x2 = (40)(40)

41. What is the positive solution to the given equation?

40

20
42. A company has a customer loyalty program. In January 2018, there were 900
customers enrolled in the loyalty program. For the next 24 months after January
2018, the total number of customers enrolled in the loyalty program each month
was 2% greater than the total number enrolled the previous month. Which
equation gives the total number of customers, c, enrolled in the company’s
loyalty program m months after January 2018, where m ≤ 24?
(A) c = 900(0.02)m
(B) c = 900(1.02)m
(C) c = 900(1.2)m
(D) c = 900(2)m

21
 t
43. The function f (t) = 10, 000(2) 330 gives the number of bacteria in a popula-
tion t minutes after an initial observation. How much time, in minutes, does it
take for the number of bacteria in the population to double?

330

22
44. In right triangle ABC, angles A and B are acute, side AC has a length of
21.7 and tan B = 81 . What is the length of side BC, rounded to the nearest
tenth?
(A) 470.9
(B) 173.6
(C) 4.7
(D) 2.7

23
45. A rectangular banner has an area of 2,500 square inches. A copy of the
banner is made in which the length and width of the original banner are each
increased by 40%. What is the area of the copy in square inches?
(A) 2,540
(B) 2,580
(C) 3,500
(D) 4,900

A = 2500 = ℓw
(1.4ℓ)(1.4w) = 1.96ℓw = 1.96 × 2500 = 4900

24
46. Point F lies on a unit circle in the xy-plane and has coordinates (1, 0).
Point G is the center of the circle and has coordinates (0, 0). Point H also lies
on the circle and has coordinates (−1, y), where y is a constant. Which of the
following could be the positive measure of angle F GH, in radians?
(A) 27π
2

(B) 29π
2

(C) 24π
(D) 25π

25
47. In triangle P QR, QR is extended to point S. The measure of ∠P QR is
142◦ , and the measure of ∠P RS is 166◦ . What is the measure of ∠QP R ?
(A) 14◦
(B) 19◦
(C) 24◦
(D) 38◦

C) 24

26
 x
f (x) = 24 (1.30) 3
48. For the given function f , the value of f (x) increases by p% for every increase
of x by 6 . What is the value of p?
A) 30
B) 41
C) 60
D) 69

27
49. A carpenter charges a flat rate of $234 for the first 3 hours of work and $65
for each additional hour of work. Which equation gives the total amount y, in
dollars, that the carpenter charges for x hours of work, where x > 3?
(A) y = 65x + 39
(B) y = 234x + 65
(C) y = 65x + 234
(D) y = 234x + 429

234 + (x − 3)65 = 234 + 65x − 195 = 65x + 39

28
 √
5
√
6
2
119n 119n

50. For what value of x is the given expression equivalent to (119n)30x , where
n>1?

1/5+1/3 8/15
(119) = (119)
8
30x = =⇒ x = 4/225
15

29
51. The table summarizes the distribution of age and assigned group for 105
participants in a study.
0-9 years 10-19 years 20 + years Total
Group A 5 19 11 35
Group B 4 8 23 35
Group C 26 8 1 35
Total 35 35 35 105
One of these participants will be selected at random. What is the probability
of selecting a participant from group A, given that the participant is at least 10
years of age?
A) 2
7

B) 3
7

C) 19
35

D) 6
7

30
 x g(x)
−20 4
−8 0
10 6
52. The table shows three values of x and their corresponding values of g(x),
where g(x) = fx+5
(x)
and f is a linear function. What is the y-intercept of the
graph of y = f (x) in the xy-plane?
(A) (0, −8)
(B) (0, 5)
(C) (0, 8)
(D) (0, 40)

f (x) = mx + b = (x + 5)g(x)
g(−20) = 4
−20m + b = −60
20m − b = 60
g(−8) = 0
−8m + b = 0 =⇒ b = 8m
=⇒ 12m = 60 =⇒ m = 5
=⇒ b = 40
f (0) = 40
(0, 40)

31
 1 x 1
= +
cx 152 c
53. In the given equation, c is a constant. If the equation has exactly one
solution, what is the value of c?

1 x x
− =
cx cx 152
1−x x
=
cx 152
cx2 + 152x − 152 = 0
∆ = 1522 + 4 · 152c = 0
152 + 4c = 0 =⇒ c = −38

32