Sandboxes

Placement test

Try the following sandbox, and create a quiz.

%%% enumeration type for a printable version
\renewcommand{\theenumii}{\alph{enumii}}
%%% Used in Problem 26
\newcommand{\aaint}[1]{\left\{x\,\left|\,x\neq #1, x
    \mbox{ is a nonnegative real number}\right.\right\}}
\newcommand{\bbint}[1]{(-\infty, -#1) \cup (#1, \infty)}
%%% Used in Problem 27
\newcommand{\cotfun}[1]{\cot(\theta #1)}
\newcommand{\tanfun}[1]{\tan(\theta #1)}
\newcommand{\negcotfun}[1]{-\cot(\theta #1)}
\newcommand{\negtanfun}[1]{-\tan(\theta #1)}

{\bf Directions.}
\begin{enumerate}
\item
  Placement Test consists of five parts, Part I, II, III, IV, and V.

\begin{tabular}{lrl}
  \hline
  Section& Question& Content\\
  \hline
  Part I& 1--6& Basic Algebra\\
  Part II& 7--13& Intermediate Algebra\\
  Part III& 14--19& Precalculus Algebra\\
  Part IV& 20--25& Precalculus Trigonometry\\
  Part V& 26, 27& Advanced Precalculus\\
  \hline
\end{tabular}

\item
  Each question is followed by five suggested answers.
\item
  Select the one best answer to each question.
\item
  Do not spend too much time on any one question.
\item
  Be honest: Do not use a calculator or any other resources like
  books, notes, tables, etc.
\item
  Suggested time for the test: 40 minutes.
\end{enumerate}

% Replace true with seednum in make_random_state
% to reproduce exactly the same random numbers
\maximacode
  seednum: 20230802;
  seedstate: make_random_state(true);
  set_random_state(seedstate);
  pick([list]) := block([i], i:random(length(list))+1, return(list[i]));
  rcar(list) := block([x], x:list[random(length(list))+1], return(x));
  rcadr(list) := block([x], x:list[random(length(list))+1], return([x,delete(x,list)]));
  pmsign(x) := block(if x >= 0 then return("+") else return("-"));
  round(x) := ?round(float(x));
\endmaximacode

{\bf Questions.}

\problemset

%1
\problem

\maximacode
  kill(x);
  x1: pick(-2,-1,1,2);
  x2: pick(-3,-5,-7,-9,-11,3,5,7,9,11);
  y1: pick(-2,-4,-6,-8,-11,2,4,6,8,11);
  y2: pick(1,3,-1,-3);
\endmaximacode

If \maxima x = x1/x2 \endmaxima then \maxima x + y2/x + y1\endmaxima = ?

\multiplechoice
\correct
\maxima x1/x2 + y2*x2/x1 + y1 \endmaxima

\incorrect
\maxima x1/x2 + y2*x2/x1 - y1 \endmaxima

\incorrect
\maxima x1/x2 - y2*x2/x1 - y1 \endmaxima

\incorrect
\maxima x1/x2 - y2*x2/x1 + y1 \endmaxima

\incorrect
\maxima (x1-1)/x2 - y2*x2/x1 + y1 \endmaxima

\endmultiplechoice

%2
\problem

\maximacode
  kill(x);
  x1: pick(7,9,11);
  x2: pick(1,2,4,5);
  x3: pick(3,7,6);
  y1: pick(-1,-2,-3,-4,1,2,3,4);
\endmaximacode

If \maxima eq: x/x3 + y1 = x1 / x2 \endmaxima, then x = ?

\multiplechoice
\correct
\maxima solve( eq, x )[1] \endmaxima

\incorrect
\maxima solve( x/x3 - y1 - x1/x2, x)[1] \endmaxima

\incorrect
\maxima solve( x/x3 - y1 + x1/x2, x)[1] \endmaxima

\incorrect
\maxima solve( x/x3 + y1 + x1/x2, x)[1] \endmaxima

\incorrect
\maxima solve( x/x3 + y1 - x2/x1, x)[1] \endmaxima

\endmultiplechoice

%3
\problem

\maximacode
  kill(a,b); 
  x1: pick(1,3,5,7,9,-1,-3,-5,-7,-9);
  x2: pick(2,4,6,8,10,-2,-4,-6,-8,-10);
\endmaximacode

$\displaystyle
 \maxima* a/(x1*b) \endmaxima*
 \maxima* pmsign(x2) \endmaxima*
 \maxima* a /(abs(x2)*b) \endmaxima*$ = ?

\multiplechoice
\correct
\maxima a/(x1*b) + a/(x2*b) \endmaxima

\incorrect
\maxima a/(x1*b) - a/(x2*b) \endmaxima

\incorrect
\maxima a/((x1*b) + (x2*b)) \endmaxima

\incorrect
\maxima ((x1*b) + (x2*b))/a \endmaxima

\incorrect
\maxima a/((x1*b)*(x2*b)) \endmaxima

\endmultiplechoice

%4
\problem

\maximacode 
  kill(y);
  m: pick([2,1],[3,1],[3,2],[4,1],[4,2],[4,3]);
  a: m[1]^2-m[2]^2;
  b: 2*m[1]*m[2];
  c: m[1]^2 + m[2]^2;
\endmaximacode

If $y > 0$ then $\sqrt{\maxima* a^2 * y^2 \endmaxima*
  + \maxima* b^2 * y^2 \endmaxima*} =$

\multiplechoice
\correct
\maxima c*y \endmaxima

\incorrect
\maxima y \endmaxima

\incorrect
\maxima (a+b)*y \endmaxima

\incorrect
\maxima (a^2+b^2)*y \endmaxima

\incorrect
\maxima a*y \endmaxima

\endmultiplechoice

%5
\problem

\maximacode
  kill(x,y);
  x0: pick(-8,-6,-4,-2,2,4,6,8);
  x1: pick(-9,-7,-5,-3,-1,1,3,5,7,9);
  rc: pick(-5,-4,-3,-2,-1,1,2,3,4,5);
\endmaximacode

The slope of the line \maxima x0*x + x1*y + rc = 0 \endmaxima is

\multiplechoice
\correct
\maxima -x0/x1 \endmaxima

\incorrect
\maxima x1/x0 \endmaxima

\incorrect
\maxima -x1/x0 \endmaxima

\incorrect
\maxima x0/x1 \endmaxima

\incorrect
\maxima x0/x1 - 1 \endmaxima

\endmultiplechoice

%6
\problem

\maximacode
  x0: pick(-5,-4,-3,-2,-1,0,1,2,3,4,5);
  y0: pick(-5,-4,-3,-2,-1,0,1,2,3,4,5);
  a: pick(-1,-2,-3,1,2,3);
  b: pick(-1,-2,-3,1,2,3);
\endmaximacode

If a rectangle has vertices 
  (\maxima x0   \endmaxima, \maxima y0   \endmaxima), \hspace{1ex}
  (\maxima x0+a \endmaxima, \maxima y0   \endmaxima), \hspace{1ex}
  (\maxima x0   \endmaxima, \maxima y0+b \endmaxima), and
  (\maxima x0+a \endmaxima, \maxima y0+b \endmaxima),
  then the length of a diagonal is

\multiplechoice
\correct
\maxima sqrt(a^2+b^2) \endmaxima

\incorrect
\maxima abs(a)+abs(b) \endmaxima

\incorrect
\maxima sqrt(abs(a)+abs(b)) \endmaxima

\incorrect
\maxima a^2+b^2 \endmaxima

\incorrect
\maxima abs(b)  \endmaxima

\endmultiplechoice

%7
\problem

\maximacode
  kill(x);
  a: pick(1,2,3,4,-1,-2,-3,-4);
  b: pick(9,16,25);
  c: pick(16,8);
\endmaximacode

$\displaystyle
 \maxima* (x+a)/(x^2-b) \endmaxima* \times
 \maxima* (c*x-c*sqrt(b))/(4*x+4*a) \endmaxima* $
= ?

\multiplechoice
\correct
\maxima (c/4)/(x+sqrt(b)) \endmaxima

\incorrect
\maxima c/(x+sqrt(b)) \endmaxima

\incorrect
\maxima (c/4)/(x-sqrt(b)) \endmaxima

\incorrect
\maxima (c/2)/(x-sqrt(b)) \endmaxima

\incorrect
\maxima (c/4)/(x^2-b) \endmaxima

\endmultiplechoice

%8
\problem

\maximacode
  a: pick(2,7,11,13);
  b: pick(2,3,4,-2,-3,-4,5,-5);
\endmaximacode

$\displaystyle
 \frac{1}{\maxima* b \endmaxima* + \maxima* sqrt(a) \endmaxima*}$ =

\multiplechoice
\correct
$\displaystyle
 \frac{\maxima* b \endmaxima* - \maxima* sqrt(a) \endmaxima*}
{\maxima* b^2 - a \endmaxima*} $

\incorrect
$\displaystyle
 \frac{\maxima* b \endmaxima* - \maxima* sqrt(a) \endmaxima*}
{\maxima* b^2 + a \endmaxima*} $

\incorrect
$\displaystyle
 \frac{\maxima* b \endmaxima* + \maxima* sqrt(a) \endmaxima*}
{\maxima* b^2 - a \endmaxima*} $

\incorrect
$\displaystyle
 \frac{\maxima* b \endmaxima* + \maxima* sqrt(a) \endmaxima*}
{\maxima* b^2 + a \endmaxima*} $

\incorrect
$\maxima* -b \endmaxima* + \maxima* sqrt(a) \endmaxima* $

\endmultiplechoice

%9
\problem

\maximacode
  kill(x,y);
  a: pick(2,3,4,5,6);
  b: pick(2,3,4);
  ex: pick(4,6,8,10);
  ey: pick(4,6,8,10);
\endmaximacode

If $x>0$ and $y>0$, then 
$\sqrt{\maxima* a^3 \endmaxima* \sqrt{\maxima* b^4 \endmaxima*
x^{\maxima* ex \endmaxima*} y^{\maxima* ey \endmaxima*}}}$ =

\multiplechoice
\correct
\maxima a*b*sqrt(a)*x^quotient(ex,4)*y^quotient(ey,4)
  *sqrt(x^(remainder(ex,4)/2)*y^(remainder(ey,4)/2)) 
\endmaxima

\incorrect
\maxima a*b^2*sqrt(a)*x^quotient(ex,4)*y^quotient(ey,4)
  *sqrt(x^(remainder(ex,4)/2)*y^(remainder(ey,4)/2)) 
\endmaxima

\incorrect
\maxima a*b^2*x^quotient(ex,4)*y^quotient(ey,4)
  *sqrt(x^(remainder(ex,4)/2)*y^(remainder(ey,4)/2)) 
\endmaxima

\incorrect
\maxima b*x^(ex/2)*y^(ey/2) \endmaxima

\incorrect
\maxima a*b^2*x^(ex/2)*y^(ex/2) \endmaxima

\endmultiplechoice

%10
\problem

\maximacode
  kill(x,y);
  a: pick(-1,-2,-3,-4,1,2,3,4);
  b: pick(1,2,3,4);
\endmaximacode

The graph of the system of equations 
$\begin{cases}
  \maxima* a*x-2*a*y=b \endmaxima* \\[1ex] 
  \maxima* 3*a*x+6*a*y=3*b \endmaxima*
\end{cases}$ consists of

\multiplechoice
\correct
two lines intersecting where \maxima x=b/a \endmaxima

\incorrect
one line

\incorrect
two lines intersecting where \maxima x=b \endmaxima

\incorrect
two lines intersecting where \maxima y=b/a \endmaxima

\incorrect
two distinct parallel lines

\endmultiplechoice

%11
\problem

\maximacode
  kill(x);
  x0: pick(3,4,5,6,7,8,9,10,11,12);
\endmaximacode

The inequality \maxima x^2-x0*x < x0+1 \endmaxima is equivalent to

\multiplechoice
\correct
$\maxima* -1 \endmaxima* < x < \maxima* x0 + 1 \endmaxima*$

\incorrect
$\maxima* -1 \endmaxima* < x < \maxima* x0 \endmaxima*$

\incorrect
$\maxima* -x0-1 \endmaxima* < x < 1$

\incorrect
\maxima x < -1 \endmaxima or \maxima x > x0+1 \endmaxima

\incorrect
$\maxima* -x0 \endmaxima* < x < 1$

\endmultiplechoice

%12
\problem

\maximacode
  kill(x,y);
  x0: pick(1,2,3,4);
  y0: pick(-4,-3,-2,-1,1,2,3,4);
  k: pick(3/4,1/4,-3/4,-1/4);
\endmaximacode

An equation of the line passing through
( \maxima x0 \endmaxima , \maxima y0 \endmaxima )
having slope \maxima k \endmaxima is

\multiplechoice
\correct
\maxima 4*k*x-4*y = -4*y0 + 4*k*x0 \endmaxima

\incorrect
\maxima 4*k*x+4*y = 4*y0 - 4*k*x0 \endmaxima

\incorrect
\maxima 4*k*x-4*y = 4*y0 - 4*k*x0 \endmaxima

\incorrect
\maxima 4*k*x+4*y = -4*y0 + 4*k*x0 \endmaxima

\incorrect
\maxima 4*k*x-4*y = -4*y0 - 4*k*x0 \endmaxima

\endmultiplechoice

%13
\problem

\maximacode
  kill(x,y);
  a: pick(1,2,3,-1,-2,-3);
  b: pick(3,4,5,16,20,-3,-4,-5,-16,-20);
  c: pick(12,23,44,55,22,0);
\endmaximacode

The graph of \maxima y=a*x^2+b*x+c \endmaxima is symmetric with respect to the line

\multiplechoice
\correct
\maxima x=-b/(2*a) \endmaxima

\incorrect
\maxima x=b/(2*a) \endmaxima

\incorrect
\maxima y=-b/(2*a) \endmaxima

\incorrect
\maxima y=b/(2*a) \endmaxima

\incorrect
\maxima x=-b/a \endmaxima

\endmultiplechoice

%14
\problem

\maximacode
  kill(x);
  a: pick(1,2,3,4,5,6,7,8,9,10);
\endmaximacode

Which of the following is the domain of $f(x)=\sqrt{x^2 - \maxima* a^2 \endmaxima* }$?

\multiplechoice
\correct
$\left\{x \,\left|\, |x| \ge \maxima* a \endmaxima* ,
 \,\mbox{$x$ is a real number} \right.\right\}$

\incorrect
$(-\infty, \maxima* a \endmaxima* ]$

\incorrect
$[\maxima* -a \endmaxima* ,\infty)$

\incorrect
$\left\{x \,\left| \maxima* -a \endmaxima* \leq x \leq \maxima* a \endmaxima* ,
\,\mbox{$x$ is a real number} \right.\right\}$

\incorrect
$(-\infty,\infty)$

\endmultiplechoice

%15
\problem

\maximacode
  kill(x,y);
  a: pick(1,2,3,4,5,-1,-2,-3,-4,-5);
  b: pick(1,2,3,4,5,-1,-2,-3,-4,-5);
  d: pick(1,2,0,-1);
  c: b^2/(4*a)+d;
\endmaximacode

The graphs of the two equations \maxima y=-b*x-c \endmaxima and 
 \maxima y=a*x^2 \endmaxima intersect in how many distinct points?

\maximacode
  if b^2-4*a*c>0 then ans[1]:"two";
  if b^2-4*a*c>0 then ans[2]:"one";
  if b^2-4*a*c>0 then ans[3]:"none";

if b^2-4*a*c=0 then ans[1]:"one";
  if b^2-4*a*c=0 then ans[2]:"two";
  if b^2-4*a*c=0 then ans[3]:"none";

if b^2-4*a*c<0 then ans[1]:"none";
  if b^2-4*a*c<0 then ans[2]:"one";
  if b^2-4*a*c<0 then ans[3]:"two";

ans[4]:"three";
  ans[5]:"unknown";
\endmaximacode

\multiplechoice
\correct
\maxima* ans[1] \endmaxima*

\incorrect
\maxima* ans[2] \endmaxima*

\incorrect
\maxima* ans[3] \endmaxima*

\incorrect
\maxima* ans[4] \endmaxima*

\incorrect
\maxima* ans[5] \endmaxima*

\endmultiplechoice

%16
\problem

\maximacode
  kill(x);
  ll: [-5,-4,-3,-2,-1,1,2,3,4,5];
  x0: rcar(ll);
  x1: rcar(delete(x0,ll));
\endmaximacode

The polynomial equation \maxima x*(x^2-x0)*(x^2-x1)=0 \endmaxima has how many real roots?

\multiplechoice
\correct
\maxima*
if x0 > 0 and x1 > 0 then "five" else if x0 > 0 or x1 > 0 then "three only"
else "only one"
\endmaxima*

\incorrect
\maxima*
if x0 > 0 and x1 > 0 then "three only" else if x0 > 0 or x1 > 0 then "only one"
else "five"
\endmaxima*

\incorrect
\maxima*
if x0 > 0 and x1 > 0 then "only one" else if x0 > 0 or x1 > 0 then "five"
else "three only"
\endmaxima*

\incorrect
two only

\incorrect
four only

\endmultiplechoice

%17
\problem

\maximacode
  kill(t,x);
  x0: pick(2,4,6,8,10,-1,-3,-4,-5);
\endmaximacode

If \maxima t=e^(x+x0) \endmaxima then $x=$

\multiplechoice
\correct
\maxima -x0+log(t) \endmaxima

\incorrect
\maxima (t-2)/e \endmaxima

\incorrect
\maxima 2*x0 \endmaxima

\incorrect
\maxima -2*x0 \endmaxima

\incorrect
\maxima log(t) \endmaxima

\endmultiplechoice

%18
\problem

\maximacode 
  a: pick(2,3);
  ll: [2,3,5,6,7];
  b: rcar(delete(a,ll));
  a: pick(-1,1) * a;
\endmaximacode

$\log_{\maxima* b \endmaxima*}
 \left(\displaystyle \maxima* b^a \endmaxima* \right)$ =

\multiplechoice
\incorrect
\maxima -b \endmaxima

\incorrect
\maxima b \endmaxima

\incorrect
\maxima 1/a \endmaxima

\incorrect
\maxima -a \endmaxima

\correct
\maxima a \endmaxima

\endmultiplechoice

%19
\problem

\maximacode
  kill(x,a,b);
  i:random(5)+1;
  a[1](x):=log(x);
  a[2](x):=1-x;    
  a[3](x):=1-x^2; 
  a[4](x):=exp(-x);
  a[5](x):=sqrt(x-1);

b[1,1]:0; b[1,2]:10; b[1,3]:-10; b[1,4]:10;
  b[2,1]:-10; b[2,2]:10; b[2,3]:-10; b[2,4]:10;
  b[3,1]:-4; b[3,2]:4; b[3,3]:-18; b[3,4]:2;
  b[4,1]:-2; b[4,2]:2; b[4,3]:0; b[4,4]:8;
  b[5,1]:0; b[5,2]:20; b[5,3]:-1; b[5,4]:5;
\endmaximacode

Of the following, which best represents the graph beside?
%\begin{figure}[h!]
%\begin{center}
%\scalebox{.80}{\includegraphics{fig101.eps}}
%\end{center}
%\caption{Graph for problem 19}
%\end{figure}

\maximaplot [a[i](x),b[i,1],b[i,2],b[i,3],b[i,4]] \endmaximaplot

\multiplechoice
\correct
\maxima y=a[i](x) \endmaxima

\incorrect
\maxima y=a[remainder(i,5)+1](x) \endmaxima

\incorrect
\maxima y=a[remainder((i+1),5)+1](x) \endmaxima

\incorrect
\maxima y=a[remainder((i+2),5)+1](x) \endmaxima

\incorrect
\maxima y=a[remainder((i+3),5)+1](x) \endmaxima

\endmultiplechoice

%20
\problem

\maximacode
  kill(tfun,t);
  i:random(2)+1;
  a: pick(30,60,120,150,210,240,-30,-60);
  t[1](x):=sec(x);
  t[2](x):=csc(x);
  if i=1 then tfun:"sec";
  if i=2 then tfun:"csc";
\endmaximacode

$\mbox{\maxima* tfun \endmaxima*}(\maxima* a \endmaxima* ^\circ)$

\multiplechoice
\correct
\maxima t[i](a*%pi/180) \endmaxima

\incorrect
\maxima t[i]((90-a)*%pi/180) \endmaxima

\incorrect
\maxima 1/t[i](a*%pi/180) \endmaxima

\incorrect
\maxima tan(a*%pi/180) \endmaxima

\incorrect
\maxima 1/tan(a*%pi/180) \endmaxima

\endmultiplechoice

%21
\problem

\maximacode
  kill(t,tfun);
  i:random(6)+1;
  a: pick(90,180,270,-90,-180,-270);
  t[1](x):=cos(x);
  t[2](x):=sin(x);
  t[3](x):=tan(x);
  t[4](x):=cot(x);
  t[5](x):=sec(x);
  t[6](x):=csc(x);
  if i=1 then tfun:"cos";
  if i=2 then tfun:"sin";
  if i=3 then tfun:"tan";
  if i=4 then tfun:"cot";
  if i=5 then tfun:"sec";
  if i=6 then tfun:"csc";
\endmaximacode

$\mbox{\maxima* tfun \endmaxima*}(\maxima* a \endmaxima* ^\circ - \theta) =$

\multiplechoice
\correct
\maxima t[i](a*%pi/180 - theta) \endmaxima

\incorrect
\maxima -t[i](a*%pi/180 - theta) \endmaxima

\incorrect
\maxima t[i](%pi/2 - a*%pi/180 + theta) \endmaxima

\incorrect
\maxima -t[i](%pi/2 - a*%pi/180 + theta) \endmaxima

\incorrect
\maxima 1+t[i](a*%pi/180 - theta) \endmaxima

\endmultiplechoice

%22
\problem

\maximacode
  kill(x);
  x0: pick(1,0,1/2,-1/2,sqrt(2)/2,-sqrt(2)/2,sqrt(3)/2,-sqrt(3)/2);
  x1: pick(2,-2,3,-3,4,5,6,7,8,-4,-5,-6,-7,-8);
  if x0 = 1 then a:0;
  if x0 = 1 then b:2*%pi;
  if x0 = 0 then a:1/2*%pi;
  if x0 = 0 then b:3/2*%pi;
  if x0 = 1/2 then a:1/3*%pi;
  if x0 = 1/2 then b:5/3*%pi;
  if x0 = -1/2 then a:2/3*%pi;
  if x0 = -1/2 then b:4/3*%pi;
  if x0 = sqrt(2)/2 then a:1/4*%pi;
  if x0 = sqrt(2)/2 then b:7/4*%pi;
  if x0 = -sqrt(2)/2 then a:3/4*%pi;
  if x0 = -sqrt(2)/2 then b:5/4*%pi;
  if x0 = sqrt(3)/2 then a:1/6*%pi;
  if x0 = sqrt(3)/2 then b:11/6*%pi;
  if x0 = -sqrt(3)/2 then a:5/6*%pi;
  if x0 = -sqrt(3)/2 then b:7/6*%pi;
\endmaximacode

For which values of $x$ in the interval $0 \leq x \leq 2\pi$ does
\maxima (cos(x)-x0)*(cos(x)-x1)=0 \endmaxima ?

\multiplechoice
\correct
\maxima [x=a,x=b] \endmaxima

\incorrect
\maxima [x=a+1/6*%pi,x=2*%pi-a] \endmaxima

\incorrect
\maxima [x=a,x=11/6*%pi-a] \endmaxima

\incorrect
$[x=1,x=2]$

\incorrect
$[x=\pi]$

\endmultiplechoice

%23
\problem

\maximacode
   kill(x,tfun,a);
   i: random(6)+1;
   tfun[1](x):=sin(3*x);
   tfun[2](x):=csc(3*x);
   tfun[3](x):=cos(4*x);
   tfun[4](x):=sec(4*x);
   tfun[5](x):=tan(3*x); 
   tfun[6](x):=cot(3*x); 
   a[1,1]:30; a[1,2]:150;
   a[2,1]:30; a[2,2]:150;
   a[3,1]:0; a[3,2]:90;
   a[4,1]:0; a[4,2]:90;
   a[5,1]:15; a[5,2]:135;
   a[6,1]:15; a[6,2]:135;
\endmaximacode

For which values of $x$ in the interval $[0^\circ,180^\circ]$ is 
\maxima tfun[i](x)=1 \endmaxima

\multiplechoice
\correct
$\mbox{\maxima a[i,1] \endmaxima}^\circ$ and $\mbox{\maxima a[i,2] \endmaxima}^\circ$

\incorrect
$\mbox{\maxima a[remainder(i+1,6)+1,1] \endmaxima}^\circ$ and $\mbox{\maxima a[remainder(i+1,6)+1,2] \endmaxima}^\circ$

\incorrect
$\mbox{\maxima a[remainder(i+3,6)+1,1] \endmaxima}^\circ$ and $\mbox{\maxima a[remainder(i+3,6)+1,2] \endmaxima}^\circ$

\incorrect
$180^\circ$

\incorrect
None of the above

\endmultiplechoice

%24
\problem

\maximacode
  x0: pick(1,-1);
\endmaximacode

The value of the expression $2\arctan \left(\maxima* x0 \endmaxima*\right)$
(or equivalently, $2\tan^{-1}\left(\maxima* x0 \endmaxima*\right)$) is

\multiplechoice
\correct
\maxima 2*atan(x0) \endmaxima

\incorrect
\maxima atan(x0) \endmaxima

\incorrect
\maxima 2*x0 \endmaxima

\incorrect
0

\incorrect
$\pi$

\endmultiplechoice

%25
\problem

\maximacode
  kill(x);
  a: pick(1,2,3,4,5);
  x0: pick(-1,1) * a;
  i: pick(1,2);
  j: delete(i,[1,2])[1];
  pm: [1,-1];
\endmaximacode

For all real numbers $x$,
\maxima cos(x0*x)^2 + pm[i] * sin(x0*x)^2 \endmaxima =

\multiplechoice
\correct
\maxima
  if i = 1 then 1 else cos(2*a*x)
\endmaxima

\incorrect
\maxima
  if i = 2 then 1 else cos(2*a*x)
\endmaxima

\incorrect
\maxima
  sin(2*x0*x)
\endmaxima

\incorrect
\maxima
  -cos(2*a*x)
\endmaxima

\incorrect
0

\endmultiplechoice

%26
\problem

\maximacode
  kill(x);
  x1: pick(1,4,16,25,36);
  i: pick(1,2);
  j: delete(i,[1,2])[1];
  ff[1]: 1/(x^2-x1);
  ff[2]: sqrt(x);
  ans[1]: concat("\\aaint{", x1, "}");
  ans[2]: concat("\\bbint{", sqrt(x1), "}");
\endmaximacode

If \maxima f(x)=ff[i] \endmaxima and $g(x)=\displaystyle \maxima* ff[j] \endmaxima*$,
then the domain of $f$ composite $g$, $(f \circ g)(x)$, is

\multiplechoice
\correct
\maxima ans[i] \endmaxima

\incorrect
\maxima ans[j] \endmaxima

\incorrect
All real numbers

\incorrect
$(0,\maxima* sqrt(x1) \endmaxima*) \cup (\maxima* sqrt(x1) \endmaxima*,\infty)$    
\incorrect
$\left\{x\,\left|\,x\ge0,\, x \in (-\infty,\infty)\right.\right\}$

\endmultiplechoice

%27
\problem

%  b: ["\\cot", "\\tan"]; 
%  r: ["\\theta","(\\theta+\\pi/2)","(\\theta-\\pi/2)"];

% $\displaystyle
% \frac{\maxima* a[i] \endmaxima* \theta}
%      {\maxima* a[j] \endmaxima* \theta\,
%      \maxima* if k=1 then concat(b[i], r[k]) else "" \endmaxima* } = 
%      \maxima* if k=1 then 1 else concat("-", b[j], r[k]) \endmaxima* $

\maximacode
  kill(a,b,c,n);
  i: random(2)+1;
  j: remainder(i,2) + 1;
  a[1]:cos;
  a[2]:sin;
  b: ["\\cotfun{", "\\tanfun{"]; 
  c: ["\\negcotfun{", "\\negtanfun{"]; 
  k: pick(1,2,3);
  r: ["","+\\pi/2","-\\pi/2"];
  freq: [n*%pi/2, n*%pi, (2*n+1)*%pi/2];
\endmaximacode

$\displaystyle
\frac{\maxima* a[i] \endmaxima* \theta}
     {\maxima* a[j] \endmaxima* \theta\,
      \maxima* if k=1 then concat(b[i],r[k],"}") else "" \endmaxima* } = 
      \maxima* if k=1 then 1 else concat(c[j],r[k],"}") \endmaxima* $
is an identity and is true for all values of $\theta$ in the set

\multiplechoice
\correct
$\displaystyle\left\{\theta \,\left|\,
 \theta \neq
 \maxima*
   if k=1 then freq[1] else if i=1 then freq[2] else freq[3]
 \endmaxima*
 ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

\incorrect
$\displaystyle\left\{\theta \,\left|\,
 \theta \neq
 \maxima*
   if k=1 then freq[2] else if i=1 then freq[3] else freq[1]
 \endmaxima*
 ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

\incorrect
$\displaystyle\left\{\theta \,\left|\,
 \theta \neq
 \maxima*
   if k=1 then freq[3] else if i=1 then freq[1] else freq[2]
 \endmaxima*
 ,\,n \mbox{ is an integer},\, \theta \in (-\infty,\infty)\right.\right\}$

\incorrect
$\displaystyle\left\{\theta \,\left|\, -\infty < \theta < \infty \right.\right\}$

\incorrect
$(0,2\pi)$

\endmultiplechoice

\endproblemset