diff options
author | Karl Berry <karl@freefriends.org> | 2017-07-13 23:06:59 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2017-07-13 23:06:59 +0000 |
commit | 03542c01781307bd8cb29571d8a39197a4de83e2 (patch) | |
tree | b11e221ce28f24eee3995a8efb51d2e76993472c /Master/texmf-dist/doc/latex/probsoln/samples | |
parent | 04f93eb1202717fcb407f1271d28f4153aaa0ca0 (diff) |
probsoln (10jul17)
git-svn-id: svn://tug.org/texlive/trunk@44783 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/probsoln/samples')
33 files changed, 712 insertions, 462 deletions
diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-1stprncp.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-1stprncp.tex new file mode 100644 index 00000000000..343d6b3e1c0 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-1stprncp.tex @@ -0,0 +1,63 @@ + % This file is public domain + % + % These problems all involve differentiating from 1st principles + +\newproblem{dfp:xcube}{% +Differentiate $f(x) = x^3$ with respect to $x$ by first principles.}{% +\begin{eqnarray*} +\frac{dy}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{f(x+\Delta x) - f(x)}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{(x+\Delta x)^3-x^3}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{(x+\Delta x)(x^2+2x\Delta x+(\Delta x)^2)-x^3}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{x^3+3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3-x^3}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}3x^2+3x\Delta x + (\Delta x)^2\\ + & = & 3x^2 +\end{eqnarray*}} + +\newproblem{dfp:Ioverxsq}{% +Differentiate $\displaystyle f(x) = \frac{1}{x^2}$ with respect to $x$ by first principles.}{% +\begin{eqnarray*} +\frac{df}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{\frac{1}{(x+\Delta x)^2}-\frac{1}{x^2}}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{\frac{x^2-(x+\Delta x)^2}{x^2(x+\Delta x)^2}}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{x^2-(x^2+2x\Delta x+(\Delta x)^2)}{x^2\Delta x(x+\Delta x)^2}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{-2x\Delta x-(\Delta x)^2}{x^2\Delta x(x+\Delta x)^2}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{-2x-\Delta x}{x^2(x+\Delta x)^2}\\ + & = & \frac{-2x}{x^2x^2}\\ + & = & -\frac{2}{x^3} +\end{eqnarray*}} + +\newproblem{dfp:sqrtx}{% +Differentiate from first principles $f(x) = \surd x$}{% +\begin{eqnarray*} +\frac{df}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{\sqrt{x+\Delta x}-\surd x}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{(\sqrt{x+\Delta x}-\surd x)(\sqrt{x+\delta x}+\surd x)}{\Delta x(\sqrt{x+\Delta x}+\surd x)}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{x+\Delta x - x}{\Delta x(\sqrt{x+\Delta x}+\surd x)}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{\Delta x}{\Delta x(\sqrt{x+\Delta x}+\Delta x)}\\ + & = & \lim_{\Delta x\rightarrow 0}\frac{1}{\sqrt{x+\Delta x}+\surd x}\\ + & = & \frac{1}{2\surd x} +\end{eqnarray*}} + +\newproblem{dfp:cons}{% +Differentiate from first principles $f(x) = c$ where $c$ is a constant.}{% +\begin{eqnarray*} +\frac{df}{dx} & = & \lim_{\Delta x\rightarrow 0}\frac{c-c}{\Delta x}\\ + & = & \lim_{\Delta x\rightarrow 0}0\\ + & = & 0 +\end{eqnarray*}} + +\newproblem{dfp:cosx}{% +Given +\begin{eqnarray*} +\lim_{x \rightarrow 0} \frac{\cos x - 1}{x} & = & 0\\ +\lim_{x \rightarrow 0} \frac{\sin x}{x} & = & 1 +\end{eqnarray*} +differentiate from first principles $f(x) = \cos x$.}{% +\begin{eqnarray*} +\frac{df}{dx} & = & \lim_{\Delta x \rightarrow 0}\frac{f(x + \Delta x) - f(x)}{\Delta x}\\ + & = & \lim_{\Delta x \rightarrow 0} \frac{\cos(x + \Delta x) - \cos(x)}{\Delta x}\\ + & = & \lim_{\Delta x \rightarrow 0} \frac{\cos x\cos\Delta x - \sin x\sin\Delta x - \cos x}{\Delta x}\\ + & = & \lim_{\Delta x \rightarrow 0} \frac{\cos x(\cos\Delta x - 1) - \sin x\sin\Delta x}{\Delta x}\\ + & = & \cos x\lim_{\Delta x \rightarrow 0}\frac{\cos\Delta x - 1}{\Delta x} + - \sin x\lim_{\Delta x \rightarrow 0}\frac{\sin\Delta x}{\Delta x}\\ + & = & -1 \qquad\mbox{(using given results)} +\end{eqnarray*}} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-args.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-args.tex new file mode 100644 index 00000000000..8276790feb6 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-args.tex @@ -0,0 +1,49 @@ + % This file is public domain + % + % These problems require arguments +% + % Arguments: #1->a_2, #2->a_1 and #3->a_0 + % (Arguments must be integers) +\newcount\ctr +\newproblem[3][{1}{2}{3}]{diff:quad}{% +\(f(x) = +\ifnum#1=0 +\else +\ifnum#1=1\else#1\fi x^2 +\fi +\ifnum#2=0 +\else +\ifnum#2>0 \ifnum#1=0 \else + \fi \fi +\ifnum#2=1\else#2\fi x +\fi +\ifnum#3=0 +\else +\ifnum#3>0 \ifnum#2=0 \ifnum#1=0 \else + \fi \else + \fi\fi +#3 +\fi\) +}{% +\(f'(x) = +\ifnum#1=0 +\else +\ctr=2 +\multiply\ctr by #1 +\the\ctr x +\fi +\ifnum#2=0 +\else +\ifnum#2>0 \ifnum#1=0 \else + \fi \fi +#2 +\fi + % print 0 if both #1 and #2 are 0 +\ifnum#1=0 \ifnum#2=0 0 \fi\fi +\) +} + +\begin{defproblem}[1][{6}]{diff:sin} +\begin{onlyproblem} + \(f(x) = \sin(#1x)\) +\end{onlyproblem} +\begin{onlysolution} + \(f'(x) = #1\cos(#1x)\) +\end{onlysolution} +\end{defproblem} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-easy.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-easy.tex new file mode 100644 index 00000000000..0527e3e4647 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-easy.tex @@ -0,0 +1,114 @@ + % This file is public domain + % + % These are all easy differentiation problems + +\newproblem{diffeasy:gpowh}{% +\(f(x) = g(x)^{h(x)}.\)}{% +\begin{eqnarray*} +f(x) & = & e^{\ln g(x)^{h(x)}}\\ + & = & e^{h(x)\ln g(x)}\\ +f'(x) & = & e^{h(x)\ln g(x)}(h'(x)\ln g(x) + h(x)\frac{g'(x)}{g(x)})\\ + & = & g(x)^{h(x)}(h'(x)\ln g(x) + \frac{h(x)g'(x)}{g(x)}) +\end{eqnarray*}} + +\newproblem{diffeasy:arcsin}{% +\(y = \arcsin(x)\)}{% +\[\sin(y) = x\] +diff. w.r.t. $x$: +\begin{eqnarray*} +\cos y \frac{dy}{dx} & = & 1\\ +\frac{dy}{dx} & = & \frac{1}{\cos y}\\ + & = & \frac{1}{\sqrt{1 - \sin^2y}}\\ + & = & \frac{1}{\sqrt{1-x^2}}. +\end{eqnarray*}} + +\newproblem{diffeasy:arccos}{% +$y = \arccos x$.}{% +\(\cos y = x\) +diff. w.r.t. $x$: +\begin{eqnarray*} +-\sin y \frac{dy}{dx} & = & 1\\ +\frac{dy}{dx} & = & \frac{-1}{\sin y}\\ + & = & \frac{-1}{\sqrt{1-\cos^2y}}\\ + & = & \frac{-1}{\sqrt{1-x^2}} +\end{eqnarray*}} + +\newproblem{diffeasy:tan}{% +\(y = \tan x\)}{% +\begin{eqnarray*} +y & = & \tan x\\ + & = & \frac{\sin x}{\cos x}\\ +\frac{dy}{dx} & = & \frac{\cos x}{\cos x} + \sin x\times\frac{-1}{\cos^2x}\times -\sin x\\ + & = & 1 + \tan^2x\\ + & = & \sec^2x. +\end{eqnarray*}} + +\newproblem{diffeasy:arctan}{% +\(y = \arctan x = \tan^{-1}x\)}{% +\[\tan y = x\] +diff w.r.t. $x$: +\begin{eqnarray*} +\sec^2y\frac{dy}{dx} & = & 1\\ +\frac{dy}{dx} & = & \frac{1}{\sec^2y}\\ + & = & \frac{1}{1+\tan^2y}\\ + & = & \frac{1}{1+x^2} +\end{eqnarray*}} + +\newproblem{diffeasy:cot}{% +\(y = (\tan x)^{-1} = \cot x\)}{% +\begin{eqnarray*} +\frac{dy}{dx} & = & -(\tan x)^{-2}\sec^2x\\ + & = & -\frac{\cos^2x}{\sin^2x}\cdot\frac{1}{\cos^2x}\\ + & = & \frac{-1}{\sin^2x}\\ + & = & -\csc^2x. +\end{eqnarray*}} + +\newproblem{diffeasy:cosxsqsinx}{% +$y = \cos(x^2)\sin x$.}{% +\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\]} + +\newproblem{diffeasy:xlnx}{% +$y = (x+1)\ln(x+1)$.}{% +\begin{eqnarray*} +\frac{dy}{dx} & = & \ln(x+1) + \frac{x+1}{x+1}\\ + & = & 1 + \ln(x+1). +\end{eqnarray*}} + +\newproblem{diffeasy:glng}{% +$f(x) = g(x)\ln(g(x))$.}{% +\begin{eqnarray*} +f'(x) & = & g'(x)\ln(g(x)) + \frac{g(x)}{g(x)}g'(x)\\ + & = & g'(x)(1+\ln(g(x))). +\end{eqnarray*}} + +\newproblem{diffeasy:sinx/x}{% +$y = \frac{\sin x}{x}$.}{% +\[\frac{dy}{dx} = \frac{\cos x}{x} - \frac{\sin x}{x^2}\]} + +\newproblem{diffeasy:exp4x}{% + $y = \exp(4x)$ +}% +{% + \[\frac{dy}{dx} = 4\exp(4x)\] +} + +\newproblem{diffeasy:exp3x+2}{% + $y = \exp(3x+2)$ +}% +{% + \[\frac{dy}{dx} = 3\exp(3x+2)\] +} + +\newproblem{diffeasy:cubic}{% + $y=x^3 + 4x^2 - x + 3$ +}% +{% + \[\frac{dy}{dx} = 3x^2 + 8x - 1\] +} + +\newproblem{diffeasy:quad}{% + $y=2x^3 + 6x -1$ +}% +{% + \[\frac{dy}{dx} = 6x + 6 = 6(x+1)\] +} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-easy2.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-easy2.tex new file mode 100644 index 00000000000..d6edc7ee3ce --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-easy2.tex @@ -0,0 +1,137 @@ + % This file is public domain + % + % These are all easy differentiation problems + +\begin{defproblem}{diffeasy:gpowh}% +\begin{onlyproblem}% +\(f(x) = g(x)^{h(x)}.\)% +\end{onlyproblem}% +\begin{onlysolution}% +\begin{eqnarray*} +f(x) & = & e^{\ln g(x)^{h(x)}}\\ + & = & e^{h(x)\ln g(x)}\\ +f'(x) & = & e^{h(x)\ln g(x)}(h'(x)\ln g(x) + h(x)\frac{g'(x)}{g(x)})\\ + & = & g(x)^{h(x)}(h'(x)\ln g(x) + \frac{h(x)g'(x)}{g(x)}) +\end{eqnarray*}% +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:arcsin}% +\begin{onlyproblem}% +\(y = \arcsin(x)\)% +\end{onlyproblem}% +\begin{onlysolution}% +\[\sin(y) = x\] +diff. w.r.t. $x$: +\begin{eqnarray*} +\cos y \frac{dy}{dx} & = & 1\\ +\frac{dy}{dx} & = & \frac{1}{\cos y}\\ + & = & \frac{1}{\sqrt{1 - \sin^2y}}\\ + & = & \frac{1}{\sqrt{1-x^2}}. +\end{eqnarray*} +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:arccos}% +\begin{onlyproblem}% +$y = \arccos x$.% +\end{onlyproblem}% +\begin{onlysolution}% +\(\cos y = x\) +diff. w.r.t. $x$: +\begin{eqnarray*} +-\sin y \frac{dy}{dx} & = & 1\\ +\frac{dy}{dx} & = & \frac{-1}{\sin y}\\ + & = & \frac{-1}{\sqrt{1-\cos^2y}}\\ + & = & \frac{-1}{\sqrt{1-x^2}} +\end{eqnarray*} +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:tan}% +\begin{onlyproblem}% +\(y = \tan x\)% +\end{onlyproblem} +\begin{onlysolution}% +\begin{eqnarray*} +y & = & \tan x\\ + & = & \frac{\sin x}{\cos x}\\ +\frac{dy}{dx} & = & \frac{\cos x}{\cos x} + \sin x\times\frac{-1}{\cos^2x}\times -\sin x\\ + & = & 1 + \tan^2x\\ + & = & \sec^2x. +\end{eqnarray*} +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:arctan}% +\begin{onlyproblem}% +\(y = \arctan x = \tan^{-1}x\)% +\end{onlyproblem}% +\begin{onlysolution}% +\[\tan y = x\] +diff w.r.t. $x$: +\begin{eqnarray*} +\sec^2y\frac{dy}{dx} & = & 1\\ +\frac{dy}{dx} & = & \frac{1}{\sec^2y}\\ + & = & \frac{1}{1+\tan^2y}\\ + & = & \frac{1}{1+x^2} +\end{eqnarray*} +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:cot}% +\begin{onlyproblem}% +\(y = (\tan x)^{-1} = \cot x\)% +\end{onlyproblem} +\begin{onlysolution}% +\begin{eqnarray*} +\frac{dy}{dx} & = & -(\tan x)^{-2}\sec^2x\\ + & = & -\frac{\cos^2x}{\sin^2x}\cdot\frac{1}{\cos^2x}\\ + & = & \frac{-1}{\sin^2x}\\ + & = & -\csc^2x. +\end{eqnarray*} +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:cosxsqsinx}% +\begin{onlyproblem}% +$y = \cos(x^2)\sin x$.% +\end{onlyproblem}% +\begin{onlysolution}% +\[\frac{dy}{dx} = -\sin(x^2)2x\sin x + \cos(x^2)\cos x\] +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:xlnx}% +\begin{onlyproblem}% +$y = (x+1)\ln(x+1)$. +\end{onlyproblem}% +\begin{onlysolution}% +\begin{eqnarray*} +\frac{dy}{dx} & = & \ln(x+1) + \frac{x+1}{x+1}\\ + & = & 1 + \ln(x+1). +\end{eqnarray*} +\end{onlysolution} +\end{defproblem} + +\begin{defproblem}{diffeasy:glng}% +\begin{onlyproblem}% +$f(x) = g(x)\ln(g(x))$. +\end{onlyproblem} +\begin{onlysolution}% +\begin{eqnarray*} +f'(x) & = & g'(x)\ln(g(x)) + \frac{g(x)}{g(x)}g'(x)\\ + & = & g'(x)(1+\ln(g(x))). +\end{eqnarray*} +\end{onlysolution}% +\end{defproblem} + +\begin{defproblem}{diffeasy:sinx/x} +\begin{onlyproblem}% +$y = \frac{\sin x}{x}$. +\end{onlyproblem} +\begin{onlysolution}% +\[\frac{dy}{dx} = \frac{\cos x}{x} - \frac{\sin x}{x^2}\] +\end{onlysolution}% +\end{defproblem} + diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-implicit.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-implicit.tex new file mode 100644 index 00000000000..dd847d96e30 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-implicit.tex @@ -0,0 +1,52 @@ + % This file is public domain + % + % These are all implicit differentiation problems + +\newproblem{imd:circ}{% +Find the gradient of the unit circle ($x^2 + y^2 = 1$).}{% +Differentiating with respect to $x$ gives: +\begin{eqnarray*} +2x + 2y\frac{dy}{dx} & = & 0\\ +\frac{dy}{dx} & = & \frac{-2x}{2y}\\ + & = & \frac{-x}{\sqrt{1-x^2}}. +\end{eqnarray*}} + +\newproblem{imd:ellipse}{% +Find the gradient of the ellipse given by $4x^2 + 3y^2 = 25$.}{% +Differentiating with respect to $x$ gives: +\begin{eqnarray*} +8x + 6y\frac{dy}{dx} & = & 0\\ +\frac{dy}{dx} & = & \frac{-8x}{6y}\\ + & = & \frac{-4x}{\sqrt{25-4x^2}}. +\end{eqnarray*}} + +\newproblem{imd:ysq:xcuov2mx}{% +Find $\frac{dy}{dx}$, given +\begin{displaymath} +y^2 = \frac{x^3}{2-x} +\end{displaymath}}{% +Differentiating both sides w.r.t.\ $x$: +\begin{eqnarray*} +2y\frac{dy}{dx} & = & \frac{(2-x)3x^2 - x^3(-1)}{(2-x)^2}\\ + & = & \frac{3x^2(2-x) + x^3}{(2-x)^2}\\ + & = & \frac{6x^2 - 3x^3 + x^3}{(2-x)^2}\\ + & = & \frac{6x^2-2x^3}{(2-x)^2}\\ + & = & 2x^2\frac{3-x}{(2-x)^2} +\end{eqnarray*} +Therefore +\begin{displaymath} +y\frac{dy}{dx} = x^2\frac{3-x}{(2-x)^2} +\end{displaymath}} + +\newproblem{imd:exy:IIxay}{% +Differentiate w.r.t.\ $x$: +\begin{displaymath} +e^{xy} = 2x + y +\end{displaymath}}{% +Differentiating both sides w.r.t.\ $x$: +\begin{eqnarray*} +e^{xy}(1y + x\frac{dy}{dx}) & = & 2 + \frac{dy}{dx}\\ +xe^{xy}\frac{dy}{dx} - \frac{dy}{dx} & = & 2 - ye^{xy} \\ +\frac{dy}{dx}(xe^{xy}-1) & = & 2 - ye^{xy}\\ +\frac{dy}{dx} & = & \frac{2-ye^{xy}}{xe^{xy}-1} +\end{eqnarray*}} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-mchoice.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-mchoice.tex new file mode 100644 index 00000000000..22886ce9b2c --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-mchoice.tex @@ -0,0 +1,37 @@ + % This file is public domain + % + % These problems are for multiple choice questions +\newproblem{mc:prod}{% +Which of the following is the derivative of $x\sin(x)$? +(Circle the correct answer.) +\ifthenelse{\boolean{showanswers}}{}% +{\begin{description} +\item[A] $\sin(x)$ +\item[B] $x\cos(x)$ +\item[C] $\sin(x) + x\cos(x)$ +\end{description} +}}{% +\begin{description} +\item[A] $\sin(x)$ +\item[B] $x\cos(x)$ +\item[\textcircled{C}] $\sin(x) + x\cos(x)$ (product rule). +\end{description} +} + +\newproblem{mc:quot}{% +Which of the following is the derivative of $\frac{\sin(x)}{x}$? +(Circle the correct answer.) +\ifthenelse{\boolean{showanswers}}{}% +{\begin{description} +\item[A] $\sin(x)$ +\item[B] $\cos(x)$ +\item[C] $\frac{\cos(x)x-\sin(x)}{x^2}$ +\end{description} +}}{% +\begin{description} +\item[A] $\sin(x)$ +\item[B] $\cos(x)$ +\item[\textcircled{C}] $\frac{\cos(x)x-\sin(x)}{x^2}$ +(quotient rule) +\end{description} +} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-mixed.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-mixed.tex new file mode 100644 index 00000000000..1f43968b8a4 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-mixed.tex @@ -0,0 +1,78 @@ + % This file is public domain + % + % These problems are a mixture of essay-style and questions with + % answers. One of these problems requires the tikz package + +\newproblem*{oop}{Describe what is meant by object-oriented +programming.} + +\begin{defproblem}{inheritance} + Describe what is meant by the term \emph{inheritance} in + object-oriented programming. Use examples. +\end{defproblem} + +\begin{defproblem}{weightedcoin}% + \begin{onlyproblem} + A coin is weighted so that heads is four times as likely + as tails. Find the probability that: + \begin{textenum} + \item tails appears, + \item heads appears + \end{textenum}% + \end{onlyproblem}% + \begin{onlysolution} + Let $p=P(T)$, then $P(H)=4p$. We require $P(H)+P(T)=1$, + so $4p+p=1$, hence $p=\frac{1}{5}$. Therefore: + \begin{textenum} + \item $P(T)=\frac{1}{5}$, + \item $P(H)=\frac{4}{5}$ + \end{textenum} + \end{onlysolution} +\end{defproblem} + +\begin{defproblem}{validprobspaces} +\begin{onlyproblem}% +Under which of the following functions does +$S=\{a_1,a_2\}$ become a probability space? +\par +\begin{textenum} +\begin{tabular}{ll} +\item $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$ +& +\item\label{validprobspacescorrect1} $P(a_1)=\frac{3}{4}$, +$P(a_2)=\frac{1}{4}$ +\\ +\item\label{validprobspacescorrect2} $P(a_1)=1$, $P(a_2)=0$ +& +\item $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$ +\end{tabular} +\end{textenum} +\end{onlyproblem}% +\begin{onlysolution}% +\ref{validprobspacescorrect1} and \ref{validprobspacescorrect2}% +\end{onlysolution} +\end{defproblem} + +\begin{defproblem}{digraph} + \begin{onlyproblem}\label{ex:digraph} + Identify, if any, the sinks and sources of the digraph shown in Figure~\ref{fig:digraph}. + + \begin{figure}[tbh] + \centering + \begin{tikzpicture}[every node/.style={draw,circle}] + \path (0,0) node (A) {$A$} + (1,0) node (B) {$B$} + (0,1) node (C) {$C$}; + \draw[->] (A) -- (B); + \draw[->] (B) -- (C); + \draw[->] (A) -- (C); + \end{tikzpicture} + \par + \caption{Digraph for Question~\ref{ex:digraph}} + \label{fig:digraph} + \end{figure} + \end{onlyproblem} + \begin{onlysolution} + $A$ is a souce and $C$ is a sink. + \end{onlysolution} +\end{defproblem} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-newdata.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-newdata.tex new file mode 100644 index 00000000000..946f0e11248 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-newdata.tex @@ -0,0 +1,27 @@ + % This file is public domain +\begin{defproblem}{sample} +\begin{onlyproblem} +Differentiate $y=\sin x$ +\end{onlyproblem} +\begin{onlysolution} +$y'=\cos x$ +\end{onlysolution} +\end{defproblem} + +\begin{defproblem}[1]{sample2} +\begin{onlyproblem} +Differentiate $y = \sin(#1x)$ +\end{onlyproblem} +\begin{onlysolution} +$y'=#1\cos #1x$ +\end{onlysolution} +\end{defproblem} + +\begin{defproblem}{sample3} +\begin{onlyproblem} +Differentiate $y = x^2$. +\end{onlyproblem} +\begin{onlysolution} +$y' = 2x$ +\end{onlysolution} +\end{defproblem} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-nosoln.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-nosoln.tex new file mode 100644 index 00000000000..9909651b86d --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-nosoln.tex @@ -0,0 +1,9 @@ + % This file is public domain + % + % these problems don't have solutions + +\newproblem*{oop}{Describe what is meant by object-oriented +programming.} + +\newproblem*{inheritance}{Describe what is meant by the term +\emph{inheritance} in object-oriented programming. Use examples.} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces.tex new file mode 100644 index 00000000000..4862e5caefb --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces.tex @@ -0,0 +1,33 @@ + % This file is public domain + % + % Finite probability spaces +\newproblem{weightedcoin}{% +A coin is weighted so that heads is four times as likely +as tails. Find the probability that: +\begin{textenum} +\item tails appears, +\item heads appears +\end{textenum}}{% +Let $p=P(T)$, then $P(H)=4p$. We require $P(H)+P(T)=1$, +so $4p+p=1$, hence $p=\frac{1}{5}$. Therefore: +\begin{textenum} +\item $P(T)=\frac{1}{5}$, +\item $P(H)=\frac{4}{5}$ +\end{textenum}} + +\newproblem*{validprobspaces}{% +Under which of the following functions does +$S=\{a_1,a_2\}$ become a probability space? +\par +\begin{textenum} +\begin{tabular}{ll} +\incorrectitem $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$ +& +\correctitem $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$ +\\ +\correctitem $P(a_1)=1$, $P(a_2)=0$ +& +\incorrectitem $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$ +\end{tabular} +\end{textenum} +} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex new file mode 100644 index 00000000000..dacddb510cf --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-probspaces2.tex @@ -0,0 +1,43 @@ + % This file is public domain + % + % Finite probability spaces +\begin{defproblem}{weightedcoin} +\begin{onlyproblem}% +A coin is weighted so that heads is four times as likely +as tails. Find the probability that: +\begin{textenum} +\item tails appears, +\item heads appears +\end{textenum} +\end{onlyproblem} +\begin{onlysolution}% +Let $p=P(T)$, then $P(H)=4p$. We require $P(H)+P(T)=1$, +so $4p+p=1$, hence $p=\frac{1}{5}$. Therefore: +\begin{textenum} +\item $P(T)=\frac{1}{5}$, +\item $P(H)=\frac{4}{5}$ +\end{textenum} +\end{onlysolution} +\end{defproblem} + +\begin{defproblem}{validprobspaces} +\begin{onlyproblem}% +Under which of the following functions does +$S=\{a_1,a_2\}$ become a probability space? +\par +\begin{textenum} +\begin{tabular}{ll} +\item $P(a_1)=\frac{1}{3}$, $P(a_2)=\frac{1}{2}$ +& +\item\label{validprobspacescorrect1} $P(a_1)=\frac{3}{4}$, $P(a_2)=\frac{1}{4}$ +\\ +\item\label{validprobspacescorrect2} $P(a_1)=1$, $P(a_2)=0$ +& +\item $P(a_1)=\frac{5}{4}$, $P(a_2)=-\frac{1}{4}$ +\end{tabular} +\end{textenum} +\end{onlyproblem}% +\begin{onlysolution}% +\ref{validprobspacescorrect1} and \ref{validprobspacescorrect2}% +\end{onlysolution} +\end{defproblem} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-tabmchoice.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-tabmchoice.tex new file mode 100644 index 00000000000..9555b97dd32 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-tabmchoice.tex @@ -0,0 +1,18 @@ + % This file is public domain + % + % These problems are designed to be placed in a + % tabular environment + % +\newproblem{tab:1}{% +What is $(3+2)\times5$? & +25 \ifshowanswers\selected\else\notselected\fi & +13 \notselected & +10 \notselected & +}{Brackets come first}% + +\newproblem{tab:2}{% +What is $-1+2\times3$? & +3 \notselected & +-7 \notselected & +5 \ifshowanswers\selected\else\notselected\fi & +}{Multiplication comes first}% diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/prob-verb.tex b/Master/texmf-dist/doc/latex/probsoln/samples/prob-verb.tex new file mode 100644 index 00000000000..07e0f835134 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/prob-verb.tex @@ -0,0 +1,28 @@ +\begin{defproblem}{code-helloworld} +This problem has a code fragment. +\begin{onlyproblem} +\lstset{language=Java} +\begin{lstlisting} +public class HelloWorld +{ + public static void main(String[] args) + { + System.out.println("Hello World!"); + } +} +\end{lstlisting} +\end{onlyproblem} +\begin{onlysolution} +\lstset{language=Java} +\begin{lstlisting} +public class HelloWorld +{ + public static void main(String[] args) + { + System.out.println("Hello " + + (args.length==0 ? "anon" : args[0])+"!"); + } +} +\end{lstlisting} +\end{onlysolution} +\end{defproblem} diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.pdf Binary files differnew file mode 100644 index 00000000000..a0e6571cacb --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.tex index 8295015352e..0120d310ed2 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample-exclude.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample-exclude.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample-exclude.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here % This file is public domain \documentclass[a4paper]{article} @@ -63,11 +15,11 @@ % Exclude problems that have been used this year or the previous % two academic years. (Creates a file called 'excluded.tex' to % store labels of used problems. Also creates a file called - % \jobname.prb that stores labels of problems used in this + % \jobname.prb that stores labels of problems used in this % document, so they don't get excluded on subsequent runs.) \ExcludePreviousFile[3]{excluded} - % To clear the used problems file (\jobname.prb) of the labels + % To clear the used problems file (\jobname.prb) of the labels % generated in the previous run, comment the above and uncomment % below: % \ClearUsedFile{excluded} @@ -96,6 +48,7 @@ % and store in database 'nosoln': \loadrandomproblems[nosoln]{1}{prob-nosoln} + \begin{document} \title{Sample Problem Sheet} \author{Nicola Talbot} @@ -124,6 +77,3 @@ \foreachproblem[nosoln]{\item \thisproblem} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample-exclude.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample.pdf Binary files differindex 43f13544672..3a44bed21a3 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample.pdf +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample.tex index c5b631659e6..b6bd6658259 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here % This file is public domain \documentclass[a4paper]{article} @@ -81,6 +33,7 @@ % and store in database 'nosoln': \loadrandomproblems[nosoln]{1}{prob-nosoln} + \begin{document} \title{Sample Problem Sheet} \author{Nicola Talbot} @@ -109,6 +62,3 @@ \foreachproblem[nosoln]{\item \thisproblem} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample2.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample2.pdf Binary files differindex a54bc6f77d3..007f6d906b5 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample2.pdf +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample2.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample2.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample2.tex index 72a2f6df6a3..cd13c89f309 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample2.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample2.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample2.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample2.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here % This file is public domain \documentclass[a4paper]{article} @@ -94,6 +46,3 @@ \end{enumerate} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample2.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample3.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample3.pdf Binary files differindex 1b0e3717ade..d6f6ff4909a 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample3.pdf +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample3.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample3.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample3.tex index f40e4755ae4..6922f9538ed 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample3.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample3.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample3.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample3.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here % This file is public domain \documentclass[a4paper]{article} @@ -66,11 +18,8 @@ \begin{document} \begin{longtable}{lrrrl} -\bfseries Question & \bfseries A & \bfseries B & +\bfseries Question & \bfseries A & \bfseries B & \bfseries C & \ifshowanswers \bfseries Reason\fi\\ \selectrandomly{prob-tabmchoice}{2} \end{longtable} \end{document} -\endinput -%% -%% End of file `sample3.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample4.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample4.pdf Binary files differindex fba702a13fb..7aadf56ca1f 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample4.pdf +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample4.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample4.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample4.tex index e79fd08340d..b432182d01e 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample4.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample4.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample4.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample4.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here % This file is public domain \documentclass[a4paper]{article} @@ -67,6 +19,3 @@ Differentiate the following functions: \foreachproblem{\item \thisproblem} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample4.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample5.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample5.pdf Binary files differindex 3d50533dc6c..f4ac8c7fdc0 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample5.pdf +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample5.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample5.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample5.tex index 4f515585196..ac294c11caf 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample5.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample5.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample5.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample5.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here % This file is public domain \documentclass[a4paper]{report} @@ -80,6 +32,3 @@ \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample5.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample6.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample6.pdf Binary files differnew file mode 100644 index 00000000000..2a8be97bbc7 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample6.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample6.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample6.tex index 321fda452a9..65769d3c97b 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample6.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample6.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample6.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample6.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here \documentclass{article} \usepackage[usedefaultargs]{probsoln} @@ -57,6 +9,3 @@ \foreachproblem{\item \thisproblem} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample6.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample7.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample7.pdf Binary files differnew file mode 100644 index 00000000000..12b0da7dad8 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample7.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample7.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample7.tex index 0b48c4cc85e..00ccf637d46 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample7.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample7.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample7.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample7.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here \documentclass{article} \usepackage{tikz} @@ -66,6 +18,3 @@ \foreachsolution{\item[\ref{q-\thisproblemlabel}] \thisproblem} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample7.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample8.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample8.pdf Binary files differnew file mode 100644 index 00000000000..f931368efa3 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample8.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample8.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample8.tex index 503488f5e2e..e68954daf24 100644 --- a/Master/texmf-dist/doc/latex/probsoln/samples/sample8.tex +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample8.tex @@ -1,51 +1,3 @@ -%% -%% This is file `sample8.tex', -%% generated with the docstrip utility. -%% -%% The original source files were: -%% -%% probsoln.dtx (with options: `sample8.tex,package') -%% -%% probsoln.dtx -%% Copyright 2013 Nicola Talbot -%% -%% This work may be distributed and/or modified under the -%% conditions of the LaTeX Project Public License, either version 1.3 -%% of this license of (at your option) any later version. -%% The latest version of this license is in -%% http://www.latex-project.org/lppl.txt -%% and version 1.3 or later is part of all distributions of LaTeX -%% version 2005/12/01 or later. -%% -%% This work has the LPPL maintenance status `maintained'. -%% -%% The Current Maintainer of this work is Nicola Talbot. -%% -%% This work consists of the files probsoln.dtx and probsoln.ins and the derived files probsoln.sty, sample-exclude.tex, sample.tex, sample2.tex, sample3.tex, sample4.tex, sample5.tex, sample6.tex, sample7.tex, sample8.tex, prob-1stprncp.tex, prob-args.tex, prob-easy.tex, prob-easy2.tex, prob-implicit.tex, prob-mchoice.tex, prob-mixed.tex, prob-newdata.tex, prob-nosoln.tex, prob-probspaces.tex, prob-probspaces2.tex, prob-tabmchoice.tex, prob-verb.tex. -%% -%% \CharacterTable -%% {Upper-case \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z -%% Lower-case \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z -%% Digits \0\1\2\3\4\5\6\7\8\9 -%% Exclamation \! Double quote \" Hash (number) \# -%% Dollar \$ Percent \% Ampersand \& -%% Acute accent \' Left paren \( Right paren \) -%% Asterisk \* Plus \+ Comma \, -%% Minus \- Point \. Solidus \/ -%% Colon \: Semicolon \; Less than \< -%% Equals \= Greater than \> Question mark \? -%% Commercial at \@ Left bracket \[ Backslash \\ -%% Right bracket \] Circumflex \^ Underscore \_ -%% Grave accent \` Left brace \{ Vertical bar \| -%% Right brace \} Tilde \~} -%% randomly select 25 problems from derivatives.tex and add to -%% the data set called 'deriv' -%% Display the problems -%% You may need to change \theenumi back here -%% randomly select 25 problems from probspaces.tex and add to -%% the data set called 'spaces' -%% Display the problems -%% You may need to change \theenumi back here \documentclass{article} \usepackage{listings} @@ -61,6 +13,3 @@ \foreachproblem{\item \thisproblem} \end{enumerate} \end{document} -\endinput -%% -%% End of file `sample8.tex'. diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample9.pdf b/Master/texmf-dist/doc/latex/probsoln/samples/sample9.pdf Binary files differnew file mode 100644 index 00000000000..9632dc35dfa --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample9.pdf diff --git a/Master/texmf-dist/doc/latex/probsoln/samples/sample9.tex b/Master/texmf-dist/doc/latex/probsoln/samples/sample9.tex new file mode 100644 index 00000000000..79ac7c5f5e9 --- /dev/null +++ b/Master/texmf-dist/doc/latex/probsoln/samples/sample9.tex @@ -0,0 +1,19 @@ + % This file is public domain +\documentclass[a4paper]{article} + +\usepackage{probsoln} + % uncomment the following line to display the answers + % \showanswers + + % Load 10 problems randomly selected from the given files +\loadrandomproblems{10}{prob-1stprncp,prob-easy,prob-implicit,prob-probspaces} + +\begin{document} +\title{Sample Problem Sheet} +\author{Nicola Talbot} +\maketitle + +\begin{enumerate} + \foreachproblem{\item \thisproblem} +\end{enumerate} +\end{document} |