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Mathematics LibreTexts

Precalculus Review

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    10610

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    Exercise \(\PageIndex{1}\)

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

    Answer

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    Exercise \(\PageIndex{2}\)

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

    Answer

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    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

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    Exercise \(\PageIndex{4}\)

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

    Answer

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    Exercise \(\PageIndex{5}\)

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

    Answer

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    Exercise \(\PageIndex{6}\)

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

    Answer

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    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

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    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

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    Exercise \(\PageIndex{9}\)

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

    Answer

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    Exercise \(\PageIndex{10}\)

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

    Answer

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    Exercise \(\PageIndex{11}\)

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

    Answer

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    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

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    Exercise \(\PageIndex{13}\)

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

    Answer

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    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

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