Name: ________________________ Class: ___________________ Date: __________
ID: A
PSAT Practice
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
____
1. Which of the following expresses the prime factorization of 36?
a. 2 × 3 × 3
b. 6 × 6
c. 2 × 2 × 3 × 3 d. 2 × 3 × 6
2. Which of the following numbers is prime?
a. 74
b. 63
c. 51
d. 39
1
3.6 × 10
e.
71
e.
−1 3
5
3. 3 3 − 4 6 = ?
1
a.
b.
−1 2
8
4. After
5
16
c.
1
d.
−6 3
1
86
1
1
2
____
e.
3
has been simplified to an improper fraction in lowest terms what is the denominator?
4
a.
____
____
5.
70
10
3
+
b.
7
100
+
7
1000
17
c.
6
d.
15
4
e.
7.077
=?
a. 0.777
b. 7.77
c. 70.77
d. 7.707
6. Which of the following must be true?
I.
The product of two consecutive nonzero integers is odd.
II.
The product of two consecutive nonzero integers is even.
III. The product of two consecutive nonzero integers is positive.
a.
b.
c.
e.
II and III only
I, II, and III
I only
d.
e.
II only
I and II only
1
of them are over the age of 30 and
____
7. There are 45 students in a college computer science course. If
____
remaining are under 25, how many students are from 25 to 30 years old?
a. 13
b. 5
c. 40
d. 27
e. 24
8. − |−3 + 5| − 2 |−7| = ?
b. 16
c. −28
d. −16
e. −12
a. −20
9. If n ÷ 11 has a remainder of 6, then which of the following has a remainder of 2?
____
a.
n−8
11
b.
n+1
11
c.
n−4
d.
11
9
n−1
11
e.
3
5
of the
n+4
11
____ 10. The selling prices for the last 5 houses sold in Tanya’s neighborhood were $120,500, $129,000, $122,000,
$120,500, and $128,000. What is the mode of these selling prices?
a. $124,000
b. $120,500
c. $128,000
d. $125,000
e. $122,000
____ 11. If the average (arithmetic mean) of 5 distinct integers is 13, what is the greatest possible value of any one of
the integers?
a. 68
b. 65
c. 55
d. 50
e. 53
____ 12. What must be the value of n in the set {0, n, −2, 5} if the range of the set is 7 and the median and mean are
equal?
a. 1
b. 0
c. 4.5
d. 4
e. 3
1
Name: ________________________
ID: A
2
____ 13. For all x ≠ 2,
3x − 6
x2 − x − 2
a.
____ 14. If
x − 4x + 4
x
b.
=?
c.
x
x−2
d.
3
1
e.
x+2
x+2
3
= z with y ≠ 0 and y = 2z, then all of the following are true EXCEPT
y
x = 2z 2
a.
b.
x = yz
c.
y = xz
d.
2z =
x
z
e.
2x
= 2z
y
____ 15. If 3x + 7y = 12 and x − y = 1, then what is the value of 5x + 5y?
a. 10
b. 14
c. 2
d. 8
e. 7
____ 16. At what point (x, y) do the lines with the equations y = 3x + 1 and 4x − 2y = 10 intersect?
a. (11, 34)
d. (−7.5, −6.5)
e. (−6, −17)
b. (−4.5, −12.5)
c. (10, 31)
____ 17. The sum of two positive even integers is x. In terms of x, what is the value of the greater of these two
integers?
x−1
a.
____ 18. If
3+x
=
7+x
a.
(ab ) b
7
x
+1
2
c.
x
d.
2
x+1
2
e.
x
−1
2
3
+ 7 , then x = ?
b.
3
c.
0
d.
7
e.
c.
b3
d.
b4
e.
21
3
=?
2
a b
a.
3
14
2
____ 19.
b.
2
1
ab
2
b.
a
b
4
4
b
4
a
____ 20. Quadrilateral ABCD is a parallelogram. What must be the coordinates of point C?
a.
b.
c.
(x, y)
ÊÁ x + b − a, y ˆ˜
Ë
¯
ÊÁ x, y + b − a ˆ˜
Ë
¯
d.
e.
ÁÊ x, y + a + b ˜ˆ
Ë
¯
ÊÁ x, a + b ˆ˜
Ë
¯
____ 21. The equation 9x 2 + y 2 − 18x + 6y − 18 = 0 represents which of the following?
a. circle
b. line
c. ellipse
d. parabola
e.
2
hyperbola
Name: ________________________
ID: A
4
____ 22. In rectangle ABCD below, x = 5 y. What is the value of y in terms of the perimeter p?
a.
p
5
b.
5p
18
c.
5p
d.
14
18p
e.
5
p
18
____ 23. In the figure below, ∆ABC and ∆ACD are right triangles, DC = 12, and BC = 18. If the area of ∆ACD = 96,
what is the area of polygon ABCD?
a. 520
b. 456
c. 276
d. 240
e. 16
____ 24. If the circumference of a circle is x, then what is the area of the circle in terms of x?
a.
x
2x
b.
2πx 2
c.
x
2
d.
4π
x
2
4π
e.
2
x
2
2π
____ 25. If the measure of one of the angles in a parallelogram is z, what is the measure of an adjacent angle?
a.
180 − z
b.
360 − 2z
c.
360 − z
z
d.
180 −
d.
120 − x
2
e.
z
e.
x
____ 26. In the figure below, what is the value of y in terms of x?
a.
x + 60
b.
2x
c.
300 − x
3
Name: ________________________
ID: A
____ 27. In the figure below, which pair of angles are supplementary?
a. ∠3 and ∠7
d. ∠4 and ∠7
b. ∠1 and ∠4
e. ∠2 and ∠5
c. ∠5 and ∠7
____ 28. The base of a suitcase is 22 inches long and 18 inches wide. If umbrellas come in integer lengths only, what
is the longest umbrella that will fit flat on the base of the suitcase?
a. 31 inches
b. 28 inches
c. 32 inches
d. 30 inches
e. 29 inches
____ 29. A bag contains 3 green balls, 5 black balls, and 7 red balls. If two balls are removed at random and no ball is
returned to the bag after the removal, what is the probability that the first ball is red and the second ball is
black?
a.
1
9
b.
1
6
3
c.
d.
14
7
45
e.
1
10
____ 30. A coin was flipped 10 times and came up heads 4 times and tails 6 times. If the first and eighth flips were
both tails, what is the greatest number of consecutive tails that could have occurred?
a. 8
b. 5
c. 4
d. 10
e. 6
____ 31. When one student is chosen at random from the Debate Club, the probability that a boy is chosen is
2
5
. There
are currently 25 students on the Debate Club. How many boys would have to join the club in order for the
1
probability of choosing a boy at random to be 2 ?
a. 3
b. 2
c. 5
d. 1
e. 4
____ 32. Let x* be defined as the number of prime numbers less than equal or equal to x. What is the value of
22* − 11*?
a. 3
b. 1
c. 5
d. 2
e. 7
____ 33. If x ⊗ y = x 2 − y, what is the value of
a.
1
18
b.
5
36
1
2
1
⊗ 9?
c.
1
d.
−5
7
18
____ 34. If x @ y = 2x + ay and 2 @ (−3) = 16, what is the value of a?
d. 4
a. 5
b. 1
c. −4
4
e.
e.
2
11
−1
ID: A
PSAT Practice
Answer Section
MULTIPLE CHOICE
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
C
E
A
C
E
A
A
D
C
B
C
E
C
C
B
E
B
E
D
C
C
B
C
C
A
A
C
B
B
B
C
A
B
C
1