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# Diagnostic Tests:

Changed:
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<

Welcome to the Math Support Center!

Link to: MathTest for example MathMode syntax.

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## Algebra

Combine and simplify expressions as much as possible.
Solve equations for x.

### 1.

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### 2.

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### 3.

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Cannot be simplified.
however, if we are told further that  then we have a common factor in the denominator:

, provided

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### 4.

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### 5.

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### 6.

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### 7.

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### 8.

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No algebraic simplification.
however... A beautiful geometric simplification is possible:
is the hypotenuse of the right triangle with sides  and

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### 9.

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Alternatively:
Recall Pascal's Triangle:

1    1
1    2    1
1    3    3    1
1    4     6    4     1
1    5   10   10    5    1

...in which elements in a row are the sum of the two elements in the row above it. These numbers are the Binomial Coefficients.
is the cube of the binomial  so the coefficients can be taken from the third row above:
1  3  3  1 and the exponents on  start with  and count down, while the exponents on

which simplifies to:

as previously.

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### 10.

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### 11.

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either  or  or

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if a product is zero one of its factors must be zero so:

either  or  or

and either  or  or

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### 12.

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Rearrange so the equation is of the form:

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## Trig

Answer the following questions without calculators or trig tables.
Leave answers like or as is.

### 1. Convert:

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Recall that a full circle is:
Use the principle of Dimensional Analysis to convert the units:

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### 3. Sketch the graph of

(Make your vertical scale as large as possible.)

### 5. Solve the following right triangle:

( i.e. determine missing sides and angles.)

### 7. Express in terms of and of A and B :

-- DickFurnas - 01 Mar 2007 Uses: DiagnosticTestAlgebra  |  DiagnosticTestTrig

 META TOPICMOVED by="DickFurnas" date="1172782266" from="Main.MathSupportCenter" to="MSC.DiagnosticTest"
Error during latex2img:
ERROR: problems during latex
INPUT:
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{
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\begin{math}\displaystyle 30^{\circ} \dot $\frac{ 2\Pi radians }{ 360^{\circ}$ }\end{math}
}
\clearpage
{
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{
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\begin{math}\displaystyle \frac{\Pi}{6}\end{math}
}
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{
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\begin{math}\displaystyle = 360^{\circ}\end{math}
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STDERR:
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)
restricted \write18 enabled.
entering extended mode
(/tmp/CSlXcbb5Pi/QrK2OnicQS
LaTeX2e <2011/06/27>
Babel  and hyphenation patterns for english, dumylang, nohyphenation, lo
(/usr/share/texlive/texmf-dist/tex/latex/base/article.cls
Document Class: article 2007/10/19 v1.4h Standard LaTeX document class
(/usr/share/texlive/texmf-dist/tex/latex/base/fleqn.clo)
(/usr/share/texlive/texmf-dist/tex/latex/base/size12.clo))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsmath.sty
For additional information on amsmath, use the ?' option.
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amstext.sty
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsgen.sty))
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsbsy.sty)
(/usr/share/texlive/texmf-dist/tex/latex/amsmath/amsopn.sty))
(/usr/share/texlive/texmf-dist/tex/latex/xcolor/xcolor.sty
(/usr/share/texlive/texmf-dist/tex/latex/latexconfig/color.cfg)
(/usr/share/texlive/texmf-dist/tex/latex/graphics/dvips.def))
(/usr/share/texlive/texmf-dist/tex/latex/base/latexsym.sty)
No file QrK2OnicQS.aux.
(/usr/share/texlive/texmf-dist/tex/latex/base/ulasy.fd) [1] [2]
! Extra }, or forgotten $. } l.27 \begin{math}\displaystyle 30^{\circ} \dot$
l.27 \begin{math}\displaystyle 30^{\circ} \dot $\frac{ 2\Pi radians }{ 360^{... ! Missing } inserted. } l.27 ...dot$\frac{ 2\Pi radians }{ 360^{\circ}$} \end{math} ! Extra }, or forgotten \endgroup. \frac #1#2->{\begingroup #1\endgroup \@@over #2} l.27 ...dot$\frac{ 2\Pi radians }{ 360^{\circ}$} \end{math} ! LaTeX Error: Bad math environment delimiter. See the LaTeX manual or LaTeX Companion for explanation. Type H for immediate help. ... l.27 ...{ 2\Pi radians }{ 360^{\circ}$ }\end{math}
`