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%TCIDATA{<META NAME="Title" CONTENT="Are you ready for calculus? - my version">}
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
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\chead{\color{black} \LARGE Are you ready for calculus? - Answers}
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\begin{document}


\begin{enumerate}
\item a) \ $\dfrac{x\left( x+3\right) }{x-4}$ \ \ \ \ \ \ b) \ $\dfrac{x-4}{%
x\left( x-1\right) }$ \ \ \ \ \ \ c) \ $\dfrac{5x}{x+5}$ \ \ \ \ \ \ d) $%
\dfrac{3x-1}{x}$

\item a) \ $2\left( \sqrt{3}-\sqrt{2}\right) $ \ \ \ \ \ \ b) \ $-1-\sqrt{5}$

\item a) \ $8a^{6}b^{-1}$ \ \ \ \ b) \ $3a^{\tfrac{1}{2}}b^{\tfrac{3}{2}}$ \
\ \ c) \ $\dfrac{2}{3}a^{2}b^{-1}$ \ \ \ \ d) \ $ab^{-1}$ \ \ \ \ e) $\ a^{-%
\tfrac{3}{2}}b$ \ \ \ \ f) \ $a^{\tfrac{5}{6}}b^{\tfrac{1}{2}}$

\item a) \ $1$ \ \ \ \ \ b) \ $-\dfrac{3}{2}$ \ \ \ \ \ c) \ $8$ \ \ \ \ \
d) \ $\pm \dfrac{4}{25}$

\item a) $\log _{2}\left( 5\left( x+1\right) \right) $ \ \ \ \ \ \ \ \ b) \ $%
25$ \ \ \ \ \ \ \ \ \ c) \ $\log _{2}3$

\item a) \ $\dfrac{1}{2}$ \ \ \ \ b) \ $-x$ \ \ \ c) \ $2\log _{10}x$

\item a) \ $\dfrac{bcx}{bc-cy-bz}$\ \ \ \ b) \ $\dfrac{S-2bc}{2\left(
b+c\right) }$ \ \ c) \ $\dfrac{-\pi h+\sqrt{\pi ^{2}h^{2}+2A\pi }}{2\pi }$ \
\ d) \ $\dfrac{A}{nr+1}$ \ \ \ e) \ $\dfrac{2x-y}{x+2y}$ \ \ \ f) \ $\dfrac{%
\pi }{\pi -1}$

\item a) \ $\left( -2,-1\right) $ \ \ \ \ b) \ $\left( -\dfrac{1}{2},\dfrac{3%
}{8}\right) $ \ \ \ c) \ $\left( -10,\dfrac{1}{3}\right) $

\item a) \ $-4,0,4$ \ \ \ \ \ \ \ b) \ $-\dfrac{5}{2},\dfrac{5}{2},2$ \ \ \
\ \ \ \ c) \ $-\dfrac{3}{2}$ \ \ \ \ \ d) \ $-1,1$

\item a) \ $\dfrac{-3\pm \sqrt{6}}{2}$ \ \ \ \ \ \ b) \ $-3,\dfrac{1}{2}$ \
\ \ \ \ \ c) \ $-\dfrac{1}{2}$

\item a) \ $-89$ \ \ \ \ \ \ \ b) \ $x^{2}+3$

\item $-\dfrac{1}{3},\dfrac{1}{4},2$

\item a) $-3\leq x\leq 1$ \ \ \ \ \ \ \ b) \ $x<\dfrac{2}{3}$ \ or \ $x\geq 1
$ \ \ \ \ \ \ \ \ c) \ all $x$

\item a) \ $-\dfrac{6}{5},2$ \ \ \ \ \ \ \ \ \ \ b) \ $-\dfrac{4}{3},2$

\item a) \ $7x+3y=2$ \ \ \ \ \ \ b) \ $3x+2y=1$ \ \ \ \ \ c) \ $y=3$

\item a) \ $\left( 2,-1\right) $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ b)

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \FRAME{itbpF}{2.3895in}{%
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\item a) $C\left( -3,2\right) $ \ $r=\sqrt{10}$ \ \ \ \ \ \ b) \ $x+3y=13$

\item a) $\ \left( x-1\right) ^{2}+\left( y-2\right) ^{2}=18$ \ \ \ \ \ \ b)
\ $\left( x-\dfrac{1}{2}\right) ^{2}+\left( y-1\right) ^{2}=\dfrac{5}{4}$ \
\ \ \ \ \ \ c) \ $\left( x-5\right) ^{2}+\left( y-3\right) ^{2}=25$

\item a) \ \ i) \ $D:$ \ all real numbers \ $R=\left\{ 7\right\} $\ \ \ \ 
\newline
\qquad ii) \ $D:$ \ all real numbers except $-\dfrac{1}{2}$ \ \ $R:$ all
real numbers except $\dfrac{5}{2}$

b) \ $\ x<-2$ \ \ or \ \ $x>1$

\item a) \ $2$\ \ \ \ b) $\ h+2x$ \ \ \ c) \ \ $\dfrac{-1}{\left( x+1\right)
\left( x+h+1\right) }$

\item \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ b) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ c) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d)

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\item \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ b)

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\item \ \ \ \ \ \ a) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ b) \ $y=-x^{2}+2x+3$

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\item a) \ $f^{-1}\left( x\right) =\dfrac{x-3}{2}$ \ \ \ b) \ $f^{-1}\left(
x\right) =\dfrac{x+2}{5x-1}$ \ \ \ c) \ $f^{-1}\left( x\right) =\sqrt{x+2}%
-1, $ \ \ $x>-1$

\item 
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\item a) \ $x=t\left( \dfrac{r-h}{h}\right) $ \ \ \ \ \ \ \ \ b) \ $\dfrac{rt%
}{\sqrt{r^{2}-h^{2}}}$

\item $x^{2}-6x+y^{2}+4y+5=0$ \ \ \ (a circle)

\item $D:$ all numbers except $0;$ \ $R=\left\{ -1,1\right\} $

\item a) \ $1-\dfrac{\pi }{4}$ \ \ \ \ \ \ \ \ \ b) \ $4r+\pi r$ \ \ \ \ \ \
\ \ \ \ c) \ $\dfrac{9\pi }{4}\unit{m}^{2}$ \ \ \ \ \ \ \ \ \ \ d) \ $100%
\sqrt{5}\unit{km}$ \ \ \ \ \ \ \ e) \ $\dfrac{\pi }{6}$ $\ $\ or $\ \
30^{\circ }$

\item a) \ $-\dfrac{\sqrt{3}}{2}$ \ \ \ \ b) \ $-\dfrac{\sqrt{3}}{2}$ \ \ \
c) \ $-\dfrac{\pi }{4}$ \ \ d) \ $-\dfrac{\pi }{2}$ \ \ \ \ e) \ $\dfrac{%
\sqrt{2}}{2}$ \ \ \ \ \ f) \ $\dfrac{\pi }{3}$ \ \ \ \ \ g) \ $\dfrac{\sqrt{3%
}}{3}$ \ \ \ h) \ $\pi $

\item a) \ $\dfrac{\pi }{6},\dfrac{5\pi }{6},\dfrac{7\pi }{6},\dfrac{11\pi }{%
6}$ \ \ \ \ \ \ \ \ b) \ $-\dfrac{\pi }{2},\dfrac{\pi }{6},\dfrac{5\pi }{6}$
\ \ \ \ \ c) \ $\dfrac{\pi }{6}+2k\pi $ \ or \ $\dfrac{5\pi }{6}+2k\pi $ \
where $k$ is any integer

\item 
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\item \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ a) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ b)

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\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ c) $\ \ $ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ d) $\ \ \ \ \ \ \ \ \
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $e)
\end{enumerate}

\end{document}