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:

$\frac{(2^6 3^9)^{\frac{1}{3}}}{6^3} =$
(a) $~2$ (b) $~\frac{1}{3}$ (c) $~\frac{1}{2}$
(d) $~\frac{2}{3}$ (e) $~\sqrt[3]{6}$
QUESTION 3:

$\frac{1}{\sqrt{10}+\sqrt{6}} =$
(a) $~\frac{1}{\sqrt{10}}+\frac{1}{\sqrt{6}}$ (b) $~\frac{\sqrt{10}+\sqrt{6}}{4}$ (c) $~\frac{\sqrt{10}-\sqrt{6}}{4}$
(d) $~\frac{1}{4}$ (e) $~4$
QUESTION 4:

$\frac{2}{x-3}+\frac{2}{x+3} =$
(a) $~\frac{4x+12}{x^2-9}$ (b) $~\frac{2}{x}$ (c) $~0$
(d) $~\frac{4x}{x^2-9}$ (e) $~-\frac{1}{3}$
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:

$(x+3)(x-6) =$
(a) $x^2+3x+18$ (b) $~x^2-3x-18$ (c) $~x^2-3x+18$
(d) $~x^2-18$ (e) $~x-3$
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 $y=(4x-1)^5$ then $x=$
(a) $~\frac{\sqrt[5]{y}-1}{\sqrt[5]{4}}$ (b) $~\frac{\sqrt[5]{y}+1}{4}$ (c) $~\frac{y-1}{\sqrt[5]{4}}$
(d) $~\sqrt[5]{\frac{4y-1}{4}}$ (e) $~\frac{\sqrt[5]{y-4}}{4}$
QUESTION 10:

Find the remainder when $x^3+2x^2+4$ is divided by $x+1$
(a) $~5$ (b) $~x^2$ (c) $~x-1$
(d) $~x^2+x-1$ (e) $~-1$
QUESTION 11:

If $|-2x+5| > 9$ then
(a) $~x < 2$ (b) $~-2 < x < 7$ (c) $~x > 2 \text{ or } x < -7$
(d) $~x < -2 \text{ or } x > 7$ (e) $~x > -7$
QUESTION 12:

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

Which of the following numbers is closest to $\log_5(26)$?
(a) $~0$ (b) $~1$ (c) $~2$
(d) $~3$ (e) $~4$
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) Power (b) Exponential (c) Logarithmic
(d) Polynomial (e) Trigonometric
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 $f(x) = \frac{1}{x+7}$, for what value of $x$ does $f(x)=6$?
(a) $~\frac{1}{13}$ (b) $~\frac{6}{7}$ (c) $~13$
(d) $~\frac{-41}{6}$ (e) $~6$
QUESTION 22:

What is the domain $D$ and range $R$ of the function $f(x)=\cos(x)$?
(a) $D=[-1, 1]; ~R=(-\infty, \infty)$ (b) $D=(-\infty, \infty); ~R=[-1, 1]$ (c) $D=(-\infty, \infty); ~R=(-\infty, \infty)$
(d) $D=[-1, 1]; ~R=[-1, 1]$ (e) $D=[0, \infty); ~R=[-1, 1]$
QUESTION 23:

Let $f(x)$ be the function obtained when the graph of the function $y=\sqrt{x}$ is shifted 1 unit to the right 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:

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 $13$, $\cos(\theta) =$
(a) $~\frac{5}{12}$ (b) $~\frac{12}{13}$ (c) $~\frac{12}{5}$
(d) $~\frac{5}{13}$ (e) $~\frac{13}{5}$
QUESTION 26:

If $\sin(\theta) = \frac{2}{5}$ and $\theta$ is in the second quadrant, then $\cos(\theta)=$
(a) $~\frac{34}{5}$ (b) $~\frac{5}{\sqrt{21}}$ (c) $~\frac{\sqrt{21}}{5}$
(d) $~\frac{-2}{5}$ (e) $~\frac{-\sqrt{21}}{5}$
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 $\tan(\theta)$.
(a) $~\frac{-1}{\sqrt{3}}$ (b) $~\frac{-1}{\sqrt{2}}$ (c) $~-\sqrt{3}$
(d) $~\sqrt{3}$ (e) $~\frac{1}{\sqrt{3}}$
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