(r8) DiagnosticTest < MSC

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---+ Diagnostic Tests:

%BEGINOVERVIEW%
Welcome to the Math Support Center!

_Link to:_ Main.MathTest

%ENDOVERVIEW%


---++ Algebra

__Combine and simplify expressions as much as possible.%BR%Solve equations for x.__

%RENDERLIST{"org" depth="2"}%

---+++ 1.  %$\mbox{ \small $\frac{1}{a+b} - \frac{2a}{a^2+b^2}$ }$% 
      *  icon:see %$\mbox{ \small $\frac{1}{a+b} \cdot \frac{a-b}{a-b} - \frac{2a}{(a+b)(a-b)}$ }$%
      *  %$\mbox{ \small $\frac{a-b}{(a+b)(a-b)} - \frac{2a}{(a+b)(a-b)}$ }$%
      *  %$\mbox{ \small $\frac{a-b-2a}{(a+b)(a-b)}$ }$%
      *  %$\mbox{ \small $\frac{-b-a}{(a+b)(a-b)}$ }$%
      *  %$\mbox{ \small $\frac{-(b+a)}{(a+b)(a-b)}$ }$%
      *  %$\mbox{ \small $\frac{-(a+b)}{(a+b)(a-b)}$ }$%
      *  %$\mbox{ \small $\frac{-1}{(a-b)}$ }$%
---+++   1. %$\mbox{ \small $\frac{x^2 + 2x + 1}{2x^2} \div \frac{x+1}{x+2}$ }$% 
      =: %$\mbox{ \small $\frac{(x+1)(x+1)}{2x^2}  \cdot \frac{x+2}{x+1}$ }$%
      =: %$\mbox{ \small $\frac{(x+1)}{2x^2} \cdot \frac{(x+2)}{1}$ }$%
      =: %$\mbox{ \small $\frac{(x+1)(x+2)}{2x^2}$ }$%
      =: %$\mbox{ \small $\frac{(x^2+3x+2)}{2x^2}$ }$%
   1. %$\mbox{ \small $-\frac{a+b}{ac+bc}$ }$%
      =: %$\mbox{ \small $ -\frac{a+b}{(a+b)c}$ }$%
      =: %$\mbox{ \small $ -\frac{1}{c}$ }$%
   1. %$\mbox{ \small $\frac{(2a)^3}{a^5}$ }$%
      =: %$\mbox{ \small $\frac{2^3a^3}{a^2a^3}$ }$%
      =: %$\mbox{ \small $\frac{8}{a^2}$ }$%
   1. %$\mbox{ \small $(0.2a^2)^4$ }$%
      =: %$\mbox{ \small $(0.2)^4 \cdot (a^2)^4$ }$%
      =: %$\mbox{ \small $(2 \cdot .1)^4 \cdot a^{2*4}$ }$%
      =: %$\mbox{ \small $2^4 \cdot 10^{-4} \cdot a^{8}$ }$%
      =: %$\mbox{ \small $16 \cdot 10^{-4} a^{8}$ }$%
      =: %$\mbox{ \small $=.0016 a^{8}$ }$%
   1. %$\mbox{ \small $\frac{8y^n}{-2y^{n-1}}$ }$%
      =: %$\mbox{ \small $\frac{8y^n}{-2y^{n-1}} \cdot \frac{y}{y}$ }$%
      =: %$\mbox{ \small $\frac{8(y^n) \cdot y}{-2(y^{n})} $ }$%
      =: %$\mbox{ \small $\frac{8 \cdot y}{-2} $ }$%
      =: %$\mbox{ \small $-\frac{8 \cdot y}{2} $ }$%
   1. %$\mbox{ \small $\sqrt[3]{-8y^{27}}$ }$%
      =: %$\mbox{ \small $ \sqrt[3]{-1} \cdot \sqrt[3]{8} \cdot \sqrt[3]{y^{27}} $ }$%
      =: %$\mbox{ \small $ \sqrt[3]{-1} \cdot \sqrt[3]{8} \cdot y^{\frac{27}{3}}$ }$%
      =: %$\mbox{ \small $ -1 \cdot 2 \cdot y^{9}$ }$%
      =: %$\mbox{ \small $ -2 y^{9}$ }$%
   1. %$\mbox{ \small $\sqrt{a^2 + b^2}$ }$%
   1. %$\mbox{ \small $( \sqrt{x} + 3\sqrt{y} ) ( \sqrt{x} - \sqrt{y} )$ }$%
   1. %$\mbox{ \small $x^3 - x^2 - 6x = 0$ }$%
   1. %$\mbox{ \small $x^2 + 7x = -3$ }$%

---++ Trig
__Answer the following questions without calculators or trig tables.%BR%\
Leave answers like %$ 53 \pi $% or %$ \sin{13^{\circ}}$% as is.__
   1. Convert:
      a. %$\mbox{ \small $ 30^{\circ}$ }$% to radians.
      a. %$\mbox{ \small $ \frac{ 3 \pi }{2} radians$ }$% to degrees.
      a. %$\mbox{ \small $ 127^{\circ} $ }$% to radians.
   1. Evaluate:
      a. %$\mbox{ \small $\sin{60^{\circ}}$ }$%
      a. %$\mbox{ \small $\tan{\frac{3\pi}{4}}$ }$%
      a. %$\mbox{ \small $\sec{\frac{pi}{2}}$ }$%
   1. Sketch the graph of %$\mbox{ \small $\sin{x}$ }$%%BR%
       (Make your vertical scale as large as possible.)
   1. Given %$\mbox{ \small $\tan{\theta} = \frac{6}{7}, find \sin{\theta}$ }$%
   1. Solve the following right triangle:%BR%
       ( _i.e._ determine missing sides and angles.)
      a. %$\overline{AB} = $%
      a. %$\overline{AC} = $%
      a. %$\angle{A} = $%
   1. Relate to  %$\mbox{ \small $\sin{ \theta } $ }$%  and  %$\mbox{ \small $ \cos{ \theta } $ }$%
      a.  %$\mbox{ \small $\cos{-\theta}$ }$%
      a.  %#$\mbox{ \small $\sin{\frac{\pi}{2} -\theta}$ }$%
      a.  %#$\mbox{ \small $\sin{2\theta}$ }$%
   1. Express in terms of  %$\mbox{ \small $\sin{} and cos{}$ }$%  of  %$\mbox{ \small $A and B$ }$%



-- Main.DickFurnas - 01 Mar 2007
Topic revision: r8 - 2007-04-06 - DickFurnas