View of /trunk/NationalProblemLibrary/LoyolaChicago/Precalc/Chap2Sec1/Connally3-2-1-25-Input-and-output.pg

    1 ## DESCRIPTION
    2 ## Functions: Input and Output
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('functions','evaluating','solving','input','output')
    6 
    7 ## DBsubject('Precalculus')
    8 ## DBchapter('Functions')
    9 ## DBsection('Input and Output')
   10 ## Date('01/01/10')
   11 ## Author('Paul Pearson')
   12 ## Institution('Fort Lewis College')
   13 ## TitleText1('Functions Modeling Change')
   14 ## EditionText1('3')
   15 ## AuthorText1('Connally')
   16 ## Section1('2.1')
   17 ## Problem1('25')
   18 ## TitleText2('Functions Modeling Change');
   19 ## EditionText2('4')
   20 ## AuthorText2('Connally')
   21 ## Section2('2.Review')
   22 ## Problem2('51')
   23 
   24 DOCUMENT();
   25 
   26 loadMacros(
   27 "PGstandard.pl",
   28 "PGchoicemacros.pl",
   29 "MathObjects.pl",
   30 "AnswerFormatHelp.pl",
   31 "PGcourse.pl",
   32 );
   33 
   34 TEXT(beginproblem());
   35 
   36 ###############################################
   37 #  Setup
   38 
   39 @month = (1 .. 8);
   40 @monthname = ("blank", # since indexing starts at 0
   41 "January","February","March",
   42 "April","May","June",
   43 "July","August","September",
   44 "October","November","December"
   45 );
   46 
   47 @rainfall = ( 1.8, 1.8, 2.7, 3.1, 3.5, 3.7, 3.5, 3.4 );
   48 # @perm = shuffle(scalar(@rainfall));
   49 # @invperm = invert(@perm);
   50 # @rainfallperm = @rainfall[@perm];
   51 
   52 ############
   53 #  Part A
   54 #
   55 $selecta = random(0,3,1);
   56 # indices for months 3=March, 4=April, 6=June and 8=August in @rainfall
   57 @parta = (2,3,5,7);
   58 $raina = @rainfall[$parta[$selecta]];
   59 
   60 # $answera = @month[$invperm[$parta[$selecta]]];
   61 $answera = $month[$parta[$selecta]];
   62 
   63 $dummy = random(1,8,1);
   64 while ($dummy == $answera) { $dummy = random(1,8,1); }
   65 
   66 $mca = new_multiple_choice();
   67 $mca -> qa(
   68 "The solution(s) to \( f(t) = $raina \) can be interpreted as saying",
   69 "Chicago's average rainfall in the month of @monthname[$answera] is $raina inches."
   70 );
   71 $mca -> extra(
   72 "Chicago's average rainfall is greatest in the month of @monthname[$dummy].",
   73 "Chicago's average rainfall is least in the month of @monthname[$answera].",
   74 "Chicago's average rainfall increases by $raina inches in the month of @monthname[$dummy]."
   75 );
   76 $mca -> makeLast("None of the above");
   77 
   78 
   79 ############
   80 #  Part B
   81 #
   82 $selectb = random(0,1,1);
   83 if ($selectb == 0) {
   84 @partb = (0,1); # indices for months 1=January, 2=February in @rainfall
   85 } else {
   86 @partb = (4,6); # indices for months 5=May, 7=July in @rainfall
   87 }
   88 # $inputb1 = @month[$invperm[$partb[$selectb]]];
   89 # $inputb2 = @month[$invperm[$partb[$selectb-1]]];
   90 ($inputb1, $inputb2) = num_sort( $month[$partb[$selectb]],
   91          $month[$partb[$selectb-1]] );
   92 
   93 $rainb = $rainfall[$partb[$selectb]];;
   94 
   95 $mcb = new_multiple_choice();
   96 $mcb -> qa(
   97 "The solution(s) to \( f(t) = f($inputb1) \) can be interpreted as saying",
   98 "Chicago's average rainfall is $rainb inches in the months of @monthname[$inputb1] and @monthname[$inputb2]."
   99 );
  100 $mcb -> extra(
  101 "Chicago's average rainfall is $rainb inches in the month of @monthname[$inputb1].",
  102 "Chicago's average rainfall is $rainb inches in the month of @monthname[$inputb2].",
  103 "Chicago's average rainfall is greatest in the month of @monthname[$inputb1].",
  104 );
  105 $mcb -> makeLast("None of the above");
  106 
  107 
  108 
  109 ##################################################
  110 #  Main text
  111 
  112 # for debugging, use this table
  113 #\{ row( "t, month", @month ) \}
  114 #\{ row( "t, month", @month[@invperm] ) \}
  115 #\{ row( "R, inches", @rainfall ) \}
  116 #\{ row( "R, inches", @rainfall[@perm] ) \}
  117 
  118 Context()->texStrings;
  119 BEGIN_TEXT
  120 
  121 Chicago's average monthly rainfall, \( R = f(t) \) inches,
  122 is given as a function of the month, \( t \), where January
  123 is \( t = 1 \), in the table below.
  124 $BR
  125 $BCENTER
  126 \{ begintable(13) \}
  127 \{ row( "t, month", @month ) \}
  128 \{ row( "R, inches", @rainfall ) \}
  129 \{ endtable() \}
  130 $ECENTER
  131 $BR
  132 (a) Solve \( f(t) = $raina \).
  133 $BR
  134 \( t = \) \{ ans_rule(10) \}
  135 \{ AnswerFormatHelp("number") \}
  136 $PAR
  137 \{ $mca->print_q() \}
  138 \{ $mca->print_a() \}
  139 $BR
  140 (b) Solve \( f(t) = f($inputb1) \).
  141 $BR
  142 \( t = \) \{ ans_rule(10) \}
  143 \{ AnswerFormatHelp("number") \}
  144 $PAR
  145 \{ $mcb->print_q() \}
  146 \{ $mcb->print_a() \}
  147 
  148 END_TEXT
  149 Context()->normalStrings;
  150 
  151 #################################################
  152 #  Answer evaluation
  153 
  154 $showPartialCorrectAnswers = 1;
  155 
  156 ANS(Real("$answera")->cmp());
  157 
  158 ANS(radio_cmp($mca->correct_ans));
  159 
  160 ANS(List(Real("$inputb1"),Real("$inputb2"))->cmp());
  161 
  162 ANS(radio_cmp($mcb->correct_ans));
  163 
  164 $tb1 = $partb[0]+1;
  165 $tb2 = $partb[1]+1;
  166 
  167 Context()->texStrings;
  168 SOLUTION(EV3(<<'END_SOLUTION'));
  169 $PAR
  170 $BBOLD SOLUTION $EBOLD
  171 $PAR
  172 (a) The table shows \(f($answera)=$raina\), so \(t=$answera\).
  173 Chicago's average rainfall in the month of @monthname[$answera]
  174 is $raina inches.
  175 $PAR
  176 (b) First evaluate \(f($partb[0])=$rainb\). Solving \(f(t)=$rainb\) gives
  177 \(t=$tb1\) or \(t=$tb2\). Chicago's average rainfall is $rainb inches in
  178 @monthname[$inputb1] and @monthname[$inputb2].
  179 
  180 END_SOLUTION
  181 Context()->normalStrings;
  182 
  183 COMMENT('MathObject version');
  184 ENDDOCUMENT();