
# Precalculus Review

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Exercise $$\PageIndex{1}$$

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

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Exercise $$\PageIndex{2}$$

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

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

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Exercise $$\PageIndex{4}$$

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

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Exercise $$\PageIndex{5}$$

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

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Exercise $$\PageIndex{6}$$

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

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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 $${\rm cm}^{3}$$)

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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. $$y-5x=2$$

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Exercise $$\PageIndex{9}$$

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

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Exercise $$\PageIndex{10}$$

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

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Exercise $$\PageIndex{11}$$

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

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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 $$C$$.)

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Exercise $$\PageIndex{13}$$

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

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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 $${\rm m}^{2}$$)