Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

Precalculus Review

  1. Last updated
  2. Save as PDF
  • Page ID
    10610

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    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. \(1\)
    2. \(1/(xy)\)
    3. \(xy/(x+y)^{2}\)
    4. \(x+y\)
    5. \(1/(x+y)^{2}\)
    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

    1. \(5y-x=1\),
    2. \(5x+y=0\),
    3. \(x+5y=3\)
    4. \(y-5x=2\)
    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.