summaryrefslogtreecommitdiff
path: root/Master/texmf-dist/doc/latex/webquiz/examples/quiz-page.tex
diff options
context:
space:
mode:
Diffstat (limited to 'Master/texmf-dist/doc/latex/webquiz/examples/quiz-page.tex')
-rw-r--r--Master/texmf-dist/doc/latex/webquiz/examples/quiz-page.tex251
1 files changed, 251 insertions, 0 deletions
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}