# Diagnostic Quiz 1: Some precalculus

Question

## Question 1

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) $-\frac{1}{30}$

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 2

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) $\frac{6-\sqrt{5}}{2}$

Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 3

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) $y=4x-2$

Not correct. Choice (a) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 4

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) $\left(2x-3\right)\left(x+5\right)$

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.

## Question 5

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) $\frac{4\pi }{3}$

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 6

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) $y=x\left(2-x\right)$

Not correct. Choice (a) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 7

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) ${e}^{10x\left(1+x\right)}$

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 8

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) $lna-3lnb+2lnc$

Not correct. Choice (a) is false.
Not correct. Choice (c) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 9

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) $-1$

Not correct. Choice (a) is false.
Not correct. Choice (b) is false.
Not correct. Choice (d) is false.
Not correct. Choice (e) is false.

## Question 10

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) $x=2$

Not correct. Choice (a) is false.