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diff --git a/macros/latex/contrib/jeopardy/example/game2.tex b/macros/latex/contrib/jeopardy/example/game2.tex new file mode 100644 index 0000000000..c9589b5cb3 --- /dev/null +++ b/macros/latex/contrib/jeopardy/example/game2.tex @@ -0,0 +1,288 @@ +\pdfoutput=1 + +\documentclass{article} + +\usepackage{color} + +\usepackage{amsmath} +\DeclareMathOperator{\arctg}{arctg} +\everymath{\displaystyle} + +\usepackage[pdftex,designi]{web} +\usepackage[noxcolor,pdftex]{exerquiz} +\usepackage[ImplMulti]{dljslib} + +\parindent 0pt +\def\correctColor{color.green} +\def\wrongColor{color.red} + +\usepackage[twoplayers]{jeopardy} +\pagestyle{empty} +\everyCategoryHead{\color{darkgreen}\tiny} + +\def\logoB{\rotatebox{90}{% + \vbox{\normalsize\hbox{\color{red}{Robert Ma\v{r}\'{i}k}} + \hbox{\color{green}Jeopardy game}}} + \vfill} + +\let\rmdefault\sfdefault +\hypersetup{pdfpagemode=Window, pdfnewwindow=true, pdfmenubar=true,% + pdftoolbar=true,colorlinks, pdfwindowui=false, + pdfpagemode=Window} + + +\begin{document} +%\CellHeight=24bp +\SetGameHeight{0.4\textheight} +\ScoreCellHeight=0.5\CellHeight + +\everyRadioButton{%\BG{1 1 1} +\BC{1 1 0} \textColor{0 1 0 rg} +} + +\Playertoks{\BC{1 0 0}\textColor{0 1 0 rg}} + + +\MakeGameBoard + +\begin{category}{Precalculus} + +\begin{question} +$\ln \frac xy=$ +\Ans0 $\ln x+\ln y$ +\Ans1 $\ln x-\ln y$ +\Ans0 $x\ln y$ +\Ans0 $y\ln x$ +\Ans0 none of them +\end{question} + +\begin{question} +The function $y=x^2\cdot \sin x$ is +\Ans1 odd +\Ans0 even +\Ans0 neither odd nor even +\end{question} + +\begin{question} +$\arctan 1=$ +\Ans0 $\infty$ +\Ans0 $\frac \pi3$ +\Ans1 $\frac \pi4$ +\Ans0 $\frac \pi6$ +\Ans0 none of them +\end{question} + +\begin{question} +The equivalence "$a<b$ if and only if $f(a)<f(b)$" is the property of +\Ans0 even functions +\Ans0 one-to-one functions +\Ans0 continuous functions +\Ans1 increasing functions +\Ans0 none of them +\end{question} + +\end{category} + + +\begin{category}{Functions} + +\begin{question} +How many points of inflection is on the graph of the function $y=\sin x$ in +the open interval $(0,2\pi)$ +\Ans0 none +\Ans1 one +\Ans0 two +\Ans0 three +\Ans0 none of them +\end{question} + +\begin{question} +Find points of discontinuity of the function $y=\frac {x-4}{(x-2)\ln x}$ +\Ans0 none +\Ans0 $0$ +\Ans0 $0$, $1$ +\Ans1 $0$, $1$, $2$ +\Ans0 $0$, $2$ +\Ans0 $0$, $1$, $4$ +\Ans0 $0$, $4$ +\Ans0 none of them +\end{question} + +\begin{question} +Let $f$ be a function and $f^{-1}$ be its inverse. Then $f^{-1}\bigl(f(x)\bigr)=$ +\Ans0 $0$ +\Ans0 $1$ +\Ans1 $x$ +\Ans0 $f(x)$ +\Ans0 $f^{-1}(x)$ +\Ans0 none of them +\end{question} + +\begin{question} +$\arcsin(\sin x)=x$ for every $x\in\mathbf{R}$ +\Ans0 Yes +\Ans1 No +\end{question} + +\end{category} + + +\begin{category}{Limits} + +\begin{question} +$\lim_{x\to-\infty} \arctg x=$ +\Ans0 $0$ +\Ans0 $\frac\pi2$ +\Ans1 $-\frac\pi2$ +\Ans0 $\infty$ +\Ans0 $-\infty$ +\Ans0 none of them +\end{question} + +\begin{question} +$\lim_{x\to\infty}\sin x=$ +\Ans0 $1$ +\Ans0 $-1$ +\Ans1 does not exist +\Ans0 none of them +\end{question} + +\begin{question} +$\lim_{x\to\infty}\frac{2x^3+x^2+4}{x^2-x+2}=$ +\Ans1 $\infty$ +\Ans0 $2$ +\Ans0 $0$ +\Ans0 none of them +\end{question} + +\begin{question} +$\lim_{x\to 0^+}\frac{e^{1/x}(x-1)}{x}$ +\Ans0 $0$ +\Ans0 $1$ +\Ans0 $e$ +\Ans0 $\infty$ +\Ans0 $-1$ +\Ans0 $-e$ +\Ans1 $-\infty$ +\Ans0 none of them +\end{question} + +\end{category} + +\begin{category}{Derivative} + + +\begin{question} +$\left(\frac 1{\sqrt[3]x}\right)'=$ +\Ans0 $\frac 13 x^{-2/3}$ +\Ans0 $-\frac 13 x^{-2/3}$ +%\Ans0 $\frac 13 x^{1/3}$ +\Ans0 $-\frac 13 x^{1/3}$ +\Ans0 $\frac 13 x^{-4/3}$ +\Ans1 $-\frac 13 x^{-4/3}$ +\Ans0 none of them +\end{question} + + +\begin{question} +$(x-x\ln x)'=$ +\Ans0 $\ln x$ +\Ans1 $-\ln x$ +\Ans0 $1+\ln x$ +\Ans0 $1-\ln x$ +\Ans0 $0$ +\Ans0 $1-\frac 1x$ +\Ans0 none of them +\end{question} + +\begin{question} +$\left(x^2e^{x^2}\right)'$ +\Ans0 $2xe^{2x}$ +\Ans0 $2xe^{x^2}2x$ +\Ans0 $2xe^{x^2}+x^2e^{x^2}$ +\Ans1 $2xe^{x^2}+x^2e^{x^2}2x$ +\Ans0 $2xe^{x^2}2x+x^2e^{x^2}2x$ +\Ans0 none of them +\end{question} + +\begin{question} +The definition of the derivative of the function $f$ at the point $a$ is +\Ans0 $\lim_{h\to 0}\frac{f(x+h)+f(x)}{h}$ +\Ans0 $\lim_{h\to 0}\frac{f(x+h)}{h}$ +\Ans1 $\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}$ +\Ans0 $\lim_{h\to 0}\frac{f(x)-f(x+h)}{h}$ +\Ans0 $\lim_{h\to 0}\frac{f(x-h)-f(x)}{h}$ +\Ans0 none of them +\end{question} + +\end{category} + +\everyRespBoxMath{\BG{1 1 1}} +\begin{category}{Evaluation of derivatives} + \begin{question}$(x^2+1)'=$ + \RespBoxMath{2x}{3}{0.001}{[1,5]} + \end{question} + \begin{question}$(xe^x)'=$ + \RespBoxMath{(x+1)e^x}{3}{0.001}{[1,5]} + \end{question} + \begin{question}$\ln(\sin x)=$ + \RespBoxMath{cos(x)/sin(x)}{3}{0.001}{[1,2]} + \end{question} + \begin{question}$(xe^{-x})'=$ + \RespBoxMath{(1-x)e^{-x}}{3}{0.001}{[1,5]} + \end{question} +\end{category} + + + +\begin{category}{Theory} + +\begin{question} By theorem of Bolzano, the polynomial $y=x^3+2x+4$ has zero on +\Ans0 $(0,1)$ +\Ans0 $(1,2)$ +\Ans0 $(2,3)$ +\Ans0 $(-1,0)$ +\Ans1 $(-2,-1)$ +\Ans0 $(-3,-2)$ +\Ans0 none of them +\end{question} + + +\begin{question} +Let $a\in Im(f)$. Then the solution of the equation $f(x)=a$ exists. This +solution is unique if and only if +\Ans1 $f$ is one-to-one +\Ans0 $f$ is increasing +\Ans0 $f$ continuous +\Ans0 $f$ differentiable +\Ans0 none of them +\end{question} + + +\begin{question} +If the function has a derivative at the point $x=a$, then it is +\Ans0 increasing at $a$. +\Ans0 decreasing at $a$. +\Ans0 one-to-one at $a$. +\Ans1 continuous at $a$. +\Ans0 undefined at $a$. +\end{question} + +\begin{question} +If both $y(a)=y'(a)=y''(a)=0$, then the function +\Ans0 has local maximum at $a$. +\Ans0 has local minimum at $a$. +\Ans0 has point of inflection at $a$. +\Ans1 any of these possibilites may be true, we need more informations. +\end{question} + +\end{category} + + +\end{document} +%%% Local Variables: +%%% mode: latex +%%% TeX-master: t +%%% End: + + |