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Contrib/SVSU/College_Algebra/absolute_values/absolute1.pg

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+# DESCRIPTION
+# Rewriting absolute value expressions
+# written by Jan Hlavacek ([email protected])
+# ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Algebra of real numbers and simplifying expressions)
+## DBsection(Simplifying expressions)
+## Institution(SVSU)
+## Author(Jan Hlavacek)
+## Level(2)
+## TitleText1('Algebra and Trigonometry')
+## AuthorText1('Swokowski, Cole')
+## EditionText1('13')
+## Section1('.')
+## Problem1('')
+## KEYWORDS('algebra,absolute value')
+
+DOCUMENT();
+loadMacros(
+"PGstandard.pl",
+"MathObjects.pl",
+"PGML.pl",
+"PGcourse.pl",
+"AnswerFormatHelp.pl",
+"contextLimitedRadical.pl",
+);
+Context("Numeric");
+
+# Define variables here:
+
+$a = list_random(2,3,5,7);
+do {$b = list_random(2,3,5,7);} until ($b != $a);
+
+$c = ceil(sqrt($a));
+$d = floor(sqrt($b));
+
+Context("LimitedRadical");
+Context()->functions->disable("abs");
+Context()->parens->remove("|");
+Context()->{error}{convert} = sub {
+ my $message = shift;
+ $message =~ s/Unexpected character '~~|'/You cannot use absolute value/;
+ return $message;
+};
+
+$dif1 = Formula("$c - sqrt($a)");
+$dif2 = Formula("$d - sqrt($b)");
+
+$ans1 = Formula("$c - sqrt($a)");
+$ans2 = Formula("sqrt($b) - $d");
+
+# Actual problem goes here:
+TEXT(beginproblem());
+BEGIN_PGML
+Write each of the following numbers without using absolute value:
+
+1. [`\left| [$dif1] \right| = `] [_________]{$ans1}
+
+2. [`\left| [$dif2] \right| = `] [_________]{$ans2}
+
+([@ AnswerFormatHelp("formulas", "Help entering formulas") @]*)
+END_PGML
+
+# Solution:
+BEGIN_PGML_SOLUTION
+1.  Since [$c] is greater than [` \sqrt{[$a]} `], the difference inside the absolute value is positive, so we can just drop the absolute value:
+
+    [`\left| [$dif1] \right| = [$ans1] `]
+
+2.  Since [$d] is smaller than [` \sqrt{[$b]} `], the difference inside the absolute value is _negative_, so if we drop the absolute value, we need to change the sign:
+
+    [`\left| [$dif2] \right| = [$ans2] `]
+END_PGML_SOLUTION
+
+ENDDOCUMENT();

Contrib/SVSU/College_Algebra/absolute_values/absolute2.pg

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+# DESCRIPTION
+# Rewrite absolute value of difference
+# written by Jan Hlavacek ([email protected])
+# ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Algebra of real numbers and simplifying expressions)
+## DBsection(Simplifying expressions)
+## Institution(SVSU)
+## Author(Jan Hlavacek)
+## Level(2)
+## TitleText1('Algebra and Trigonometry')
+## AuthorText1('Swokowski, Cole')
+## EditionText1('13')
+## Section1('.')
+## Problem1('')
+## KEYWORDS('algebra,absolute value')
+
+DOCUMENT();
+loadMacros(
+"PGstandard.pl",
+"MathObjects.pl",
+"PGML.pl",
+"PGcourse.pl",
+"AnswerFormatHelp.pl",
+"answerHints.pl",
+);
+Context("Numeric");
+Context()->functions->disable("abs");
+Context()->parens->remove("|");
+Context()->{error}{convert} = sub {
+ my $message = shift;
+ $message =~ s/Unexpected character '~~|'/You cannot use absolute value in this problem/;
+ return $message;
+};
+
+# Define variables here:
+
+$a = random(1,9,1);
+
+$dir = random(0,1,1);
+$ord = random(0,1,1);
+
+$fst = Compute("$a - x");
+$snd = Compute("x - $a");
+
+if ($dir) {
+$ineq = "\le";
+$ans = Compute("$a - x");
+} else {
+$ineq = "\ge";
+$ans = Compute("x - $a");
+}
+
+if ($ord) {
+$p1 = $fst;
+$p2 = $snd;
+} else {
+$p1 = $snd;
+$p2 = $fst;
+}
+
+# Actual problem goes here:
+TEXT(beginproblem());
+BEGIN_PGML
+Write each of the following numbers without using absolute value, given that [` x [$ineq] [$a] `]:
+
+1. [`\left| [$p1] \right| = `] [_________]{$ans}
+
+2. [`\left| [$p2] \right| = `] [_________]{$ans}
+
+([@ AnswerFormatHelp("formulas", "Help entering formulas") @]*)
+END_PGML
+
+# Solution:
+BEGIN_PGML_SOLUTION
+The two absolute value expressions are actually equal, so the two answers are actually the same.  They are both equal to
+[`[$ans]`], which is the _non-negative_ difference.
+END_PGML_SOLUTION
+
+ENDDOCUMENT();

Contrib/SVSU/College_Algebra/absolute_values/distance1.pg

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+# DESCRIPTION
+# Absolute value of difference as distance
+# written by Jan Hlavacek ([email protected])
+# ENDDESCRIPTION
+
+## DBsubject(Algebra)
+## DBchapter(Algebra of real numbers and simplifying expressions)
+## DBsection(Algebraic expressions)
+## Institution(SVSU)
+## Author(Jan Hlavacek)
+## Level(2)
+## TitleText1('Algebra and Trigonometry')
+## AuthorText1('Swokowski, Cole')
+## EditionText1('13')
+## Section1('.')
+## Problem1('')
+## KEYWORDS('algebra,absolute value')
+
+DOCUMENT();
+loadMacros(
+"PGstandard.pl",
+"MathObjects.pl",
+"PGML.pl",
+"PGcourse.pl",
+"AnswerFormatHelp.pl",
+"answerHints.pl",
+);
+Context("Numeric");
+
+# Define variables here:
+
+$a = random(1,9,1);
+$b = random($a+1,15,1);  # $a < $b
+
+$c = random(7, 18, 1);
+$d = random(2,$c-1,1);  # $c > $d
+
+$ans1 = Compute("$b - $a");
+$ans2 = Compute("$c - $d");
+
+$ans3 = Compute("x - $a");
+$ans4 = Compute("$d - x");
+
+$ans5 = Compute("|x - $b|");
+
+# Actual problem goes here:
+TEXT(beginproblem());
+BEGIN_PGML
+This problem is about the _distance between numbers on the number line_.
+
+1. What is the distance between [$a] and [$b] on the number line?
+
+    [_________]{$ans1}
+
+2. What is the distance between [$c] and [$d] on the number line?
+
+    [_________]{$ans2}
+
+3. Write a formula giving the distance between an unknown number [`x`] and [$a] if we know that [`x > [$a]`]:
+
+    [_________]{$ans3}
+
+4. Write a formula giving the distance between an unknown number [`x`] and [$d] if we know that [`x < [$d]`]:
+
+    [_________]{$ans4}
+
+5. Finally, write a formula that will always give the distance between an unknown number [`x`] and [$b] if we do not have any additional 
+   information about [`x`]:
+
+    [_________]{$ans5}
+
+([@ AnswerFormatHelp("formulas", "Help entering formulas") @]*)
+END_PGML
+
+# Solution:
+BEGIN_PGML_SOLUTION
+1. The distance between [$a] and [$b] is simply [`[$b] - [$a] = [$ans1]`].
+2. The distance between [$c] and [$d] is simply [`[$c] - [$d] = [$ans2]`].
+3. Since the distance between the unknown number [`x`] and [$a] must be _positive_ and [`x > [$a]`], we need to subtract [$a] from [`x`],
+   so the answer is [`[$ans3]`].
+4. Since the distance between the unknown number [`x`] and [$d] must be _positive_ and [`x < [$d]`], we need to subtract [`x`] from [$d],
+   so the answer is [`[$ans4]`].
+5. Since we do not know whether [`x`] is less than or larger than [$b], we do not know in which order to subtract the numbers. To make sure the
+   distance turns out positive, we have to use absolute value:  the correct answer is [: |x - [$b]| :] or [: |[$b] - x| :].  Because of the absolute value, the order does not matter.
+END_PGML_SOLUTION
+
+#hint:
+$showHint = 2;
+
+BEGIN_PGML_HINT
+Remember that *distance* between things is never negative!
+END_PGML_HINT
+
+ENDDOCUMENT();