## MATH1011 Diagnostic Quizzes

Diagnostic Quiz 1: Some precalculus
Question 1 Questions
Evaluate the following expression: $\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\frac{1}{2}-\frac{1}{3}+\frac{1}{4}-\frac{2}{5}$
 a) $\frac{1}{30}$ b) $\frac{1}{120}$ c) $\frac{1}{60}$ d) $-\frac{1}{60}$ e) $-\frac{1}{30}$

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Choice (e) is incorrect
Simplify the following expression: $\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\frac{\sqrt{5}+1}{\sqrt{5}-1}$
 a) $\frac{3+\sqrt{5}}{2}$ b) $\frac{3-\sqrt{5}}{2}$ c) $\frac{\sqrt{5}-3}{2}$ d) $\frac{6+\sqrt{5}}{2}$ e) $\frac{6-\sqrt{5}}{2}$

Choice (a) is correct!
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
The equation of the line passing through the points (1,2) and (2,7) in the $xy\phantom{\rule{2.77695pt}{0ex}}$-plane is
 a) $y=3x-1$ b) $y=5x-3$ c) $y=3x+1$ d) $y=4x-1$ e) $y=4x-2$

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
The quadratic $2{x}^{2}+7x-15\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}$ factorises as
 a) $\left(2x+3\right)\left(x-5\right)$ b) $\left(2x-5\right)\left(x+3\right)$ c) $\left(2x-5\right)\left(x-3\right)$ d) $\left(2x+5\right)\left(x-3\right)$ e) $\left(2x-3\right)\left(x+5\right)$

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is correct!
Find the number of radians that are represented by the following angle: $\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}30{0}^{\circ }$
 a) $\frac{3\pi }{2}$ b) $\frac{2\pi }{3}$ c) $\frac{5\pi }{3}$ d) $\frac{5\pi }{6}$ e) $\frac{4\pi }{3}$

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Choice (e) is incorrect
Which of the following functions describes the above graph?
 a) $y=-{\left(x-1\right)}^{2}+2$ b) $y=2x\left(2-x\right)$ c) $y=-2{\left(x+1\right)}^{2}+2$ d) $y=2{\left(x-1\right)}^{2}+2$ e) $y=x\left(2-x\right)$

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
Find an equivalent expression to the following: ${e}^{2x}{e}^{5{x}^{2}}$
 a) ${e}^{7{x}^{2}}$ b) ${e}^{10{x}^{3}}$ c) ${e}^{x\left(2+5x\right)}$ d) ${e}^{2x}+{e}^{5{x}^{2}}$ e) ${e}^{10x\left(1+x\right)}$

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Choice (e) is incorrect
Find an equivalent expression to the following:$\phantom{\rule{1em}{0ex}}ln\left(\frac{a{b}^{3}}{{c}^{2}}\right)$
 a) $lna+ln3b-ln2c$ b) $lna+3lnb-2lnc$ c) $3lnab-2lnc$ d) $3lnab-ln2c$ e) $lna-3lnb+2lnc$

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect
Evaluate the following expression: $\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}tan\left(5\pi ∕6\right)$
 a) $\sqrt{3}$ b) $-\sqrt{3}$ c) $-\frac{1}{\sqrt{3}}$ d) $\frac{1}{\sqrt{3}}$ e) $-1$

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Choice (e) is incorrect
Solve for $x$ for the following equation: $\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\phantom{\rule{2.77695pt}{0ex}}\frac{1}{x-1}+\frac{1}{x+3}=2$
 a) $x=\frac{1±\sqrt{17}}{2}$ b) $x=\frac{-1±\sqrt{17}}{2}$ c) $x=±\sqrt{5}$ d) $x=±2$ e) $x=2$

Choice (a) is incorrect
Choice (b) is correct!
Choice (c) is incorrect
Choice (d) is incorrect
Choice (e) is incorrect