UPEI Mathematics Assessment Test - Practice Test

QUESTION 1:

$\frac{2}{7}-\frac{1}{12} =$
(a) $~-\frac{1}{41}$ (b) $~\frac{1}{5}$ (c) $~\frac{33}{21}$
(d) $~\frac{17}{84}$ (e) $~-\frac{1}{5}$
QUESTION 2:

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

$\frac{1}{\sqrt{5}-\sqrt{3}} =$
(a) $~\frac{\sqrt{5}+\sqrt{3}}{2}$ (b) $~\frac{1}{\sqrt{5}}-\frac{1}{\sqrt{3}}$ (c) $~\frac{\sqrt{5}+\sqrt{3}}{8}$
(d) $~\frac{1}{\sqrt{2}}$ (e) $~\sqrt{2}$
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 triangle, find the length of the side marked $x$.


(a) $~\sqrt{45}$ (b) $~45$ (c) $~5$
(d) $~25$ (e) $~\sqrt{193}$
QUESTION 6:

$(x-3)(x-7) =$
(a) $x^2+21$ (b) $~x^2+10x-5$ (c) $~x^2-10x+21$
(d) $~x^2-10x-21$ (e) $~x-10$
QUESTION 7:

If $x^2+9x+18=0$ then $x=$
(a) $~-3 \text{ only}$ (b) $~3 \text{ or } -6$ (c) $~-3 \text{ or } -6$
(d) $~-3 \text{ or } 6$ (e) $~3 \text{ or } 6$
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 $y=(5x-2)^7$ then $x=$
(a) $~\frac{\sqrt[5]{y}+2}{\sqrt[7]{2}}$ (b) $~\frac{\sqrt[7]{y+2}}{5}$ (c) $~\frac{y+2}{\sqrt[7]{5}}$
(d) $~\sqrt[7]{\frac{y+2}{5}}$ (e) $~\frac{\sqrt[7]{y}+2}{5}$
QUESTION 10:

Find the remainder when $x^3-4x^2+x-3$ is divided by $x-2$
(a) $~-2x-3$ (b) $~-9$ (c) $~x^2-2x$
(d) $~-3$ (e) $~x^2-2x-3$
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:

$3^k+3^k+3^k =$
(a) $~3^{k+1}$ (b) $~9^{3k}$ (c) $~9^k$
(d) $~3^{3k}$ (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 $(0,1)$ and $(-2, 5)$ is
(a) $~3$ (b) $~7$ (c) $~\sqrt{34}$
(d) $~\sqrt{20}$ (e) $~49$
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:

What is a possible equation of the following graph?



(a) $x^2+y^2=25$ (b) $\frac{x^2}{5}+\frac{y^2}{4}=1$ (c) $\frac{x^2}{25}+\frac{y^2}{16}=1$
(d) $\frac{x^2}{16}+\frac{y^2}{25}=1$ (c) $\frac{x^2}{4}+\frac{y^2}{5}=1$
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) Logarithmic (b) Exponential (c) Polynomial
(d) Trigonometric (e) Power
QUESTION 20:

If $g(x) = x^3$ then $g(x+h)$ =
(a) $~x^3+h^3$ (b) $~x^2+2xh+h^2-x+h$ (c) $~x^3+3x^2h+3xh^2+h^3$
(d) $~x^3+x+h$ (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 $f(x)=\ln(x)$?
(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:

A bucket is leaking water at a rate of 2 litres every minute. How long will it take for the bucket to empty (in minutes)?
(a) $~2$ (b) $~4$ (c) $~6.5$
(d) $~7.2$ (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 $\sin(\theta) = \frac{2}{5}$ and $\theta$ is in the first quadrant, then $\tan(\theta)=$
(a) $~\frac{2}{5}$ (b) $~\frac{-2}{\sqrt{21}}$ (c) $~\frac{2}{\sqrt{21}}$
(d) $~\frac{-2}{5}$ (e) $~\frac{\sqrt{21}}{5}$
QUESTION 27:

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

$\sin^2(3x)+\cos^2(3x) =$
(a) $~\cos^2(6x)$ (b) $~\sin^2(6x)$ (c) $~0$
(d) $~1$ (e) $~2$
QUESTION 30:

What is the exact value of $\arccos(0)$ in radians? Note: This is the same as asking for the value of $\cos^{-1}(0)$.
(a) $\frac{\pi}{3}$ (b) $\frac{\pi}{2}$ (c) $90$
(d) Does not exist (e) Impossible without a calculator