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diff --git a/Master/texmf-dist/doc/latex/webquiz/examples/quiz-page.tex b/Master/texmf-dist/doc/latex/webquiz/examples/quiz-page.tex new file mode 100644 index 00000000000..d4436fc5fa4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/webquiz/examples/quiz-page.tex @@ -0,0 +1,251 @@ +\documentclass[]{webquiz} +\usepackage[MATH1001]{sms-uos} +\BreadCrumbs{department | unitcode | quizindex | title} +\DeclareMathOperator{\cis}{cis} +\newcommand{\R}{\mathbb R} +\newcommand{\C}{\mathbb C} +\usepackage{pst-all} + +\title{Quiz 1: Numbers and sets} + +\begin{document} + + \begin{question} + Which of the following are correct ways of writing the set + \[ A=\{x \in \mathbb{R} \mid -3 < x \leq -1 \text{ or } x\geq 0\} ?\] + \begin{choice}[columns=2] + \incorrect $(-3,\infty)$ + \feedback The interval $(-3,\infty)$ includes the real numbers + between $-1$ and $0$, which do not belong to $A$. + + \incorrect $[-3,\infty)$ + \feedback The interval $[-3,\infty)$ includes $-3$, and + the real numbers between $-1$ and $0$, which do not belong to $A$. + + \incorrect $[-3,-1]\cap[0,\infty)$ + \feedback The interval $[-3,-1]\cap[0,\infty)$ is the empty set + $\emptyset$. As $A$ is not empty (for example, $A$ includes + $-1$), this option cannot be correct. + + \incorrect $(-3,-1)\cup[0,\infty)$ + \feedback The interval $-1$ is not in $(-3,-1)\cup[0,\infty)$, + but $-1$ is in $A$. + + \correct $(-3,-1]\cup[0,\infty)$ + + \end{choice} + \end{question} + +%%%% 2 +\begin{question} +What is another way of writing the set +\[B= \{x \in {\mathbb R}\ |\ |x-3|<2 \}\ \rm{?}\] +\begin{choice}[columns=2] +\incorrect $(2,3]$ +\feedback For example, $4$ belongs to $B$ but is not in $(2,3]$. + +\incorrect $[2,4]$ +\feedback For example, $1.5$ belongs to $B$ but is not in $[2,4]$. + +\correct $(1,5)$ + +\feedback $B$ is the set of all points whose distance from 3 on the +number line is less than 2. \\ +The solution to $|x-3|<2$ is $1<x<5$. + +\incorrect $[1,5]$ +\feedback Neither $1$ nor $5$ belong to $B$, but both $1$ and $5$ belong to $[1,5]$. + +\incorrect $[2,3)$ +\feedback For example, $4$ belongs to $B$ but is not in $[2,3)$. + +\end{choice} +\end{question} + + +%%%%%%%%%% 3 +\begin{question} +If $A=\{7,8,9,10\}$ and $B=\{5,6,7,8\}$ then $(A\backslash +B)\cup(B\backslash A)$ is +\begin{choice}[columns=2] +\incorrect $\{5,6,7,8,9,10\}$ + +\correct $\{5,6,9,10\}$ + +\feedback $A\backslash B=\{9,10\}$ and $B\backslash A=\{5,6\}$ so +$(A\backslash B)\cup(B\backslash A)=\{5,6,9,10\}$. + +\incorrect $\emptyset$, the empty set. + +\incorrect $\{7,8\}$ + +\incorrect None of the above. + +\end{choice} +\end{question} + +%%%%%%%%%%%%%% 4 +\begin{question} +The set \(\{0,1,\pm\sqrt{-1},\pi,12\}\) is a subset of +\begin{choice}[columns=2] +\incorrect $\mathbb N$ +\feedback The number \(\pi\) is not a natural number. + +\incorrect $\mathbb Z$ +\feedback The number \(\pi\) is not an integer. + +\incorrect $\mathbb Q$ +\feedback The number \(\pi\) is not a rational number. + +\incorrect $\mathbb R$ +\feedback \(\sqrt{-1}\) is not real. + +\correct $\mathbb C$ +\feedback Since \(\pm\sqrt{-1}\) denotes the two imaginary numbers $i$ and $-i$, the given set cannot be +in any of the sets $\mathbb{N,Z,Q}\ \rm{or}\ \mathbb{R}$. \\ +Hence the +right answer must be ${\mathbb C}$ which contains all imaginary +numbers. + +\end{choice} +\end{question} + +%%%%%%%%%% 5 +\begin{question} +Which of the following alternatives is the best feedback to `Solve +$x^{2}-3x+4=0$ over $\mathbb{C}$'. +\begin{choice}[columns=2] +\incorrect There are no real solutions. +\feedback As the question asks us to solve the equation over $\mathbb C$ (that is, to find all solutions belonging to the set of complex numbers), this is not the best feedback. + +\incorrect $x=1,4$ + +\incorrect \(x=\dfrac{3\pm\sqrt{7}}{2}\) + +\correct \(x=\dfrac{3\pm i\sqrt{7}}{2}\) + +\feedback Using the quadratic formula, +\(x =\dfrac{3\pm\sqrt{9-16}}{2} = \dfrac{3\pm\sqrt{-7}}{2}\). + + +\incorrect None of the above is correct. +\end{choice} +\end{question} + +%%%%%%% 6 +\begin{question} +If $z=9+3i$ and $w=2-i$ then $z+w$ equals +\begin{choice}[columns=2] +\incorrect $9-i$ + +\correct $11+2i$ +\feedback $z+w=(9+3i)+(2-i)=(9+2)+(3-1)i=11+2i$. + +\incorrect $6+3i$ + +\incorrect $8$ + +\incorrect None of the above + +\end{choice} +\end{question} + +%%%%%%% 7 + +\begin{question} +If $w=2-i$ then $\overline{w}$ equals +\begin{choice}[columns=2] +\incorrect $2-i$ + +\incorrect $2$ + +\correct $2+i$ + +\feedback +$\overline{w}=\overline{2-i}=2+i$. + +\incorrect $-2+i$ + +\incorrect None of the above +\end{choice} +\end{question} + +%%%%%%%%% 8 +\begin{question} +If $p=9+3i$ and $q=2-i$ then $p\overline{q}$ equals +\begin{choice}[columns=2] + +\correct $15+15i$ + +\feedback +$p\overline{q}=(9+3i)\overline{(2-i)}$ \\ +$=(9+3i)(2+i)= (18-3)+(6+9)i$\\ +$=15+15i$. + +\incorrect $21+15i$ + +\incorrect $18+3i$ + +\incorrect $1-i$ + +\incorrect None of the above + +\end{choice} +\end{question} + + +%%%%%%%%% 9 +\begin{question} +If $z=9+3i$ and $w=2-i$ then $\dfrac{z}{w}$ equals +\begin{choice}[columns=2] +\incorrect $15+15i$ + +\incorrect $6+3i$ + +\incorrect $12+15i$ + +\incorrect $3-3i$ + +\correct None of the above + +\feedback +\(\dfrac{z}{w}=\dfrac{9+3i}{2-i} + =\dfrac{9+3i}{2-i}\times \dfrac{2+i}{2+i} + =\dfrac{15+15i}{5}=3+3i\). +\end{choice} +\end{question} + +%%%%%%%%%% 10 +\begin{question} +The shaded region in the graph +\begin{center}\begin{pspicture}(-3,-1.5)(3,4) +\pscircle[linewidth=2pt,linestyle=dashed,fillcolor=blue,fillstyle=solid](1,1){2} +\psaxes[linecolor=red,linewidth=1pt,labels=none]{->}(0,0)(-1.5,-1.5)(3.5,3.5) +\rput(3.75,0){$x$} +\rput(0,3.85){$iy$} +\rput(3,-0.4){3} +\rput(-0.4,3){3$i$} +\psdots(1,1) +\end{pspicture} +\end{center} +corresponds to which set of complex numbers? +\begin{choice}[columns=2] +\correct\(\{z \in \C : |z-(i+1)|<2\}\) + + +\incorrect \(\{z \in \C : |z|-|1+i|<2\}\) +\feedback This set corresponds to the interior of a circle, centre the origin, radius $2+\sqrt 2$. + + +\incorrect \(\{z \in \C : \text{Re}(z+(i+1))<2 \}\) +\feedback This set corresponds to the open half plane containing all complex numbers $z=x+iy$ with $x<1$. + +\incorrect \(\{z \in \C : |z-2|<|i+1-2|\}\) +\feedback This set corresponds to the interior of a circle, centre $2$, radius $\sqrt 2$. + +\incorrect None of the above. + +\end{choice} +\end{question} + +\end{document} |