Precalculus Review

Last updated

Nov 20, 2020
Save as PDF
- Mock Exams (Celebration of Learning)
- Test 1

This page is a draft and is under active development.

$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$

$\newcommand{\id}{\mathrm{id}}$ $\newcommand{\Span}{\mathrm{span}}$

( \newcommand{\kernel}{\mathrm{null}\,}\) $\newcommand{\range}{\mathrm{range}\,}$

$\newcommand{\RealPart}{\mathrm{Re}}$ $\newcommand{\ImaginaryPart}{\mathrm{Im}}$

$\newcommand{\Argument}{\mathrm{Arg}}$ $\newcommand{\norm}[1]{\| #1 \|}$

$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$\newcommand{\Span}{\mathrm{span}}$

$\newcommand{\id}{\mathrm{id}}$

$\newcommand{\Span}{\mathrm{span}}$

$\newcommand{\kernel}{\mathrm{null}\,}$

$\newcommand{\range}{\mathrm{range}\,}$

$\newcommand{\RealPart}{\mathrm{Re}}$

$\newcommand{\ImaginaryPart}{\mathrm{Im}}$

$\newcommand{\Argument}{\mathrm{Arg}}$

$\newcommand{\norm}[1]{\| #1 \|}$

$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$

$\newcommand{\Span}{\mathrm{span}}$ $\newcommand{\AA}{\unicode[.8,0]{x212B}}$

$\newcommand{\vectorA}[1]{\vec{#1}} % arrow$

$\newcommand{\vectorAt}[1]{\vec{\text{#1}}} % arrow$

$\newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vectorC}[1]{\textbf{#1}}$

$\newcommand{\vectorD}[1]{\overrightarrow{#1}}$

$\newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}}$

$\newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}}$

$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$

$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$

$\newcommand{\avec}{\mathbf a}$

$\newcommand{\bvec}{\mathbf b}$

$\newcommand{\cvec}{\mathbf c}$

$\newcommand{\dvec}{\mathbf d}$

$\newcommand{\dtil}{\widetilde{\mathbf d}}$

$\newcommand{\evec}{\mathbf e}$

$\newcommand{\fvec}{\mathbf f}$

$\newcommand{\nvec}{\mathbf n}$

$\newcommand{\pvec}{\mathbf p}$

$\newcommand{\qvec}{\mathbf q}$

$\newcommand{\svec}{\mathbf s}$

$\newcommand{\tvec}{\mathbf t}$

$\newcommand{\uvec}{\mathbf u}$

$\newcommand{\vvec}{\mathbf v}$

$\newcommand{\wvec}{\mathbf w}$

$\newcommand{\xvec}{\mathbf x}$

$\newcommand{\yvec}{\mathbf y}$

$\newcommand{\zvec}{\mathbf z}$

$\newcommand{\rvec}{\mathbf r}$

$\newcommand{\mvec}{\mathbf m}$

$\newcommand{\zerovec}{\mathbf 0}$

$\newcommand{\onevec}{\mathbf 1}$

$\newcommand{\real}{\mathbb R}$

$\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}$

$\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}$

$\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}$

$\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}$

$\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$

$\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}$

$\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$

$\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}$

$\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}$

$\newcommand{\laspan}[1]{\text{Span}\{#1\}}$

$\newcommand{\bcal}{\cal B}$

$\newcommand{\ccal}{\cal C}$

$\newcommand{\scal}{\cal S}$

$\newcommand{\wcal}{\cal W}$

$\newcommand{\ecal}{\cal E}$

$\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}$

$\newcommand{\gray}[1]{\color{gray}{#1}}$

$\newcommand{\lgray}[1]{\color{lightgray}{#1}}$

$\newcommand{\rank}{\operatorname{rank}}$

$\newcommand{\row}{\text{Row}}$

$\newcommand{\col}{\text{Col}}$

$\renewcommand{\row}{\text{Row}}$

$\newcommand{\nul}{\text{Nul}}$

$\newcommand{\var}{\text{Var}}$

$\newcommand{\corr}{\text{corr}}$

$\newcommand{\len}[1]{\left|#1\right|}$

$\newcommand{\bbar}{\overline{\bvec}}$

$\newcommand{\bhat}{\widehat{\bvec}}$

$\newcommand{\bperp}{\bvec^\perp}$

$\newcommand{\xhat}{\widehat{\xvec}}$

$\newcommand{\vhat}{\widehat{\vvec}}$

$\newcommand{\uhat}{\widehat{\uvec}}$

$\newcommand{\what}{\widehat{\wvec}}$

$\newcommand{\Sighat}{\widehat{\Sigma}}$

$\newcommand{\lt}{<}$

$\newcommand{\gt}{>}$

$\newcommand{\amp}{&}$

$\definecolor{fillinmathshade}{gray}{0.9}$

Exercise $\PageIndex{1}$

Write down an equation of a line passing through the points $(1,2)$ and $(3,5)$ .

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{2}$

For what value(s) of $m$ is $x^{3}+6x^{2}-m$ divisible by $(x+4)$ .

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{3}$

The expression $\displaystyle\frac{\left(1/x+1/y\right) } {x+y}$ is equal to

$1$
$1/(xy)$
$xy/(x+y)^{2}$
$x+y$
$1/(x+y)^{2}$

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{4}$

Solve the following quadratic equation for $m$ , where $m^2-5m=-6$

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{5}$

Simplify $\displaystyle {\left( {xy \over y^{-3}z^{-1}} \right)^{-1}}$ .

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{6}$

If $\displaystyle{f(x)={1-x \over 1+x}}$ , find $\displaystyle{f \left( {-1 \over x} \right)}$

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{7}$

A hollow cylinder has height $10{\rm cm}$ and radius $5{\rm cm}$ .
Another cylinder has height $10{\rm cm}$ and radius $4{\rm cm}$ . The
smaller cylinder is inserted into the larger one. How much space is left
inside the larger cylinder but outside the smaller one (in ${\rm cm}^{3}$ )

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{8}$

An equation for a line parallel to the line $5x-y=2$ is

$5y-x=1$ ,
$5x+y=0$ ,
$x+5y=3$
$y-5x=2$

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{9}$

Find $x$ if $\displaystyle{ -4 = {2x+3 \over 1-x}}$ .

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{10}$

Write down an equation of a line passing through the point $(1,3)$ and with the slope $m=-1/2$ '

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{11}$

Express the function in piecewise form without using absolute values $F(x)=3|x+2|-2|x-1|$ .

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{12}$

In a general triangle $ABC$ , the angle at $A$ is $30^{\circ}$ ,
the length of $AB$ is $6$ , and the length of $AC$ is $4$ . Find the length
of $CE$ . ( $E$ is the point on $AB$ closest to $C$ .)

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{13}$

Suppose $\log(a)=2$ , $\log(b)=3$ and $\log(c)=5$ . Find $\displaystyle{ \log \left( {c \over ab} \right)}$ .

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Exercise $\PageIndex{14}$

A rectangular field is bounded by a fence $500{\rm m}$ long. The field is $150{\rm m}$ longer than it is wide. Find the area of the field (in ${\rm m}^{2}$ )

Answer: Add answer text here and it will automatically be hidden if you have a "AutoNum" template active on the page.

Search

Text Color

Text Size

Margin Size

Font Type

Support Center

How can we help?