Math Placement Test — Form D
Question 1
$$\frac{3}{7} + \frac{2}{7} = $$
(A) $\dfrac{5}{14}$
(B) $\dfrac{5}{7}$
(C) $\dfrac{6}{7}$
(D) $1$
Question 2
Convert $\frac{7}{20}$ to a decimal.
(A) $0.35$
(B) $0.37$
(C) $0.7$
(D) $3.5$
Question 3
$$4\frac{1}{3} \times 2\frac{1}{4} = $$
(A) $8\frac{1}{12}$
(B) $9$
(C) $9\frac{3}{4}$
(D) $8\frac{3}{4}$
Question 4
$$(-8) + (-5) - (-3) = $$
(A) $-10$
(B) $-16$
(C) $-6$
(D) $0$
Question 5
Find the GCF of $36$ and $54$.
(A) $6$
(B) $9$
(C) $12$
(D) $18$
Question 6
Express $\dfrac{2}{3}$ as a percentage.
(A) $60\%$
(B) $66.\overline{6}\%$
(C) $67\%$
(D) $75\%$
Question 7
$$\sqrt[3]{64} = $$
(A) $2$
(B) $4$
(C) $8$
(D) $16$
Question 8
Simplify: $\dfrac{x^{-2}}{x^{-5}}$
(A) $x^{-7}$
(B) $x^{-3}$
(C) $x^3$
(D) $x^7$
Question 9
The LCM of 12 and 18 is:
(A) $24$
(B) $36$
(C) $54$
(D) $72$
Question 10
Evaluate: $5 + 3 \times 2^2 - 1$
(A) $16$
(B) $31$
(C) $12$
(D) $20$
Question 11
Combine: $\dfrac{1}{x} + \dfrac{1}{x+1}$
(A) $\dfrac{2}{2x+1}$
(B) $\dfrac{2x+1}{x(x+1)}$
(C) $\dfrac{x+1}{x}$
(D) $\dfrac{2}{x^2+x}$
Question 12
Factor: $x^3 - 8$
(A) $(x-2)(x^2+2x+4)$
(B) $(x-2)(x^2-2x+4)$
(C) $(x-2)^3$
(D) $(x+2)(x^2-4)$
Question 13
Solve: $\dfrac{x+1}{3} = \dfrac{x-2}{4}$
(A) $x = 10$
(B) $x = -10$
(C) $x = 7$
(D) $x = -7$
Question 14
The lines $y = 2x + 1$ and $y = 2x - 3$ are:
(A) Perpendicular
(B) Parallel
(C) Identical
(D) Intersecting at one point
Question 15
Find the inverse of $f(x) = 3x + 6$.
(A) $f^{-1}(x) = \dfrac{x-6}{3}$
(B) $f^{-1}(x) = \dfrac{x+6}{3}$
(C) $f^{-1}(x) = \dfrac{1}{3x+6}$
(D) $f^{-1}(x) = 3x - 6$
Question 16
Solve: $2x^2 - 5x - 3 = 0$
(A) $x = 3, -\frac{1}{2}$
(B) $x = -3, \frac{1}{2}$
(C) $x = 3, \frac{1}{2}$
(D) $x = -3, -\frac{1}{2}$
Question 17
Simplify: $\dfrac{x^2-4x+4}{x^2-4}$
(A) $\dfrac{x-2}{x+2}$
(B) $\dfrac{x+2}{x-2}$
(C) $1$
(D) $\dfrac{(x-2)^2}{(x-2)(x+2)}$
Question 18
Solve: $4^x = 64$
(A) $x = 2$
(B) $x = 3$
(C) $x = 4$
(D) $x = 16$
Question 19
If $\log x + \log 5 = 2$, find $x$.
(A) $4$
(B) $20$
(C) $50$
(D) $95$
Question 20
Find the distance between $(-3, 1)$ and $(5, 7)$.
(A) $8$
(B) $10$
(C) $\sqrt{100}$
(D) Both B and C
Question 21
$$\sin\left(\frac{\pi}{4}\right) = $$
(A) $\dfrac{1}{2}$
(B) $\dfrac{\sqrt{2}}{2}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $1$
Question 22
If $\cos\theta = -\dfrac{1}{2}$ and $\pi < \theta < 2\pi$, then $\theta = $
(A) $\dfrac{2\pi}{3}$
(B) $\dfrac{4\pi}{3}$
(C) $\dfrac{5\pi}{3}$
(D) $\dfrac{\pi}{3}$
Question 23
An isosceles right triangle has legs of length 7. Find the hypotenuse.
(A) $7$
(B) $7\sqrt{2}$
(C) $7\sqrt{3}$
(D) $14$
Question 24
$$\csc 45° = $$
(A) $1$
(B) $\sqrt{2}$
(C) $\dfrac{\sqrt{2}}{2}$
(D) $2$
Question 25
If $\tan\theta = \dfrac{3}{4}$ and $\theta$ is in Quadrant I, find $\sec\theta$.
(A) $\dfrac{5}{4}$
(B) $\dfrac{5}{3}$
(C) $\dfrac{4}{3}$
(D) $\dfrac{4}{5}$
Question 26
Simplify: $\ln e^4$
(A) $1$
(B) $e$
(C) $4$
(D) $4e$
Question 27
Find the area of a triangle with base 10 and height 7.
(A) $17$
(B) $35$
(C) $70$
(D) $34$
Question 28
The range of $y = \cos x$ is:
(A) $[0, 1]$
(B) $[-1, 1]$
(C) $(-\infty, \infty)$
(D) $[0, 2\pi]$
Question 29
Solve: $\log_5(x-1) = 2$
(A) $x = 10$
(B) $x = 24$
(C) $x = 26$
(D) $x = 6$
Question 30
Half-angle identity: $\cos\left(\dfrac{\theta}{2}\right) = $?
(A) $\pm\sqrt{\dfrac{1+\cos\theta}{2}}$
(B) $\dfrac{\cos\theta}{2}$
(C) $\pm\sqrt{\dfrac{1-\cos\theta}{2}}$
(D) $\cos^2\theta$
Question 31
Find the sum: $\displaystyle\sum_{k=1}^{4} k^2$
(A) $10$
(B) $20$
(C) $30$
(D) $24$
Question 32
Two ships leave a dock. Ship A sails N $30°$ E at 20 mph, Ship B sails due east at 15 mph. After 2 hours, how far apart are they? (use law of cosines)
(A) $30$ mi
(B) $35.6$ mi
(C) $25\sqrt{2}$ mi
(D) $40.3$ mi
Question 33
Simplify: $\left(\dfrac{8}{27}\right)^{2/3}$
(A) $\dfrac{2}{3}$
(B) $\dfrac{4}{9}$
(C) $\dfrac{16}{81}$
(D) $\dfrac{8}{9}$
Question 34
Solve the inequality: $\dfrac{x-1}{x+2} > 0$
(A) $x > 1$
(B) $x < -2$ or $x > 1$
(C) $-2 < x < 1$
(D) $x > -2$
Question 35
What transformation takes $y = x^2$ to $y = (x-3)^2 + 2$?
(A) Left 3, up 2
(B) Right 3, up 2
(C) Right 3, down 2
(D) Left 3, down 2
Question 36
Solve: $e^{2x} = 7$
(A) $x = \ln 7$
(B) $x = \dfrac{\ln 7}{2}$
(C) $x = 2\ln 7$
(D) $x = \dfrac{7}{e^2}$
Question 37
$$\cos\left(\frac{\pi}{3}\right) = $$
(A) $\dfrac{1}{2}$
(B) $\dfrac{\sqrt{2}}{2}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $0$
Question 38
A car depreciates 15% per year. If it's worth \$20,000 now, what is its value in 3 years?
(A) $\$12{,}282.50$
(B) $\$14{,}450$
(C) $\$11{,}000$
(D) $\$10{,}000$
Question 39
How many ways can 4 books be arranged on a shelf?
(A) $4$
(B) $12$
(C) $16$
(D) $24$
Question 40
The amplitude of $y = -3\sin(x) + 1$ is:
(A) $-3$
(B) $1$
(C) $3$
(D) $4$
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