UPEI Mathematics Assessment Test - Practice Test

QUESTION 1:

$\frac{8}{3}+\frac{11}{2} =$
(a) $~\frac{23}{9}$ (b) $~\frac{19}{5}$ (c) $~\frac{49}{6}$
(d) $~\frac{44}{3}$ (e) $~\frac{88}{7}$
QUESTION 2:

$\frac{(3^6 4^4)^{\frac{1}{2}}}{12^3} =$
(a) $~4$ (b) $~\frac{1}{4}$ (c) $~\frac{1}{2}$
(d) $~\frac{3}{4}$ (e) $~\sqrt{12}$
QUESTION 3:

$\frac{1}{\sqrt{11}-\sqrt{3}} =$
(a) $~\frac{1}{\sqrt{11}}-\frac{1}{\sqrt{3}}$ (b) $~\sqrt{11}+\sqrt{3}$ (c) $~\frac{\sqrt{11}-\sqrt{3}}{8}$
(d) $~\frac{\sqrt{11}+\sqrt{3}}{8}$ (e) $~\sqrt{8}$
QUESTION 4:

$\frac{x}{x+6}+\frac{6}{x-6} =$
(a) $~\frac{x+6}{2x}$ (b) $~\frac{x-6}{12}$ (c) $~\frac{x^2+36}{x^2-36}$
(d) $~\frac{1}{x-6}$ (e) $~\frac{6x}{x+6}$
QUESTION 5:

The following triangle is equiangular. Find the area of the triangle.


(a) $~6$ (b) $~3$ (c) $~\frac{3}{2}$
(d) $~\frac{\sqrt{3}}{2}$ (e) $~\sqrt{3}$
QUESTION 6:

$(x+4)(x+8) =$
(a) $x^2+12x-32$ (b) $~x+12$ (c) $~x^2-12x+32$
(d) $~x^2+12x+32$ (e) $~x^2+32$
QUESTION 7:

If $x^2-5x+6=0$ then $x=$
(a) $~3 \text{ only}$ (b) $~2 \text{ or } 3$ (c) $~-2 \text{ or } 3$
(d) $~-3 \text{ or } 2$ (e) $~-3 \text{ or } -2$
QUESTION 8:

If $x-3y=9$ and $-x+y=-11$ then $(x, y)$ =
(a) $~(12, 1)$ (b) $~(1, 12)$ (c) $~(-1, 12)$
(d) $~(-1, -12)$ (e) no solution
QUESTION 9:

If $y=(18x+4)^3$ then $x=$
(a) $~\frac{\sqrt[3]{y}+4}{\sqrt[3]{18}}$ (b) $~\frac{\sqrt[3]{y-4}}{18}$ (c) $~\frac{\sqrt[3]{y}-4}{18}$
(d) $~\sqrt[3]{\frac{y-4}{18}}$ (e) $~\frac{\sqrt[3]{y+4}}{18}$
QUESTION 10:

Find the remainder when $2x^4-x^2+3x-1$ is divided by $x-1$
(a) $~x+4$ (b) $~2x^3$ (c) $~3$
(d) $~2x^3+2x^2+x+4$ (e) $~4$
QUESTION 11:

If $|4x+2| > 10$ then
(a) $~-3 < x < 2$ (b) $~x < -3$ (c) $~x > 2 \text{ or } x < -3$
(d) $~x > -2 \text{ or } x < 3$ (e) $~x > -3$
QUESTION 12:

If $x^2+5x > 6$ then
(a) $~x < -6$ (b) $~x < -6 \text{ or } x > 1$ (c) $ ~ -1 < x < 6$
(d) $~x < -1 \text{ or } x > 6$ (e) No solution
QUESTION 13:

$(-2)^{k+3}=$
(a) $~(-2)^k-8$ (b) $~2^{-k-3}$ (c) $~-8(-2)^k$
(d) $~-8^{k}$ (e) None of these
QUESTION 14:

If $\ln(x^3) = 3\ln(7)-6\ln(4)$ then $x=$
(a) $~\frac{7}{4}$ (b) $~\frac{7}{16}$ (c) $~3$
(d) $~e^3$ (e) $~\frac{1}{16}$
QUESTION 15:

The distance between the points $(-4,2)$ and $(-1, 1)$ is
(a) $~\sqrt{5}$ (b) $~4$ (c) $~\sqrt{10}$
(d) $~2$ (e) $~3$
QUESTION 16:

The equation of the line through the points $(1,-3)$ and $(3,2)$ is
(a) $~y=2x-\frac{5}{2}$ (b) $~y=\frac{5}{2}x-3$ (c) $~y=2x+4$
(d) $~y=-5x+19$ (e) $~y=\frac{5x-11}{2}$
QUESTION 17:

What is a possible equation of the following graph?




(a) $y=x^2+x-12$ (b) $y=-x^2-x+12$ (c) $y=x^2-x+12$
(d) $y=-x^2+x+12$ (d) $y=x^2+8x+12$
QUESTION 18:

If $f(x) = 2x^3+x+12$ then $f(-2) =$
(a) $~-6$ (b) $~28$ (c) $~-2$
(d) $~14$ (e) $~0$
QUESTION 19:

What type of function is likely to be depicted in the following graph?



(a) Trigonometric (b) Polynomial (c) Exponential
(d) Logarithmic (e) Power
QUESTION 20:

If $g(x) = x^2+x$ then $g(x-h)$ =
(a) $~x^2+2xh+h^2+x-h$ (b) $~x^2-2xh+h^2-x+h$ (c) $~x^2+h^2+x-h$
(d) $~x^2-2xh+h^2+x-h$ (e) $~x-h$
QUESTION 21:

If $f(x) = \frac{8}{x+2}$, for what value of $x$ does $f(x)=5$?
(a) $~8$ (b) $~\frac{2}{5}$ (c) $~1$
(d) $~\frac{8}{7}$ (e) $~\frac{-2}{5}$
QUESTION 22:

What is the domain $D$ and range $R$ of the function $f(x)=3^x$?
(a) $D=(0, \infty); ~R=(-\infty, \infty)$ (b) $D=(-\infty, \infty); ~R=(-\infty, \infty)$ (c) $D=(-\infty, \infty); ~R=(0, \infty)$
(d) $D=(-\infty, 0); ~R=(-\infty, \infty)$ (e) $D=(0, \infty); ~R=(0, \infty)$
QUESTION 23:

How many times does the graph of the function $f(x)=(x^2-5)(x^2+1)(x-3)$ cross the $x$ - axis?
(a) Never (b) Once (c) Five times
(d) Four times (e) Three times
QUESTION 24:

An isosceles triangle has base length 6 cm. The other two sides measure 5 cm. The area of the triangle in $\text{cm}^2$ is
(a) $~6$ (b) $~24$ (c) $~12$
(d) $~15$ (e) Not enough information
QUESTION 25:

For a right triangle with sides of length $5, 12$ and $13$, with $\theta$ being the angle formed by the sides of length $12$ and $13$, $\tan(\theta) =$
(a) $~\frac{5}{12}$ (b) $~\frac{12}{13}$ (c) $~\frac{12}{5}$
(d) $~\frac{5}{13}$ (e) $~\frac{13}{5}$
QUESTION 26:

If $\cos(\theta) = \frac{3}{5}$ and $\theta$ is in the fourth quadrant, then $\sin(\theta)=$
(a) $~\frac{-4}{5}$ (b) $~\frac{4}{5}$ (c) $~\frac{5}{4}$
(d) $~\frac{-5}{4}$ (e) $~\frac{\sqrt{3}}{2}$
QUESTION 27:

How many degrees is $\frac{5\pi}{4}$ radians?
(a) $~50$ (b) $~90$ (c) $~120$
(d) $~225$ (e) $~95$
QUESTION 28:

If $\tan(\theta) = 1$ and $0 \leq \theta \leq 2 \pi$, then $\theta=$
(a) $~0$ (b) $~\frac{\pi}{4}$ (c) $~\frac{5\pi}{4}$
(d) $~\frac{\pi}{4} \text{ or } \frac{5\pi}{4}$ (e) $~\frac{1}{\sqrt{2}}$
QUESTION 29:

$\frac{\sin(x)}{\tan(x)} =$
(a) $~\cot(x)$ (b) $~\cos(x)$ (c) $~\sec(x)-\cos(x)$
(d) $~\cos(x)+\sec(x)$ (e) $~\csc(x)-\cos(x)$
QUESTION 30:

What is the exact value of $\arcsin(0.5)$ in radians? Note: This is the same as asking for the value of $\sin^{-1}(0.5)$.
(a) $\frac{\pi}{6}$ (b) $\frac{\pi}{3}$ (c) $30$
(d) Does not exist (e) Impossible without a calculator