Math Placement Test — Form C
Question 1
$$1{,}008 \div 42 = $$
(A) $22$
(B) $24$
(C) $26$
(D) $28$
Question 2
$$\frac{7}{8} \times \frac{4}{5} = $$
(A) $\dfrac{28}{40}$
(B) $\dfrac{7}{10}$
(C) $\dfrac{11}{13}$
(D) $\dfrac{4}{8}$
Question 3
$$5\frac{1}{6} - 2\frac{3}{4} = $$
(A) $2\frac{5}{12}$
(B) $3\frac{1}{4}$
(C) $2\frac{1}{3}$
(D) $3\frac{5}{12}$
Question 4
$$3.6 \div 0.09 = $$
(A) $4$
(B) $0.4$
(C) $40$
(D) $400$
Question 5
Express the ratio $12 : 8$ in simplest form.
(A) $6:4$
(B) $3:2$
(C) $4:3$
(D) $2:1$
Question 6
$$(-5)(-4)(-2) = $$
(A) $40$
(B) $-40$
(C) $20$
(D) $-20$
Question 7
Simplify: $\sqrt{45} + \sqrt{20}$
(A) $\sqrt{65}$
(B) $5\sqrt{5}$
(C) $7\sqrt{5}$
(D) $13$
Question 8
Evaluate: $2^{-3}$
(A) $-8$
(B) $-6$
(C) $\dfrac{1}{8}$
(D) $\dfrac{1}{6}$
Question 9
A shirt originally costs \$60 and is 25% off. What is the sale price?
(A) $\$35$
(B) $\$40$
(C) $\$45$
(D) $\$50$
Question 10
Evaluate: $-3 + 8 \times 2 - 4$
(A) $6$
(B) $9$
(C) $14$
(D) $-12$
Question 11
Simplify: $\dfrac{6x^3 y^2}{3x y^4}$
(A) $2x^2 y^{-2}$
(B) $\dfrac{2x^2}{y^2}$
(C) $2x^3 y^2$
(D) Both A and B
Question 12
Factor: $3x^2 - 12$
(A) $3(x-2)(x+2)$
(B) $3(x-4)$
(C) $(3x-6)(x+2)$
(D) $3x(x-4)$
Question 13
Solve: $4(x + 1) - 2x = 10$
(A) $x = 2$
(B) $x = 3$
(C) $x = 4$
(D) $x = 5$
Question 14
The line $3x + 2y = 12$ has slope:
(A) $\dfrac{3}{2}$
(B) $-\dfrac{3}{2}$
(C) $\dfrac{2}{3}$
(D) $-\dfrac{2}{3}$
Question 15
If $g(x) = \sqrt{x + 9}$, find $g(16)$.
(A) $4$
(B) $5$
(C) $7$
(D) $25$
Question 16
Solve using the quadratic formula: $x^2 + 2x - 8 = 0$
(A) $x = 2, -4$
(B) $x = -2, 4$
(C) $x = 1, -8$
(D) $x = 4, -2$
Question 17
Simplify: $\dfrac{2x+6}{x^2-9}$
(A) $\dfrac{2}{x+3}$
(B) $\dfrac{2}{x-3}$
(C) $\dfrac{2x}{x-3}$
(D) $\dfrac{6}{x^2}$
Question 18
Solve: $\sqrt{2x + 1} = 5$
(A) $x = 2$
(B) $x = 8$
(C) $x = 12$
(D) $x = 13$
Question 19
If $f(x) = 3x - 1$ and $g(x) = x^2$, find $f(g(2))$.
(A) $5$
(B) $9$
(C) $11$
(D) $25$
Question 20
Find the slope of a line perpendicular to $y = \dfrac{2}{3}x + 1$.
(A) $\dfrac{2}{3}$
(B) $-\dfrac{2}{3}$
(C) $\dfrac{3}{2}$
(D) $-\dfrac{3}{2}$
Question 21
Convert $315°$ to radians.
(A) $\dfrac{5\pi}{4}$
(B) $\dfrac{7\pi}{4}$
(C) $\dfrac{3\pi}{2}$
(D) $\dfrac{9\pi}{4}$
Question 22
$$\sin 60° = $$
(A) $\dfrac{1}{2}$
(B) $\dfrac{\sqrt{2}}{2}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $1$
Question 23
A right triangle has hypotenuse 17 and one leg 8. Find the other leg.
(A) $9$
(B) $12$
(C) $15$
(D) $\sqrt{225}$
Question 24
In which quadrant is $\sin\theta > 0$ and $\cos\theta < 0$?
(A) I
(B) II
(C) III
(D) IV
Question 25
$$\tan 60° = $$
(A) $\dfrac{1}{\sqrt{3}}$
(B) $1$
(C) $\sqrt{3}$
(D) $2$
Question 26
Simplify: $(x+3)^2$
(A) $x^2 + 9$
(B) $x^2 + 3x + 9$
(C) $x^2 + 6x + 9$
(D) $2x + 6$
Question 27
The circumference of a circle with diameter 14 is:
(A) $7\pi$
(B) $14\pi$
(C) $28\pi$
(D) $49\pi$
Question 28
$$\cos 0° = $$
(A) $0$
(B) $\dfrac{1}{2}$
(C) $\dfrac{\sqrt{2}}{2}$
(D) $1$
Question 29
Solve: $e^x = 1$
(A) $x = -1$
(B) $x = 0$
(C) $x = 1$
(D) $x = e$
Question 30
Double angle: $\sin(2\theta) = $?
(A) $2\sin\theta$
(B) $\sin^2\theta$
(C) $2\sin\theta\cos\theta$
(D) $\cos 2\theta$
Question 31
Find the sum of the geometric series: $4 + 2 + 1 + \frac{1}{2} + \cdots$ (infinite).
(A) $6$
(B) $7$
(C) $8$
(D) $10$
Question 32
A flagpole casts a 40 ft shadow when the angle of elevation of the sun is $35°$. Find the height of the pole. $(\tan 35° \approx 0.7)$
(A) $20$ ft
(B) $28$ ft
(C) $32$ ft
(D) $56$ ft
Question 33
Simplify: $\dfrac{\sqrt{12}}{\sqrt{3}}$
(A) $\sqrt{4}$
(B) $2$
(C) $\sqrt{3}$
(D) $4$
Question 34
Solve: $x^2 - 2x \ge 0$
(A) $x \le 0$ or $x \ge 2$
(B) $0 \le x \le 2$
(C) $x \ge 2$
(D) $x \le -2$ or $x \ge 0$
Question 35
The domain of $f(x) = \dfrac{1}{x-3}$ is:
(A) All reals
(B) $x \ne 0$
(C) $x \ne 3$
(D) $x > 3$
Question 36
Solve: $\ln x = 2$
(A) $x = 2$
(B) $x = e$
(C) $x = e^2$
(D) $x = 10$
Question 37
$$\sin\left(\frac{\pi}{6}\right) = $$
(A) $\dfrac{1}{2}$
(B) $\dfrac{\sqrt{2}}{2}$
(C) $\dfrac{\sqrt{3}}{2}$
(D) $1$
Question 38
A train travels at 55 mph. How far does it go in 2 hours 30 minutes?
(A) $110$ mi
(B) $127.5$ mi
(C) $137.5$ mi
(D) $145$ mi
Question 39
Evaluate: $P(5,2)$ (permutation).
(A) $10$
(B) $20$
(C) $25$
(D) $60$
Question 40
What is the period of $y = \sin(2x)$?
(A) $\pi$
(B) $2\pi$
(C) $4\pi$
(D) $\dfrac{\pi}{2}$
—
Your Score
0 Correct
0 Incorrect
0 Unanswered