Difference: DiagnosticTest (17 vs. 18)

Revision 182007-11-29 - DickFurnas

Line: 1 to 1
 

Diagnostic Tests:

  • What is an answer?
Changed:
<
<
    • Local BEGINANSWER = Pencil / Refactor / Edit






Welcome to the Math Support Center!

Link to: MathTest for example MathMode syntax.

Pencil

<--

.

-->








Table of Contents

Algebra

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

1.

Pencil

<--

.

-->








2.

Pencil
<--

.

-->








3.

Pencil
<--

.

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

-->








4.

Pencil
<--

.

-->








5.

Pencil
<--

.

-->








6.

Pencil
<--

.

-->








7.

Pencil
<--

.

-->








8.

Pencil
<--

.

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

-->








9.

Pencil
<--

.

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 start with and count up:

which simplifies to:

as previously.

-->








10.

Pencil
<--

.

-->








11.

Pencil
<--

either or or

.

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

either or or

and either or or

-->








12.

Pencil
<--

.

  • Rearrange so the equation is of the form:
  • and use the Quadratic Formula:

-->








Trig

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

1. Convert:

a. to radians.

Pencil
<--

.

  • Recall that a full circle is:

  • Use the principle of Dimensional Analysis to convert the units:
-->







b. to degrees.

c. to radians.

2. Evaluate:

a.

b.

c.

3. Sketch the graph of

(Make your vertical scale as large as possible.)

4. Given , find

5. Solve the following right triangle:

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

a.

b.

c.

6. Relate to and

a.

b.

c.

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:
\documentclass[fleqn,12pt]{article}
\usepackage{amsmath}
\usepackage[normal]{xcolor}
\setlength{\mathindent}{0cm}
\definecolor{teal}{rgb}{0,0.5,0.5}
\definecolor{navy}{rgb}{0,0,0.5}
\definecolor{aqua}{rgb}{0,1,1}
\definecolor{lime}{rgb}{0,1,0}
\definecolor{maroon}{rgb}{0.5,0,0}
\definecolor{silver}{gray}{0.75}
\usepackage{latexsym}
\begin{document}
\pagestyle{empty}
\pagecolor{white}
{
\color{black}
\begin{math}\displaystyle = \frac{\Pi}{6} radians\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle = \frac{60\Pi}{360} radians\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle 30^{\circ} \dot $\frac{ 2\Pi radians }{ 360^{\circ}$ }\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle = 2\Pi radians\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle \frac{\Pi}{6}\end{math}
}
\clearpage
{
\color{black}
\begin{math}\displaystyle = 360^{\circ}\end{math}
}
\clearpage
\end{document}
STDERR:
This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)
 restricted \write18 enabled.
entering extended mode
(/tmp/b2zsW91VJh/qUhkGxNseU
LaTeX2e <2011/06/27>
Babel  and hyphenation patterns for english, dumylang, nohyphenation, lo
aded.
(/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 qUhkGxNseU.aux.
(/usr/share/texlive/texmf-dist/tex/latex/base/ulasy.fd) [1] [2]
! Extra }, or forgotten $.
 }
                 
l.27 \begin{math}\displaystyle 30^{\circ} \dot $
                                                \frac{ 2\Pi radians }{ 360^{...

! Missing } inserted.
 
                }
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}
                                                  
[3] [4] [5] [6] (./qUhkGxNseU.aux) )
(see the transcript file for additional information)
Output written on qUhkGxNseU.dvi (6 pages, 1772 bytes).
Transcript written on qUhkGxNseU.log.
 
This site is powered by the TWiki collaboration platform Powered by Perl This site is powered by the TWiki collaboration platformCopyright © by the contributing authors. All material on this collaboration platform is the property of the contributing authors.