\documentclass[11pt]{book}
\usepackage[Mickael]{ammaths}
\usetikz

\begin{document}
\module{Using a scientific calculator}{1}{02}{1 period}

%\prereq{}

\object{\begin{itemize}
	\item Discover the vocabulary for the main operations.
	\item Discover how to use the calculator for basic calculus (powers, fractions and memories). 
	\item Become aware of some limitations of the calculator.
	\end{itemize}}

\mater{\begin{itemize}
	\item Calculators.
	\item Slideshow with operations.
	\item Emulators for Casio and TI.
\end{itemize}}

\modpart{Vocabulary}{10 minutes}

Using a slideshow, the teacher introduces some vocabulary of the main operations.

\modpart{Task sheet}{Remaining time}

Using their calculator, students have to answer some questions.

\newpage

\moddocdis{Using a calculator}{1}{02}{Task sheet}

\sectionblack{Basic operations}

Use your calculator to carry out each of the following computations, in just one instruction. Brackets may have to be
used.
\begin{enumerate}
\item \begin{multicols}{4}
      \begin{enumerate}
      \item $\cfrac{2}{3,5\times4}$
      \item $\cfrac{2}{3,5}+ 4$
      \item $(-2)^2$
      \item $\cfrac{2}{3,5+4}$
      \item $\sqrt{3,5+4}$
      \item $-5^2$\rule{0pt}{20pt}
      \item $2\times3^2$
      \item $\cfrac{2}{3,5}\times4$
      \end{enumerate}
      \end{multicols}
\item \begin{multicols}{4}
      \begin{enumerate}
      \item $\cfrac{3-2.25^2}{1.072-2}$
      \item $3\times\cfrac{4-\pi}{2}$
      \item $\cfrac{3}{5.1\times6.7}$
      \item $\cfrac{2+\pi}{\sqrt\frac{3}{7}}+4$
      \end{enumerate}
      \end{multicols}
\item Use your calculator to carry out the three following computations. Are the results equal ? Explain the
differences.
	\begin{center}
	\touche{$\sqrt{\hspace{0.1cm}}$} \touche{9} \touche{+} \touche{1} \touche{6}
	\quad -- \quad\touche{$\sqrt{\hspace{0.1cm}}$} \touche{(} \touche{$9$} \touche{+} \touche{$1$} \touche{$6$}
\touche{)}\\ \bigskip
	\touche{$\sqrt{\hspace{0.1cm}}$} \touche{$9$} \touche{+} \touche{$\sqrt{\hspace{0.1cm}}$}
\touche{$1$}\touche{$6$}
	\end{center}
\end{enumerate}

\sectionblack{Powers}

\begin{enumerate}
\item Find out what key must be used to compute $2^5$. Check your result by hand.
\item Use your calculator to carry out the following computations.
      \begin{multicols}{4}
      \begin{enumerate}
      \item $(2,5\times3,5)^3$
      \item $(-3,8)^4 + 7$
      \item $\cfrac{3^3}{2}$
      \item $5^{28}\times2^8$
      \end{enumerate}
      \end{multicols}
\end{enumerate}

\sectionblack{Fractions}

\begin{enumerate}
	\item Find out how to get the irreducible fraction equal to $\frac{45}{30}$ with your calculator.
	\item Give the irreducible fraction equal to each of the following expressions :
	      \begin{multicols}{3} 
	      \begin{enumerate}
	      \item $2 + \cfrac{3}{5} - 1 + \cfrac{2}{3}$
	      \item $\cfrac{2}{1+\frac{1}{3}}$
	      \item $\cfrac{\frac24}{3}$
	      \end{enumerate}
	      \end{multicols}
\end{enumerate}

\sectionblack{Negative and minus}

There are two different keys ``minus'' on your scientific calculator.\\ The key \touche{(-)} represents the sign of
a number whereas \touche{---} is used for the subtraction operation.
\begin{enumerate}
\item For each of the following expression, there is only one sign ``minus``. Find out what key should be used.
	\begin{multicols}{3}
	\begin{enumerate}
	\item $4-3$ ;
	\item $-4+3$ ;
	\item $\frac{-12}{5}$ ;
	\item $\frac{8-12}{5}$ ;
	\item $\sqrt{17-5}$ ;
	\item $10^{-5}$.
	\end{enumerate}
	\end{multicols}
\item Here are two strings of keys : \touche{5} \touche{(-)} \touche{2}\quad and \quad \touche{5} \touche{---}
\touche{2}.\\ Are they correct or not ?
% \item Entrer successivement les deux séquences ci-dessous. Expliquer pourquoi les résultats sont différents.
% 	\begin{enumerate}
% 	\item \touche{(-)} \touche{2} \touche{+} \touche{3}
% 	\item \touche{--} \touche{2} \touche{+} \touche{3}
% 	\end{enumerate}
\end{enumerate}


\sectionblack{Memories}

The key \touche{$\rightarrow$} or \touche{STO} allows to store a number in the calculator's memory. This can be
usefull if you need that number several times or in a programm.
In each of the following situations, store the value of $A$ in the memory and then compute an approximate value to 3DP 
of $B$.
\begin{multicols}{2}
\begin{enumerate}
\item $A=\cfrac{1+\sqrt5}{2}$ et $B=1-\cfrac{1}{A}-\cfrac{1}{A^2}$
\item $A=\cfrac{1-\sqrt5}{2}$ et $B=\cfrac{5A+3}{3A+2}$
%\item $A=1+\sqrt3$  et $B=A^4-8A^2+3$
\end{enumerate}
\end{multicols}

\sectionblack{Limitations of the calculator}

\en
\probpart{-- First example}

\begin{enumerate}
\item Using your calculator, compute the value of $987 654 322 \times 987 654 320 - 987 654 321^2$.
\item \begin{enumerate}
	\item What is the units digit of $987 654 322 \times 987 654 320$ ?
	\item What is the units digit of $987 654 321^2$ ?
	\end{enumerate}
\item Are the results of the first and the second question consistent ? Explain shortly.
\item \begin{enumerate}
	\item Expand and simplify : $(x+1)(x-1)-x^2$.
	\item Use the previous answer to compute the result of the first expression of this exercice.
	\end{enumerate}
\end{enumerate}

\probpart{-- Second example}

\begin{enumerate}
\item Use your calculator to find the best possible approximate value of
$A =\cfrac{941 664}{665 857}$ and $B=\sqrt2$
\item What could you deduce about the numbers $A$ and $B$ ?
\item What are the units digits of $665 857^2$ and $941 664^2$ ? 
\item What can you deduce ? Explain your answer.
\end{enumerate}


\hrulefill

\corrige


\begin{multicols}{2}

Basic operations (to 4 DP) :
\begin{enumerate}
	\item $0,1428$ ;  $4,5714$ ; $4$ ; $0,2666$ ;  $2,7386$ ; $-25$ ;  $18$ ; $2,2857$.
	\item $2,2225$ ; $1,2876$ ; $0,0878$ ; $11,8539$.
	\item $19$ ; $5$ ; $7$.
\end{enumerate}

\bigskip

Powers :
\begin{enumerate}
\item $2^5=32$
\item $669,921875$ ; $215,5136$ ; $13,5$ ; $9,53\times10^{21}$.
\end{enumerate}

\bigskip

Fractions :\\
$\frac{3}{2}$ ; $\frac{34}{15}$ ; $\frac{3}{2}$ ; $\frac{1}{6}$

\bigskip

Negative and minus :
\begin{enumerate}
\item \touche{---} ; \touche{(-)} ; \touche{(-)} ;\\ \touche{---} ; \touche{---} ; \touche{(-)}.
\item Incorrect / Correct.
\end{enumerate}

\bigskip

Memories :\\
$B=0$ ; $B=A\approx -0,618$

 
\end{multicols}




\end{document}



