Math Placement Test — Form E
Question 1
$$\frac{5}{9} \times \frac{3}{10} = $$
(A) $\dfrac{15}{90}$
(B) $\dfrac{1}{6}$
(C) $\dfrac{8}{19}$
(D) $\dfrac{1}{3}$
Question 2
$$2.7 + 0.35 + 1.006 = $$
(A) $4.006$
(B) $4.056$
(C) $4.15$
(D) $4.56$
Question 3
$$6\frac{1}{2} \div 1\frac{1}{4} = $$
(A) $4\frac{4}{5}$
(B) $5$
(C) $5\frac{1}{5}$
(D) $5\frac{1}{2}$
Question 4
$$(-6)^2 - 6^2 = $$
(A) $-72$
(B) $72$
(C) $0$
(D) $-36$
Question 5
What fraction of an hour is 45 minutes?
(A) $\dfrac{1}{2}$
(B) $\dfrac{3}{4}$
(C) $\dfrac{2}{3}$
(D) $\dfrac{4}{5}$
Question 6
Convert $0.\overline{3}$ to a fraction.
(A) $\dfrac{1}{3}$
(B) $\dfrac{3}{10}$
(C) $\dfrac{33}{100}$
(D) $\dfrac{3}{9}$
Question 7
$$\sqrt{98} = $$
(A) $7\sqrt{2}$
(B) $2\sqrt{49}$
(C) $49\sqrt{2}$
(D) $14$
Question 8
Simplify: $(3^2)^3 \div 3^4$
(A) $3$
(B) $9$
(C) $27$
(D) $81$
Question 9
A price increases from \$80 to \$100. What is the percent increase?
(A) $20\%$
(B) $25\%$
(C) $80\%$
(D) $125\%$
Question 10
Evaluate: $\dfrac{|-8| \cdot |3|}{|-6|}$
(A) $-4$
(B) $4$
(C) $\dfrac{8}{2}$
(D) $12$
Question 11
Simplify: $(x+2)(x^2 - 2x + 4)$
(A) $x^3 + 8$
(B) $x^3 - 8$
(C) $x^3 + 4x + 8$
(D) $x^3 + 2x^2 - 4$
Question 12
Factor: $6x^2 + x - 2$
(A) $(2x-1)(3x+2)$
(B) $(3x-1)(2x+2)$
(C) $(6x-2)(x+1)$
(D) $(3x+2)(2x-1)$
Question 13
Solve: $\dfrac{3}{x-1} = \dfrac{6}{x+2}$
(A) $x = 4$
(B) $x = -4$
(C) $x = 0$
(D) $x = 2$
Question 14
Write the equation of the line through $(0, -2)$ and $(4, 6)$.
(A) $y = 2x + 2$
(B) $y = 2x - 2$
(C) $y = -2x + 6$
(D) $y = \frac{1}{2}x - 2$
Question 15
If $h(x) = |2x - 5|$, find $h(1)$.
(A) $-3$
(B) $3$
(C) $7$
(D) $-7$
Question 16
The discriminant of $x^2 + 4x + 5 = 0$ is:
(A) $-4$
(B) $0$
(C) $4$
(D) $36$
Question 17
$i^2 = $? (where $i = \sqrt{-1}$)
(A) $1$
(B) $-1$
(C) $i$
(D) $-i$
Question 18
Simplify: $(2 + 3i)(1 - i)$
(A) $5 + i$
(B) $-1 + 5i$
(C) $5 - i$
(D) $-1 + i$
Question 19
Solve: $x^3 - x = 0$
(A) $x = 0$ only
(B) $x = 0, 1$
(C) $x = 0, 1, -1$
(D) $x = 1, -1$
Question 20
Find the center and radius: $x^2 + y^2 - 6x + 4y = 12$
(A) Center $(3,-2)$, $r = 5$
(B) Center $(-3,2)$, $r = 5$
(C) Center $(3,-2)$, $r = 25$
(D) Center $(6,-4)$, $r = 12$
Question 21
Convert $-45°$ to radians.
(A) $-\dfrac{\pi}{6}$
(B) $-\dfrac{\pi}{4}$
(C) $-\dfrac{\pi}{3}$
(D) $-\dfrac{\pi}{2}$
Question 22
$$\sin(-30°) = $$
(A) $\dfrac{1}{2}$
(B) $-\dfrac{1}{2}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $-\dfrac{\sqrt{3}}{2}$
Question 23
A 45-45-90 triangle has a hypotenuse of $10\sqrt{2}$. Find each leg.
(A) $5$
(B) $10$
(C) $5\sqrt{2}$
(D) $10\sqrt{2}$
Question 24
$$\sec 0° = $$
(A) $0$
(B) $1$
(C) undefined
(D) $-1$
Question 25
Solve: $2\sin\theta - 1 = 0$ for $0 \le \theta < 2\pi$.
(A) $\dfrac{\pi}{6}$ only
(B) $\dfrac{\pi}{6}, \dfrac{5\pi}{6}$
(C) $\dfrac{\pi}{3}, \dfrac{2\pi}{3}$
(D) $\dfrac{\pi}{6}, \dfrac{7\pi}{6}$
Question 26
Simplify: $\log_a(a^5)$
(A) $a$
(B) $5$
(C) $5a$
(D) $a^5$
Question 27
The volume of a sphere with radius 3 is:
(A) $12\pi$
(B) $27\pi$
(C) $36\pi$
(D) $\dfrac{4}{3}\pi(27)$
Question 28
$$\tan\left(\frac{\pi}{2}\right) = $$
(A) $0$
(B) $1$
(C) $-1$
(D) undefined
Question 29
If $\log_b 8 = 3$, find $b$.
(A) $2$
(B) $3$
(C) $4$
(D) $\sqrt{8}$
Question 30
Law of cosines: $c^2 = $?
(A) $a^2 + b^2$
(B) $a^2 + b^2 + 2ab\cos C$
(C) $a^2 + b^2 - 2ab\cos C$
(D) $a^2 - b^2 + 2ab\cos C$
Question 31
Find the 7th term of the geometric sequence: $2, 6, 18, 54, \ldots$
(A) $486$
(B) $1{,}458$
(C) $2{,}916$
(D) $4{,}374$
Question 32
Use the law of sines: In $\triangle ABC$, $A = 30°$, $a = 5$, $B = 60°$. Find $b$.
(A) $5\sqrt{3}$
(B) $10$
(C) $\dfrac{5\sqrt{3}}{2}$
(D) $\dfrac{10}{\sqrt{3}}$
Question 33
Rationalize: $\dfrac{1}{\sqrt{3}-1}$
(A) $\dfrac{\sqrt{3}+1}{2}$
(B) $\dfrac{\sqrt{3}-1}{2}$
(C) $\sqrt{3}+1$
(D) $\dfrac{1}{2}$
Question 34
Solve: $x^4 - 5x^2 + 4 = 0$
(A) $x = \pm 1, \pm 2$
(B) $x = 1, 4$
(C) $x = \pm 1$ only
(D) $x = \pm 2$ only
Question 35
The asymptotes of $y = \dfrac{1}{x-2}+3$ are:
(A) $x = 2$, $y = 3$
(B) $x = -2$, $y = -3$
(C) $x = 2$, $y = 0$
(D) $x = 0$, $y = 3$
Question 36
Solve: $2^{x+1} = 16$
(A) $x = 2$
(B) $x = 3$
(C) $x = 4$
(D) $x = 7$
Question 37
$$\cos\left(\frac{3\pi}{4}\right) = $$
(A) $\dfrac{\sqrt{2}}{2}$
(B) $-\dfrac{\sqrt{2}}{2}$
(C) $\dfrac{1}{2}$
(D) $-\dfrac{1}{2}$
Question 38
Compound interest: \$1,000 at 5% compounded annually for 3 years. Find the amount.
(A) $\$1{,}150.00$
(B) $\$1{,}157.63$
(C) $\$1{,}160.00$
(D) $\$1{,}215.51$
Question 39
How many 3-letter combinations from the word MATH?
(A) $4$
(B) $6$
(C) $12$
(D) $24$
Question 40
If $\sin\theta = \cos\theta$, which values of $\theta$ satisfy this for $0 \le \theta < 2\pi$?
(A) $\dfrac{\pi}{4}$ only
(B) $\dfrac{\pi}{4}, \dfrac{5\pi}{4}$
(C) $\dfrac{\pi}{4}, \dfrac{3\pi}{4}$
(D) $0, \pi$
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