UPEI Mathematics Assessment Test - Practice Test

QUESTION 1:

$\frac{5}{3}-\frac{9}{4} =$
(a) $~\frac{7}{12}$ (b) $~4$ (c) $~-4$
(d) $~\frac{45}{12}$ (e) $~-\frac{7}{12}$
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:

$\frac{x}{x-8}-\frac{x}{x+8} =$
(a) $~-\frac{x}{16}$ (b) $~1$ (c) $~0$
(d) $~\frac{x^2+8}{x^2-64}$ (e) $~\frac{16x}{x^2-64}$
QUESTION 5:

In the following diagram, line $BE$ is parallel to line $CD$. Find the length of the line $AC$.


(a) $~4$ (b) $~5$ (c) $~10$
(d) $~\sqrt{10}$ (e) Not enough information
QUESTION 6:

$(x+1)(x-5) =$
(a) $~x^2-4x-5$ (b) $~x^2+4x-5$ (c) $~x^2+4x+5$
(d) $~x^2-5$ (e) $~x-4$
QUESTION 7:

If $x^2-7x-18=0$ then $x=$
(a) $~-9 \text{ or } 2$ (b) $~9 \text{ or } 2$ (c) $~9 \text{ only}$
(d) $~-9 \text{ or } -2$ (e) $~9 \text{ or } -2$
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 $y=(7x+5)^3$ then $x=$
(a) $~\frac{\sqrt[3]{y}-5}{7}$ (b) $~\frac{\sqrt[3]{y-5}}{7}$ (c) $~\frac{y+5}{\sqrt[3]{7}}$
(d) $~\sqrt[3]{\frac{y-5}{7}}$ (e) $~\frac{\sqrt[3]{y}+7}{5}$
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 $|-6x+5| \leq 11$ then
(a) $~x \geq -1$ (b) $~x \leq 8$ (c) $~x \geq -1 \text{ or } x \leq \frac{8}{3}$
(d) $~x \leq \frac{8}{3}$ (e) $~-1 \leq x \leq \frac{8}{3}$
QUESTION 12:

If $x^2+3 < 4x$ then
(a) $~x < 1$ (b) $~x < 3 \text{ or } x > 1$ (c) $~1 < x < 3$
(d) $~x < -3 \text{ or } x > -1$ (e) No solution
QUESTION 13:

$4(2^k)=$
(a) $~8^{k}$ (b) $~2^{k+2}$ (c) $~6^k$
(d) $~4^{2k}$ (e) None of these
QUESTION 14:

Find the exact value of $\log_{3}(6)+\log_{3}(15)-2\log_{3}(\sqrt{10})$
(a) $~2$ (b) $~\frac{2}{3}$ (c) $~1$
(d) $~0$ (e) Impossible without a calculator
QUESTION 15:

The distance between the points $(-2,9)$ and $(-3, 15)$ is
(a) $~\sqrt{37}$ (b) $~\sqrt{35}$ (c) $~7$
(d) $~5$ (e) $~\sqrt{5}$
QUESTION 16:

The equation of the line through the points $(4,-1)$ and $(-6,-1)$ is
(a) $~y=10x$ (b) $~y=-1$ (c) $~y=-10x-6$
(d) $~y=-10x+6$ (e) Undefined equation
QUESTION 17:

The equation $x^2+(y-2)^2=25$ will generate what kind of graph?
(a) Parabola (b) Line (c) Hyperbola
(d) Circle (e) Ellipse
QUESTION 18:

If $f(x) = x^3-2x-15$ then $f(3) =$
(a) $~9$ (b) $~18$ (c) $~-12$
(d) $~6$ (e) $~-4$
QUESTION 19:

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



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

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

Let $f(x)$ be the function obtained when the graph of the function $y=\sqrt{x}$ is shifted 1 unit to the left and then shifted 10 units upwards. Find a formula for $f(x)$.
(a) $~\sqrt{x+1}+10$ (b) $~\sqrt{x-1}+10$ (c) $~10\sqrt{x+1}$
(d) $~\sqrt{x+10}+1$ (e) $~\sqrt{x-10}+1$
QUESTION 24:

What is the next number in the following sequence? $S = \{1,1,2,3,5,8,13,...\}$
(a) $~18$ (b) $~26$ (c) $~19$
(d) $~21$ (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:

What is the radian measure of an angle of $100$ degrees, starting at the positive $x$ - axis, and traversed in the clockwise direction?
(a) $~\frac{5\pi}{9}$ (b) $~\frac{-5\pi}{9}$ (c) $~\frac{9\pi}{5}$
(d) $~\frac{-9\pi}{5}$ (e) You can't measure angles clockwise
QUESTION 28:

An angle $\theta$ measures $\frac{2\pi}{3}$ radians. Find $\sin(\theta)$.
(a) $~\frac{-1}{2}$ (b) $~\frac{\sqrt{3}}{2}$ (c) $\frac{-\sqrt{3}}{2}$
(d) $\frac{-1}{\sqrt{2}}$ (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 $\arccos(2)$ in radians? Note: This is the same as asking for the value of $\cos^{-1}(2)$.
(a) $\frac{\pi}{6}$ (b) $\frac{\pi}{3}$ (c) $30$
(d) Does not exist (e) Impossible without a calculator