Precalculus Review
- Page ID
- 10610
This page is a draft and is under active development.
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 \((x+4)\).
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Exercise \(\PageIndex{3}\)
The expression \(\displaystyle\frac{\left(1/x+1/y\right) } {x+y}\) is equal to
- \(1\)
- \(1/(xy)\)
- \(xy/(x+y)^{2}\)
- \(x+y\)
- \(1/(x+y)^{2}\)
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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
- \(5y-x=1\),
- \(5x+y=0\),
- \(x+5y=3\)
- \(y-5x=2\)
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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 \({\rm m}^{2}\))
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