Math Placement Test — Form B
Question 1
$$624 \div 26 = $$
(A) $22$
(B) $24$
(C) $26$
(D) $28$
Question 2
$$\frac{5}{6} - \frac{1}{4} = $$
(A) $\dfrac{7}{12}$
(B) $\dfrac{4}{2}$
(C) $\dfrac{1}{3}$
(D) $\dfrac{11}{12}$
Question 3
$$2\frac{3}{5} + 1\frac{7}{10} = $$
(A) $3\frac{10}{15}$
(B) $4\frac{3}{10}$
(C) $4\frac{1}{5}$
(D) $3\frac{9}{10}$
Question 4
$$1.25 \times 0.08 = $$
(A) $0.01$
(B) $0.1$
(C) $1.0$
(D) $0.10$
Question 5
Round $12{,}345.678$ to the nearest hundredth.
(A) $12{,}345.67$
(B) $12{,}345.68$
(C) $12{,}346$
(D) $12{,}345.7$
Question 6
Express $3{,}150{,}000$ in scientific notation.
(A) $3.15 \times 10^6$
(B) $31.5 \times 10^5$
(C) $3.15 \times 10^7$
(D) $0.315 \times 10^7$
Question 7
$$\sqrt{128} = $$
(A) $4\sqrt{8}$
(B) $8\sqrt{2}$
(C) $16\sqrt{2}$
(D) $2\sqrt{32}$
Question 8
$$\left(-\frac{1}{2}\right)^3 = $$
(A) $\dfrac{1}{8}$
(B) $-\dfrac{1}{8}$
(C) $-\dfrac{3}{2}$
(D) $\dfrac{3}{8}$
Question 9
What is 120% of 75?
(A) $80$
(B) $85$
(C) $90$
(D) $95$
Question 10
$$|-12| + |-5| = $$
(A) $-17$
(B) $-7$
(C) $7$
(D) $17$
Question 11
Simplify: $(2a^3)^2$
(A) $2a^6$
(B) $4a^5$
(C) $4a^6$
(D) $2a^5$
Question 12
Factor: $x^2 + 5x + 6$
(A) $(x+1)(x+6)$
(B) $(x+2)(x+3)$
(C) $(x-2)(x-3)$
(D) $(x+5)(x+1)$
Question 13
Solve: $3(x - 2) = 15$
(A) $x = 3$
(B) $x = 5$
(C) $x = 7$
(D) $x = 9$
Question 14
What is the y-intercept of $y = -3x + 7$?
(A) $-3$
(B) $3$
(C) $7$
(D) $-7$
Question 15
If $f(x) = 2x^2 - 3x + 1$, find $f(2)$.
(A) $1$
(B) $3$
(C) $5$
(D) $7$
Question 16
Solve: $x^2 + x - 12 = 0$
(A) $x = 3, -4$
(B) $x = 4, -3$
(C) $x = 6, -2$
(D) $x = -6, 2$
Question 17
Simplify: $\dfrac{x^2 - 1}{x - 1}$
(A) $x - 1$
(B) $x$
(C) $x + 1$
(D) $x^2$
Question 18
$\sqrt[3]{-27} = $
(A) $3$
(B) $-3$
(C) $9$
(D) undefined
Question 19
Solve: $\dfrac{2}{x} + 3 = 5$
(A) $x = 1$
(B) $x = 2$
(C) $x = \frac{1}{2}$
(D) $x = -1$
Question 20
Find the midpoint of $(2, 8)$ and $(6, 4)$.
(A) $(3, 5)$
(B) $(4, 6)$
(C) $(8, 12)$
(D) $(4, 4)$
Question 21
Convert $\dfrac{2\pi}{3}$ to degrees.
(A) $60°$
(B) $90°$
(C) $120°$
(D) $150°$
Question 22
$$\cos 45° = $$
(A) $\dfrac{1}{2}$
(B) $\dfrac{\sqrt{2}}{2}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $1$
Question 23
In a 30-60-90 triangle, if the shortest side is 5, find the hypotenuse.
(A) $5\sqrt{2}$
(B) $5\sqrt{3}$
(C) $10$
(D) $15$
Question 24
$$\sec 60° = $$
(A) $\dfrac{1}{2}$
(B) $1$
(C) $2$
(D) $\sqrt{2}$
Question 25
If $\sin\theta = \dfrac{5}{13}$, find $\cos\theta$ (first quadrant).
(A) $\dfrac{8}{13}$
(B) $\dfrac{12}{13}$
(C) $\dfrac{5}{12}$
(D) $\dfrac{13}{12}$
Question 26
Simplify: $\log_3 81$
(A) $3$
(B) $4$
(C) $9$
(D) $27$
Question 27
The area of a circle with radius 6 is:
(A) $12\pi$
(B) $24\pi$
(C) $36\pi$
(D) $6\pi$
Question 28
$$\sin 90° = $$
(A) $0$
(B) $\dfrac{1}{2}$
(C) $\dfrac{\sqrt{2}}{2}$
(D) $1$
Question 29
Solve: $5^{x} = 125$
(A) $x = 2$
(B) $x = 3$
(C) $x = 4$
(D) $x = 5$
Question 30
Which is equivalent to $\tan\theta$?
(A) $\dfrac{\cos\theta}{\sin\theta}$
(B) $\dfrac{\sin\theta}{\cos\theta}$
(C) $\sin\theta \cdot \cos\theta$
(D) $\dfrac{1}{\sin\theta}$
Question 31
Find the 10th term of the arithmetic sequence: $3, 7, 11, 15, \ldots$
(A) $39$
(B) $41$
(C) $43$
(D) $37$
Question 32
From the top of a building 50 ft tall, the angle of depression to a point on the ground is $30°$. How far is the point from the base?
(A) $25\sqrt{3}$ ft
(B) $50\sqrt{3}$ ft
(C) $\dfrac{50}{\sqrt{3}}$ ft
(D) $100$ ft
Question 33
Rationalize: $\dfrac{3}{\sqrt{5}}$
(A) $\dfrac{3\sqrt{5}}{5}$
(B) $\dfrac{\sqrt{5}}{3}$
(C) $\dfrac{3}{5}$
(D) $\dfrac{15}{5}$
Question 34
Solve: $|x + 4| \le 3$
(A) $-7 \le x \le -1$
(B) $-1 \le x \le 7$
(C) $x \le -1$ or $x \ge 7$
(D) $1 \le x \le 7$
Question 35
For $f(x) = x^2 + 4x + 4$, what is the axis of symmetry?
(A) $x = 2$
(B) $x = -2$
(C) $x = 4$
(D) $x = 0$
Question 36
Solve the system: $2x + 3y = 12$, $\;x - y = 1$
(A) $(3, 2)$
(B) $(2, 3)$
(C) $(4, 3)$
(D) $(1, 0)$
Question 37
$$\csc 30° = $$
(A) $\dfrac{1}{2}$
(B) $\sqrt{2}$
(C) $2$
(D) $\dfrac{2\sqrt{3}}{3}$
Question 38
A recipe requires $\frac{3}{4}$ cup of sugar for 12 cookies. How much sugar for 20 cookies?
(A) $1$ cup
(B) $1\frac{1}{4}$ cups
(C) $1\frac{1}{2}$ cups
(D) $\frac{5}{4}$ cups
Question 39
Evaluate: $\dbinom{6}{2}$
(A) $12$
(B) $15$
(C) $20$
(D) $30$
Question 40
Find the equation of a circle centered at $(0, 0)$ with radius 5.
(A) $x^2 + y^2 = 5$
(B) $x^2 + y^2 = 10$
(C) $x^2 + y^2 = 25$
(D) $(x-5)^2 + y^2 = 25$
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