Math Placement Test — Form A
Question 1
$$391 \div 23 = $$
(A) $15$
(B) $17$
(C) $19$
(D) $21$
Question 2
$$\frac{2}{5} + \frac{1}{3} = $$
(A) $\dfrac{3}{8}$
(B) $\dfrac{11}{15}$
(C) $\dfrac{7}{15}$
(D) $\dfrac{1}{2}$
Question 3
$$3\frac{1}{4} - 1\frac{2}{3} = $$
(A) $1\frac{7}{12}$
(B) $2\frac{1}{3}$
(C) $1\frac{1}{2}$
(D) $2\frac{7}{12}$
Question 4
$$0.045 \times 2.4 = $$
(A) $0.108$
(B) $0.0108$
(C) $1.08$
(D) $0.18$
Question 5
Round $4{,}738.065$ to the nearest tenth.
(A) $4{,}738.1$
(B) $4{,}738.0$
(C) $4{,}738.07$
(D) $4{,}740$
Question 6
Express $0.00042$ in scientific notation.
(A) $4.2 \times 10^{-4}$
(B) $42 \times 10^{-5}$
(C) $4.2 \times 10^{-3}$
(D) $0.42 \times 10^{-3}$
Question 7
$$\sqrt{72} = $$
(A) $6\sqrt{2}$
(B) $8\sqrt{3}$
(C) $3\sqrt{8}$
(D) $36\sqrt{2}$
Question 8
$$(-3)^4 = $$
(A) $-81$
(B) $81$
(C) $-12$
(D) $12$
Question 9
$$\frac{3}{4} \div \frac{5}{8} = $$
(A) $\dfrac{15}{32}$
(B) $\dfrac{6}{5}$
(C) $\dfrac{5}{6}$
(D) $\dfrac{24}{20}$
Question 10
What is 15% of 240?
(A) $32$
(B) $34$
(C) $36$
(D) $38$
Question 11
$$|{-7}| - |{3}| = $$
(A) $-10$
(B) $-4$
(C) $4$
(D) $10$
Question 12
Simplify: $3x^2 \cdot 4x^3$
(A) $12x^5$
(B) $12x^6$
(C) $7x^5$
(D) $7x^6$
Question 13
Factor completely: $x^2 - 9$
(A) $(x-3)^2$
(B) $(x+3)(x-3)$
(C) $(x-9)(x+1)$
(D) $x(x-9)$
Question 14
If $\;\dfrac{x}{4} = \dfrac{9}{12}\;$, find $x$.
(A) $2$
(B) $3$
(C) $4$
(D) $6$
Question 15
Solve: $2x - 5 = 11$
(A) $x=3$
(B) $x=6$
(C) $x=8$
(D) $x=16$
Question 16
What is the slope of the line passing through $(2, 5)$ and $(6, 13)$?
(A) $1$
(B) $2$
(C) $4$
(D) $8$
Question 17
Solve the system: $x + y = 7$, $\;x - y = 3$
(A) $(5, 2)$
(B) $(4, 3)$
(C) $(3, 4)$
(D) $(2, 5)$
Question 18
Factor: $2x^2 + 7x + 3$
(A) $(2x+1)(x+3)$
(B) $(2x+3)(x+1)$
(C) $(2x-1)(x-3)$
(D) $(x+3)(2x-1)$
Question 19
Solve: $x^2 - 5x + 6 = 0$
(A) $x=1, 6$
(B) $x=2, 3$
(C) $x=-2, -3$
(D) $x=-1, 6$
Question 20
Simplify: $\dfrac{x^2 - 4}{x + 2}$
(A) $x+2$
(B) $x-2$
(C) $x^2 - 2$
(D) $\dfrac{x-4}{2}$
Question 21
Convert $150°$ to radians.
(A) $\dfrac{5\pi}{6}$
(B) $\dfrac{3\pi}{4}$
(C) $\dfrac{2\pi}{3}$
(D) $\dfrac{\pi}{3}$
Question 22
$$\sin 30° = $$
(A) $\dfrac{\sqrt{3}}{2}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{\sqrt{2}}{2}$
(D) $1$
Question 23
In a right triangle with legs 5 and 12, the hypotenuse is:
(A) $11$
(B) $13$
(C) $15$
(D) $17$
Question 24
$$\tan 45° = $$
(A) $0$
(B) $\dfrac{1}{2}$
(C) $1$
(D) $\sqrt{2}$
Question 25
If $\cos\theta = \dfrac{3}{5}$, find $\sin\theta$ (first quadrant).
(A) $\dfrac{4}{5}$
(B) $\dfrac{3}{4}$
(C) $\dfrac{5}{4}$
(D) $\dfrac{2}{5}$
Question 26
Simplify: $\dfrac{2^5 \cdot 2^3}{2^4}$
(A) $2^4$
(B) $2^6$
(C) $2^{12}$
(D) $2^2$
Question 27
Find the arc length of a sector with radius 10 and central angle $\dfrac{\pi}{3}$.
(A) $\dfrac{10\pi}{3}$
(B) $\dfrac{5\pi}{3}$
(C) $10\pi$
(D) $\dfrac{20\pi}{3}$
Question 28
$$\cos 60° = $$
(A) $\dfrac{\sqrt{3}}{2}$
(B) $\dfrac{1}{2}$
(C) $\dfrac{\sqrt{2}}{2}$
(D) $0$
Question 29
If $\log_2 x = 5$, then $x = $
(A) $10$
(B) $25$
(C) $32$
(D) $64$
Question 30
Which identity is correct?
(A) $\sin^2\theta + \cos^2\theta = 1$
(B) $\sin^2\theta - \cos^2\theta = 1$
(C) $\sin\theta + \cos\theta = 1$
(D) $\tan^2\theta + 1 = \sec\theta$
Question 31
Evaluate: $\displaystyle\sum_{k=1}^{5} (2k-1)$
(A) $15$
(B) $20$
(C) $25$
(D) $30$
Question 32
A ladder 20 ft long leans against a wall making a $60°$ angle with the ground. How high up the wall does the ladder reach?
(A) $10$ ft
(B) $10\sqrt{3}$ ft
(C) $15$ ft
(D) $20\sqrt{3}$ ft
Question 33
Simplify: $\sqrt{50} + \sqrt{18}$
(A) $\sqrt{68}$
(B) $8\sqrt{2}$
(C) $4\sqrt{17}$
(D) $6\sqrt{3}$
Question 34
Solve: $|2x - 1| = 7$
(A) $x = 4$ only
(B) $x = -3$ only
(C) $x = 4$ or $x = -3$
(D) $x = 3$ or $x = -4$
Question 35
Find the vertex of $y = x^2 - 6x + 5$.
(A) $(3, -4)$
(B) $(-3, -4)$
(C) $(3, 4)$
(D) $(6, 5)$
Question 36
Write the equation of the line with slope $-2$ passing through $(1, 3)$.
(A) $y = -2x + 5$
(B) $y = -2x + 1$
(C) $y = 2x + 1$
(D) $y = -2x - 5$
Question 37
$$\cot 30° = $$
(A) $\dfrac{1}{\sqrt{3}}$
(B) $\sqrt{3}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $2$
Question 38
A store marks up an item 40% over its \$50 wholesale cost. What is the retail price?
(A) $\$65$
(B) $\$70$
(C) $\$75$
(D) $\$90$
Question 39
Evaluate: $\dfrac{3!\cdot 4!}{5!}$
(A) $\dfrac{1}{5}$
(B) $\dfrac{6}{5}$
(C) $\dfrac{12}{5}$
(D) $\dfrac{24}{5}$
Question 40
Find the distance between the points $(-1, 2)$ and $(3, 5)$.
(A) $4$
(B) $5$
(C) $\sqrt{7}$
(D) $7$
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