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commit c2cb4db0ebe89f33067e0104cc3b7d62edb6964b 1 parent a897b82
spicyj authored
Showing with 1,037 additions and 1,042 deletions.
1. +3 −3 build/kathjax-config.js
9. +2 −2 exercises/age_word_problems.html
10. +21 −21 exercises/angle_bisector_theorem.html
11. +2 −2 exercises/angle_types.html
12. +123 −123 exercises/angles_1.html
13. +1 −1  exercises/angles_of_a_polygon.html
14. +3 −3 exercises/arithmetic_word_problems_2.html
15. +2 −2 exercises/changing_decimals_to_percents.html
16. +2 −2 exercises/changing_fractions_to_decimals_1.html
17. +1 −1  exercises/changing_percents_to_decimals.html
18. +2 −2 exercises/changing_percents_to_fractions.html
19. +17 −17 exercises/circles_1.html
21. +2 −2 exercises/comparing_absolute_values.html
22. +1 −1  exercises/complementary_angles.html
23. +1 −1  exercises/completing_the_square_1.html
24. +1 −1  exercises/completing_the_square_2.html
25. +12 −12 exercises/compound_inequalities.html
26. +10 −10 exercises/congruent_triangles_1.html
27. +4 −4 exercises/congruent_triangles_2.html
28. +2 −2 exercises/converting_decimals_to_fractions_1.html
29. +1 −1  exercises/converting_decimals_to_fractions_2.html
30. +1 −1  exercises/converting_decimals_to_percents.html
31. +3 −3 exercises/converting_mixed_numbers_and_improper_fractions.html
32. +1 −1  exercises/converting_percents_to_decimals.html
33. +1 −1  exercises/converting_repeating_decimals_to_fractions_1.html
34. +1 −1  exercises/converting_repeating_decimals_to_fractions_2.html
35. +3 −3 exercises/decimals_on_the_number_line.html
36. +1 −1  exercises/distance_formula.html
37. +246 −246 exercises/distributive_property_with_variables.html
38. +4 −4 exercises/divisibility_0.5.html
39. +4 −4 exercises/equivalent_fractions.html
40. +5 −5 exercises/equivalent_fractions_2.html
41. +1 −1  exercises/estimation_with_decimals.html
42. +1 −1  exercises/evaluating_expressions_2.html
43. +2 −2 exercises/even_and_odd_integers.html
44. +2 −2 exercises/fractions_cut_and_copy_1.html
45. +5 −5 exercises/fractions_cut_and_copy_2.html
46. +7 −7 exercises/fractions_on_the_number_line.html
47. +1 −1  exercises/graphing_points_2.html
48. +4 −4 exercises/herons_formula.html
49. +1 −1  exercises/inequalities_on_a_number_line.html
50. +3 −3 exercises/interpreting_linear_equations.html
51. +5 −5 exercises/kinematic_equations.html
52. +5 −5 exercises/line_relationships.html
53. +4 −4 exercises/linear_equation_word_problems.html
54. +1 −1  exercises/measuring_angles.html
55. +1 −1  exercises/multiplication_0.5.html
56. +4 −4 exercises/multiplying_expressions_1.html
57. +11 −11 exercises/multiplying_polynomials.html
59. +1 −1  exercises/one_step_equations.html
60. +6 −6 exercises/one_step_equations_0.5.html
61. +2 −2 exercises/parabola_intuition_1.html
62. +1 −1  exercises/parabola_intuition_2.html
63. +1 −1  exercises/plugging_in_values.html
64. +2 −2 exercises/point_slope_form.html
65. +24 −24 exercises/polygon_intuition.html
70. +1 −1  exercises/rate_problems_2.html
71. +1 −1  exercises/recognizing_percents.html
72. +2 −2 exercises/recognizing_rays_lines_and_line_segments.html
73. +3 −3 exercises/rounding_numbers.html
74. +4 −4 exercises/similar_triangles_1.html
75. +5 −5 exercises/solutions_to_systems_of_equations.html
76. +1 −1  exercises/special_derivatives.html
77. +9 −9 exercises/squares_and_rectangles.html
78. +2 −2 exercises/systems_of_equations_with_elimination.html
79. +5 −5 exercises/systems_of_equations_with_elimination_0.5.html
80. +6 −6 exercises/systems_of_equations_with_substitution.html
81. +9 −9 exercises/triangle_angles_1.html
82. +1 −1  exercises/trig_identities_1.html
83. +2 −2 exercises/trigonometry_2.html
84. +1 −1  exercises/writing_expressions_2.html
85. +106 −106 jquery-ui.js
86. +54 −55 jquery.js
87. +0 −1  test/exercises/power_rule.js
89. +11 −11 utils/convert-values.js
90. +38 −38 utils/exercise_maker.html
91. +5 −5 utils/exponents.js
92. +5 −5 utils/expressions.js
93. +36 −37 utils/graphie-geometry.js
94. +0 −1  utils/graphie-helpers-arithmetic.js
95. +3 −3 utils/graphie-helpers.js
96. +1 −1  utils/graphie-polygon.js
97. +2 −2 utils/graphie.js
98. +2 −3 utils/math-format.js
99. +6 −6 utils/math.js
100. +9 −9 utils/polynomials.js
101. +1 −1  utils/slice-clone.js
102. +3 −3 utils/spin.js
6 build/kathjax-config.js
 @@ -9,7 +9,7 @@
- +
randRange(5,9)*100 randRange(1,9)*10 @@ -23,16 +23,16 @@ D+E+F (2) truncate_to_max(fruit_2_integer*pow(10,-fruit_2_decimal), 2) - truncate_to_max((fruit_1+fruit_2),2) + truncate_to_max((fruit_1+fruit_2),2) []
-
+

{On a sunny morning|On a beautiful afternoon}, person(1) rode his(1) bicycle to a farm that sold bags of plural(fruit(1)) for $fruit_1 each and bags of plural(fruit(2)) for$fruit_2 each.

person(1) decided to buy a bag of plural(fruit(1)) and a bag of plural(fruit(2)) {before heading home|because those were his(1) favorite kinds of fruit|}.

How much did person(1) need to pay for his(1) produce?

- - + +
fruit_1+fruit_2
@@ -46,13 +46,13 @@
- +

person(1) needs to pay $solution. - + - + randRange(1, 3)*100 randRange(2000,9999) @@ -65,9 +65,9 @@ (2) truncate_to_max(time_3_integer*pow(10,-time_3_decimal), 2) [] - truncate_to_max((time_1-time_2),2) + truncate_to_max((time_1-time_2),2) - + {On Monday|Last week}, person(1) and person(2) decided to see how fast they could sprint meters meters. They asked their friend person(3) to time them with a stopwatch. {After time_3 minutes, person(3) agreed to time the runners.|} person(1) sprinted first and ran meters meters in time_1 seconds. When it was person(2)'s turn, he(2) sped off and completed the run in time_2 seconds. @@ -89,10 +89,10 @@ person(2) was solution seconds faster than person(1). - + - - + + randRange(2,6)*100 randRange(1,9)*10 @@ -108,16 +108,16 @@ truncate_to_max(weight_2_integer*pow(10,-weight_2_decimal), 2) randRange(16.5,22.5) randRange(16.5,22.5) - truncate_to_max((weight_1+weight_2),2) + truncate_to_max((weight_1+weight_2),2) [] {Last Monday|On Saturday}, person(1)'s parents gave birth to twins and named them person(2) and person(3). When they were first born, person(2) weighed weight_1 pounds{ and was height_1 inches tall|}, and person(3) weighed weight_2 pounds {and was height_2 inches tall|}. How much did the babies weigh in total? - - - + + + weight_1+weight_2 @@ -131,17 +131,17 @@ graph.adder.showHint(); - + graph.adder.showHint(); Together, the babies weigh solution pounds. - - + + - - + + randRange(1,9)*100 randRange(1,9)*10 @@ -156,7 +156,7 @@ (2) truncate_to_max(price_1_integer*pow(10,-price_1_decimal), 2) randRange(3, 30) - truncate_to_max((amount_paid-price_1),2) + truncate_to_max((amount_paid-price_1),2) [] @@ -180,10 +180,10 @@ person(1) received$solution in change.

- +
- - + +
randRange(101,999) (2) @@ -193,11 +193,11 @@ truncate_to_max(rain_2_integer*pow(10,-rain_2_decimal), 2) randRange(2.1,15.89) [] - truncate_to_max((rain_2-rain_1),2) + truncate_to_max((rain_2-rain_1),2)
-

During a recent rainstorm, rain_1 inches of rain fell in person(1)'s hometown, and rain_2 inches of rain fell in person(2)'s hometown. {During the same storm, snow_1 inches of snow fell in person(3)'s hometown.|}

+

During a recent rainstorm, rain_1 inches of rain fell in person(1)'s hometown, and rain_2 inches of rain fell in person(2)'s hometown. {During the same storm, snow_1 inches of snow fell in person(3)'s hometown.|}

How much more rain fell in person(2)'s town than in person(1)'s town?

rain_2-rain_1
@@ -216,10 +216,10 @@

person(2)'s town received solution inches more rain than person(1)'s town.

- - + +
- +
randRange(100,2000) (2) @@ -227,7 +227,7 @@ randRange(100,2000) (2) truncate_to_max(distance_2_integer*pow(10,-distance_2_decimal), 2) - truncate_to_max((distance_1+distance_2),2) + truncate_to_max((distance_1+distance_2),2) randRange(20.2,52.17) []
@@ -235,7 +235,7 @@

{To get to school each morning|To get to work each morning|To visit his(1) grandmother}, person(1) takes an(vehicle(1)) distance_1 plural(distance(1)) and an(vehicle(2)) distance_2 plural(distance(1)). {In total, the journey takes time_1 minutes.|}

How many plural(distance(1)) is person(1)'s journey in total?

-
+
distance_1+distance_2
@@ -249,17 +249,17 @@
- +

person(1) travels solution plural(distance(1)) in total.

- - - - + + + + - +
 @@ -57,7 +57,7 @@
REMOVE.remove(); label( [0, -1], - "\\Huge{\\color{#6495ED}{" + A + "} \\color{#28AE7B}{" + B + "} = " + "\\Huge{\\color{#6495ED}{" + A + "} \\color{#28AE7B}{" + B + "} = " + "\\color{#FF00AF}{" + ANSWER + "}}", "right" );
@@ -107,7 +107,7 @@
REMOVE.remove(); label( [0, -1], - "\\Huge{\\color{#6495ED}{" + A + "} \\color{#28AE7B}{ +" + abs( B ) + "} = " + "\\Huge{\\color{#6495ED}{" + A + "} \\color{#28AE7B}{ +" + abs( B ) + "} = " + "\\color{#FF00AF}{" + ANSWER + "}}", "right" );
 @@ -8,7 +8,7 @@ function getFakeAnswers( solution ) { var answers = []; for ( var i = 0; i < solution.getNumberOfTerms(); i++ ) { - var coefs = []; + var coefs = []; for ( var j = 0; j < solution.getNumberOfTerms(); j++ ) { var term = solution.getCoefAndDegreeForTerm( j ); @@ -16,15 +16,15 @@ if ( i === j ) { coefs[ term.degree ] = KhanUtil.randRangeNonZero( -7, 7 ); } else { - coefs[ term.degree ] = term.coef; + coefs[ term.degree ] = term.coef; } } - + for ( var j = 0; j < coefs.length; j++ ) { if ( coefs[ j ] === undefined ) { coefs[ j ] = 0; } - } + } answers.push( new KhanUtil.Polynomial(0, solution.maxDegree, coefs, solution.variable) ); } @@ -48,7 +48,7 @@ if ( i === NON_ZERO_INDICES[ j ] ) { value = randRangeNonZero( -7, 7 ); break; - } + } } coefs[ i ] = value; } @@ -61,7 +61,7 @@
 @@ -108,4 +108,4 @@ - +
 @@ -57,7 +57,7 @@
REMOVE.remove(); label( [0, -2], - "\\Huge{\\color{#6495ED}{" + A + "} \\color{#28AE7B}{" + B + "} = " + "\\Huge{\\color{#6495ED}{" + A + "} \\color{#28AE7B}{" + B + "} = " + "\\color{#FF00AF}{" + ANSWER + "}}", "right" );
 @@ -12,7 +12,7 @@ randRange ( 0, 9 )*1 randRange( 1, 8 )*10 randRange ( 0, 9 )*1 - + A_10+A_1 B_10+B_1 []
 @@ -8,7 +8,7 @@ function enFunc(innerString, usePercentages) { if (usePercentages) return "P(" + innerString + ")"; - else + else return "\\lvert" + innerString + "\\rvert"; } @@ -19,15 +19,15 @@
[0, 1, 2, 3] - + function( attrChoices1, attrChoices2 ) { att1 = randFromArray( attrChoices1 ); att2 = randFromArray( attrChoices2 ); return [ att1, att2, att1 + " or " + att2, att1 + " and " + att2 ]; - } + } [ "baseline", MIXER( ["blue"], ["hot"] ), "endline" ] - + randFromArray([ ["A local store ran a sale on two items, a watch and a shirt. There were ", ["customers who bought a watch", "customers who bought a shirt", "customers who bought a watch or a shirt", "customers who bought a watch and a shirt"], "What was the number of ", "?", false], @@ -42,65 +42,65 @@ shuffle( [0, 1, 2, 3] ) - ( function( usePercentages ) { + ( function( usePercentages ) { var rangemin = usePercentages ? 1 : 2; - var rangemax = usePercentages ? 100 : 10; - var vals = [0, 0, 0, 0]; - vals[VARINDX_X] = randRange( rangemin, rangemax ); + var rangemax = usePercentages ? 100 : 10; + var vals = [0, 0, 0, 0]; + vals[VARINDX_X] = randRange( rangemin, rangemax ); vals[VARINDX_Y] = randRange( rangemin, rangemax ); vals[VARINDX_X_AND_Y] = randRange( max( rangemin, vals[VARINDX_X]+vals[VARINDX_Y]-100 ), min( vals[VARINDX_X], vals[VARINDX_Y] ) ); vals[VARINDX_X_OR_Y] = vals[VARINDX_X] + vals[VARINDX_Y] - vals[VARINDX_X_AND_Y]; return vals; } )( USEPERCENTAGES ) - + - ( function() { - var optionalPercentage = USEPERCENTAGES ? "% are " : " "; + ( function() { + var optionalPercentage = USEPERCENTAGES ? "% are " : " "; var qstn = INTRO; for (var i=0; i< ORDER.length-1; i++) { qstn += (i===ORDER.length-2) ? " and " : ""; qstn += VARVALS[ORDER[i]] + optionalPercentage + VARDESC[ORDER[i]]; qstn += (i< ORDER.length-2) ? ", " : ". "; - } + } qstn += QSTNPRETEXT + VARDESC[ORDER[ORDER.length-1]] + QSTNPOSTTEXT; return qstn; } )() - + function (innerString) { return enFunc(innerString, USEPERCENTAGES); } - +

QUESTIONTEXT

VARVALS[ORDER[ORDER.length-1]]

Remember the addition rule of probability: P(A\cup B) = P(A) + P(B) - P(A\cap B)

-

Because the denominator of the fraction for each probability is the same, for convenience we can also just use cardinality (the number of items in each category) instead of probability: |A\cup B| = |A|+ |B| - |A\cap B|

+

Because the denominator of the fraction for each probability is the same, for convenience we can also just use cardinality (the number of items in each category) instead of probability: |A\cup B| = |A|+ |B| - |A\cap B|

Substituting variables, ENFUNC(VARDESC[2]) = ENFUNC(VARDESC[0]) + ENFUNC(VARDESC[1]) - ENFUNC(VARDESC[3])

-

Rearranging, ENFUNC(VARDESC[0]) = ENFUNC(VARDESC[3]) + ENFUNC(VARDESC[2]) - ENFUNC(VARDESC[1])

-

Rearranging, ENFUNC(VARDESC[1]) = ENFUNC(VARDESC[3]) + ENFUNC(VARDESC[2]) - ENFUNC(VARDESC[0])

-

Rearranging, ENFUNC(VARDESC[3]) = ENFUNC(VARDESC[0]) + ENFUNC(VARDESC[1]) - ENFUNC(VARDESC[2])

+

Rearranging, ENFUNC(VARDESC[0]) = ENFUNC(VARDESC[3]) + ENFUNC(VARDESC[2]) - ENFUNC(VARDESC[1])

+

Rearranging, ENFUNC(VARDESC[1]) = ENFUNC(VARDESC[3]) + ENFUNC(VARDESC[2]) - ENFUNC(VARDESC[0])

+

Rearranging, ENFUNC(VARDESC[3]) = ENFUNC(VARDESC[0]) + ENFUNC(VARDESC[1]) - ENFUNC(VARDESC[2])

-

ENFUNC(VARDESC[0]) = VARVALS[3] + VARVALS[2] - VARVALS[1] -

ENFUNC(VARDESC[1]) = VARVALS[3] + VARVALS[2] - VARVALS[0] -

ENFUNC(VARDESC[2]) = VARVALS[0] + VARVALS[1] - VARVALS[3] -

ENFUNC(VARDESC[3]) = VARVALS[0] + VARVALS[1] - VARVALS[2] +

ENFUNC(VARDESC[0]) = VARVALS[3] + VARVALS[2] - VARVALS[1] +

ENFUNC(VARDESC[1]) = VARVALS[3] + VARVALS[2] - VARVALS[0] +

ENFUNC(VARDESC[2]) = VARVALS[0] + VARVALS[1] - VARVALS[3] +

ENFUNC(VARDESC[3]) = VARVALS[0] + VARVALS[1] - VARVALS[2] -

ENFUNC(VARDESC[0]) = VARVALS[3] + VARVALS[2] - VARVALS[1] -

ENFUNC(VARDESC[1]) = VARVALS[3] + VARVALS[2] - VARVALS[0] -

ENFUNC(VARDESC[2]) = VARVALS[0] + VARVALS[1] - VARVALS[3] -

ENFUNC(VARDESC[3]) = VARVALS[0] + VARVALS[1] - VARVALS[2] +

ENFUNC(VARDESC[0]) = VARVALS[3] + VARVALS[2] - VARVALS[1] +

ENFUNC(VARDESC[1]) = VARVALS[3] + VARVALS[2] - VARVALS[0] +

ENFUNC(VARDESC[2]) = VARVALS[0] + VARVALS[1] - VARVALS[3] +

ENFUNC(VARDESC[3]) = VARVALS[0] + VARVALS[1] - VARVALS[2]

-
+ - - + +
4 exercises/age_word_problems.html
 @@ -17,8 +17,8 @@

- {person(1) is A years older than person(2)|person(2) is A years younger than person(1)}. - {For the last {four|3|two} years, person(1) and person(2) have been going to the same school.|person(1) and person(2) first met 3 years ago.|} + {person(1) is A years older than person(2)|person(2) is A years younger than person(1)}. + {For the last {four|3|two} years, person(1) and person(2) have been going to the same school.|person(1) and person(2) first met 3 years ago.|} Cardinal(B) years ago, person(1) was C times {as old as|older than} person(2).

How old is person(1) now?

42 exercises/angle_bisector_theorem.html
 @@ -13,15 +13,15 @@ [ [ 1 ], [ 2] ] function(){ - var trA = new Triangle( [ 5, -8 ], ANGLES , 14 , {} ); + var trA = new Triangle( [ 5, -8 ], ANGLES , 14 , {} ); trA.boxOut( [ [ [ 0, -10 ], [ 0, 10 ] ] ], [ 0.4 , 0 ] ); trA.boxOut( [ [ [ 11 , -10 ], [ 11, 10 ] ] ], [ -0.4 , 0 ] ); return trA; }() - + function(){ - var pointD = findIntersection( bisectAngle( TR_A.sides[ 0 ], reverseLine( TR_A.sides[ 2 ] ), 1 ), TR_A.sides[ 1 ] ); + var pointD = findIntersection( bisectAngle( TR_A.sides[ 0 ], reverseLine( TR_A.sides[ 2 ] ), 1 ), TR_A.sides[ 1 ] ); return pointD; }() @@ -49,16 +49,16 @@ TR_C.niceSideLengths[ 2 ]
- What is the length of the side AC? + What is the length of the side AC?
init({ range: TR_A.boundingRange(1.5) }) - TR_B.draw(); + TR_B.draw(); TR_B.drawLabels(); - TR_C.draw(); + TR_C.draw(); TR_C.drawLabels();
@@ -74,16 +74,16 @@
( TEMP_AB * TEMP_CD / TEMP_BD ).toFixed( 1 ) -
+
- What is the length of the side AC? (Round to 1 decimal place). + What is the length of the side AC? (Round to 1 decimal place).
AC

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

-

AC = \dfrac{AB \cdot CD }{ BD }

-

AC = AC

-
+

AC = \dfrac{AB \cdot CD }{ BD }

+

AC = AC

+
@@ -92,14 +92,14 @@ [ [ 1,2 ], [ ] ]
- What is the length of the side AB? (Round to 1 decimal place). + What is the length of the side AB? (Round to 1 decimal place).
AB

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

-

AB = \dfrac{ AC \cdot BD }{ CD }

-

AB = AB

-
+

AB = \dfrac{ AC \cdot BD }{ CD }

+

AB = AB

+
@@ -113,10 +113,10 @@
CD

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

-

CD = \dfrac{ AC \cdot BD }{ AB }

-

CD = CD

+

CD = \dfrac{ AC \cdot BD }{ AB }

+

CD = CD

-
+
( TEMP_AB * TEMP_CD / TEMP_AC ).toFixed( 1 ) @@ -129,10 +129,10 @@
BD

\dfrac{ AB }{ BD } = \dfrac{ AC }{ CD }

-

BD = \dfrac{ AB \cdot CD }{ AC }

-

BD = BD

+

BD = \dfrac{ AB \cdot CD }{ AC }

+

BD = BD

-
+
4 exercises/angle_types.html
 @@ -38,10 +38,10 @@ scale: 20 }); path([ [5 * cos( ANGLE_ONE_R ), 5 * sin( ANGLE_ONE_R )], [0, 0], [5 * cos( ANGLE_TWO_R ), 5 * sin( ANGLE_TWO_R )] ]); - + DIFF == 90 ? path([ [1 * cos( ANGLE_ONE_R ), 1 * sin( ANGLE_ONE_R )], [sqrt(2) * cos( ANGLE_ONE_R + PI / 4 ), sqrt(2) * sin( ANGLE_ONE_R + PI / 4)], [1 * cos( ANGLE_TWO_R ), 1 * sin( ANGLE_TWO_R )] ]) : arc( [0,0], 1, ANGLE_ONE, ANGLE_TWO ); - + graph.protractor = new Protractor( [22, 0], 8 ); Khan.scratchpad.disable();
246 exercises/angles_1.html
 @@ -88,32 +88,32 @@ // Label the given angles if( RAND3 == 0 ) { - label( [0.5, 1.8], "\\color{green}{ACCUTEANGLE°}", + label( [0.5, 1.8], "\\color{green}{ACCUTEANGLE°}", "above" ); arc( [0, 0], 1.2, 70, 90, { stroke: "green" } ); - ORIGINAL_LABEL = label( [-1.2, -0.75], + ORIGINAL_LABEL = label( [-1.2, -0.75], "\\color{blue}{\\angle{AGF}}= {?}", "below left" ); arc( [0, 0], 1.2, 180, 248, { stroke: "blue" } ); } else if ( RAND3 == 1 ) { - label( [-1.2, -0.75], "\\color{green}{90-ACCUTEANGLE°}", + label( [-1.2, -0.75], "\\color{green}{90-ACCUTEANGLE°}", "below left" ); arc( [0, 0], 1.2, 180, 248, { stroke: "green" } ); - ORIGINAL_LABEL = label( [0.5, 1.8], + ORIGINAL_LABEL = label( [0.5, 1.8], "\\color{blue}{\\angle{CGE}} = {?}", "above" ); arc( [0, 0], 1.2, 70, 90, { stroke: "blue" } ); } else { - label( [0, -2], "\\color{green}{ACCUTEANGLE°}", + label( [0, -2], "\\color{green}{ACCUTEANGLE°}", "below left" ); arc( [0, 0], 1.2, 248, 270, { stroke: "green" } ); - ORIGINAL_LABEL = label( [1.5, 0], + ORIGINAL_LABEL = label( [1.5, 0], "\\color{blue}{\\angle{BGE}} = {?}", "above right" ); arc( [0, 0], 1.2, 0, 70, { stroke: "blue" } ); } -

NOTE: +

NOTE: Angles not necessarily drawn to scale.

@@ -124,10 +124,10 @@

- Because we know \overline{AB} \perp \overline{CD}, we know + Because we know \overline{AB} \perp \overline{CD}, we know \color{purple}{\angle{CGB}} = 90° - label( [2.2, 1.7], "\\color{purple}{90°}", + label( [2.2, 1.7], "\\color{purple}{90°}", "above right" ); arc( [0, 0], 3, 0, 90, { stroke: "purple" } ); @@ -135,48 +135,48 @@

\color{orange}{\angle{EGB}} = \color{green}{\angle{AGF}} = 90 - ACCUTEANGLE°, - because they are opposite angles from each other. Opposite angles + because they are opposite angles from each other. Opposite angles are congruent (equal). - label( [1.2, 0], "\\color{orange}{90 - ACCUTEANGLE°}", + label( [1.2, 0], "\\color{orange}{90 - ACCUTEANGLE°}", "above right" ); arc( [0, 0], 1.2, 0, 68, { stroke: "orange" } );

- Because we know \overline{AB} \perp \overline{CD}, we know + Because we know \overline{AB} \perp \overline{CD}, we know \color{purple}{\angle{AGD}} = 90° - label( [-2.2, -1.7], "\\color{purple}{90°}", + label( [-2.2, -1.7], "\\color{purple}{90°}", "below left" ); arc( [0, 0], 3, 180, 270, { stroke: "purple" } );

- \color{orange}{\angle{EGB}} = \color{purple}{90°} + \color{orange}{\angle{EGB}} = \color{purple}{90°} - \color{green}{\angle{CGE}} = 90 - ACCUTEANGLE° - label( [1.2, 0], "\\color{orange}{90 - ACCUTEANGLE°}", + label( [1.2, 0], "\\color{orange}{90 - ACCUTEANGLE°}", "above right" ); arc( [0, 0], 1.2, 0, 68, { stroke: "orange" } );

- Because we know \overline{AB} \perp \overline{CD}, we know + Because we know \overline{AB} \perp \overline{CD}, we know \color{purple}{\angle{CGB}} = 90° - label( [2.2, 1.7], "\\color{purple}{90°}", + label( [2.2, 1.7], "\\color{purple}{90°}", "above right" ); arc( [0, 0], 3, 0, 90, { stroke: "purple" } );

- \color{orange}{\angle{AGF}} = - \color{purple}{90°} - \color{green}{\angle{DGF}} = + \color{orange}{\angle{AGF}} = + \color{purple}{90°} - \color{green}{\angle{DGF}} = 90 - ACCUTEANGLE° - label( [-1.2, 0], "\\color{orange}{90 - ACCUTEANGLE°}", + label( [-1.2, 0], "\\color{orange}{90 - ACCUTEANGLE°}", "below left" ); arc( [0, 0], 1.2, 180, 248, { stroke: "orange" } ); @@ -184,37 +184,37 @@

\color{blue}{\angle{AGF}} = \color{orange}{\angle{EGB}} = - 90 - ACCUTEANGLE°, - because they are opposite from each other. Opposite angles are + 90 - ACCUTEANGLE°, + because they are opposite from each other. Opposite angles are congruent (equal). ORIGINAL_LABEL.remove(); - label( [-1.2, -0.75], - "\\color{blue}{\\angle{AGF}}=90 - ACCUTEANGLE°", + label( [-1.2, -0.75], + "\\color{blue}{\\angle{AGF}}=90 - ACCUTEANGLE°", "below left" );

- \color{blue}{\angle{CGE}} = - \color{purple}{90°} - \color{orange}{\angle{EGB}} = + \color{blue}{\angle{CGE}} = + \color{purple}{90°} - \color{orange}{\angle{EGB}} = ACCUTEANGLE° ORIGINAL_LABEL.remove(); - label( [0.5, 1.8], - "\\color{blue}{\\angle{CGE}} = ACCUTEANGLE°", + label( [0.5, 1.8], + "\\color{blue}{\\angle{CGE}} = ACCUTEANGLE°", "above" )

- \color{blue}{\angle{BGE}} = \color{orange}{\angle{AGF}} = - 90 - ACCUTEANGLE°, - because they are opposite from each other. Opposite angles are + \color{blue}{\angle{BGE}} = \color{orange}{\angle{AGF}} = + 90 - ACCUTEANGLE°, + because they are opposite from each other. Opposite angles are congruent (equal). ORIGINAL_LABEL.remove(); - label( [1.5, 0], - "\\color{blue}{\\angle{BGE}} = 90 - ACCUTEANGLE°", + label( [1.5, 0], + "\\color{blue}{\\angle{BGE}} = 90 - ACCUTEANGLE°", "above right" );

@@ -270,36 +270,36 @@ label( [0, 3], "B", "above" ); label( [4, -2], "C", "below right" ); label( [-8, -2], "D", "below" ); - + // Label the angles acording to variation if( RAND2 == 0 ) { - label( [3, -2], "\\color{green}{Tri_Y°}", + label( [3, -2], "\\color{green}{Tri_Y°}", "above left" ); arc( [4, -2], 1.2, 130, 180, { stroke: "green" } ); - label( [0, 1.5], "\\color{purple}{Tri_Z°}", + label( [0, 1.5], "\\color{purple}{Tri_Z°}", "below" ); arc( [0, 3], 1.5, 230, 310, { stroke: "purple" } ); - ORIGINAL_LABEL = label( [-4.7, -2], "\\color{blue}{\\angle{DAB}}= {?}", + ORIGINAL_LABEL = label( [-4.7, -2], "\\color{blue}{\\angle{DAB}}= {?}", "above left" ); arc( [-4, -2], .75, 50, 180, { stroke: "blue" } ); } else { - label( [-4.7, -2], "\\color{green}{180 - Tri_X°}", + label( [-4.7, -2], "\\color{green}{180 - Tri_X°}", "above left" ); arc( [-4, -2], .75, 50, 180, { stroke: "green" } ); - label( [0, 1.5], "\\color{purple}{Tri_Z°}", + label( [0, 1.5], "\\color{purple}{Tri_Z°}", "below" ); arc( [0, 3], 1.5, 230, 310, { stroke: "purple" } ); - ORIGINAL_LABEL = label( [2.80, -2], "\\color{blue}{\\angle{ACB}} = {?}", + ORIGINAL_LABEL = label( [2.80, -2], "\\color{blue}{\\angle{ACB}} = {?}", "above left" ); arc( [4, -2], 1.2, 130, 180, { stroke: "blue" } ); }
-

NOTE: +

NOTE: Angles not necessarily drawn to scale.

@@ -307,12 +307,12 @@ Tri_Y + Tri_Z Tri_Y - +

- \color{orange}{\angle{BAC}} = - 180° - \color{purple}{\angle{ABC}} - \color{green}{\angle{ACB}} = + \color{orange}{\angle{BAC}} = + 180° - \color{purple}{\angle{ABC}} - \color{green}{\angle{ACB}} = 180 - Tri_Y - Tri_Z° , This is because angles inside a triangle add up to 180 degrees. @@ -324,11 +324,11 @@

- \color{orange}{\angle{BAC}} = - 180° - \color{green}{\angle{DAB}} = + \color{orange}{\angle{BAC}} = + 180° - \color{green}{\angle{DAB}} = 180 - Tri_Y - Tri_X° , - because supplementary angles along a line add up to + because supplementary angles along a line add up to 180 degrees. label( [-3.3, -2], "\\color{orange}{Tri_X°}", @@ -336,33 +336,33 @@ arc( [-4, -2], 0.75, 0, 49, {stroke: "orange"} );

- +

- \color{blue}{\angle{DAB}} = - 180° - \color{orange}{\angle{BAC}} = + \color{blue}{\angle{DAB}} = + 180° - \color{orange}{\angle{BAC}} = Tri_Y + Tri_Z° - , + , because supplementary angles along a line add up to 180° ORIGINAL_LABEL.remove(); - label( [-4.7, -2], - "\\color{blue}{\\angle{DAB}} = Tri_Y + Tri_Z°", + label( [-4.7, -2], + "\\color{blue}{\\angle{DAB}} = Tri_Y + Tri_Z°", "above left" );

- \color{blue}{\angle{ACB}} = - 180° - \color{orange}{\angle{BAC}} - \color{purple}{\angle{ABC}} = + \color{blue}{\angle{ACB}} = + 180° - \color{orange}{\angle{BAC}} - \color{purple}{\angle{ABC}} = Tri_Y° , because angles inside a triangle add up to 180°. ORIGINAL_LABEL.remove(); - label( [2.80, -2], - "\\color{blue}{\\angle{ACB}} = Tri_Y°", + label( [2.80, -2], + "\\color{blue}{\\angle{ACB}} = Tri_Y°", "above left" );

@@ -442,29 +442,29 @@ //draw given angles if( RAND3 == 0 ) { - ORIGINAL_LABEL = label( [0, -2.50], + ORIGINAL_LABEL = label( [0, -2.50], "\\color{blue}{\\angle{AIH}} = {?}", "left" ); arc( [1.25, -3], .75, 135, 190, {stroke: "blue"} ); label( [-4.2, 4.25], "\\color{green}{Tri_Z°}", "below" ); arc( [-4.47, 5.25], 1, 255, 330, {stroke: "green"} ); - label( [-5.5, -3.5], "\\color{purple}{Tri_X°}", + label( [-5.5, -3.5], "\\color{purple}{Tri_X°}", "above right" ); arc( [-6, -4], 1, 10, 80, {stroke: "purple"} ); } else if( RAND3 == 1 ) { - ORIGINAL_LABEL = label( [3.5, -2.6], + ORIGINAL_LABEL = label( [3.5, -2.6], "\\color{blue}{\\angle{AKJ}} = {?}", "above" ); arc( [5.7, -2.3], 0.75, 139, 194, {stroke: "blue"} ); label( [-4.4, 0.65], "\\color{green}{Tri_Z°}", "below" ); arc( [-5.07, 1.75], 1, 257, 326, {stroke: "green"} ); - label( [-5.5, -3.5], "\\color{purple}{Tri_X°}", + label( [-5.5, -3.5], "\\color{purple}{Tri_X°}", "above right" ); arc( [-6, -4], 1, 10, 80, {stroke: "purple"} ); } else { - ORIGINAL_LABEL = label( [-5.5, -3.5], + ORIGINAL_LABEL = label( [-5.5, -3.5], "\\color{blue}{\\angle{BAC}} = {?}", "above right" ); arc( [-6, -4], 1, 10, 80, {stroke: "blue"} ); @@ -476,7 +476,7 @@ }
-

NOTE: +

NOTE: Angles not necessarily drawn to scale.

@@ -487,21 +487,21 @@

- \color{orange}{\angle{AHI}} = \color{green}{\angle{AJK}}, - because they are corresponding angles formed by 2 parallel lines and + \color{orange}{\angle{AHI}} = \color{green}{\angle{AJK}}, + because they are corresponding angles formed by 2 parallel lines and a transversal line. Corresponding angles are congruent (equal). - label( [-4.60, 0.75], "\\color{orange}{Tri_Z°}", + label( [-4.60, 0.75], "\\color{orange}{Tri_Z°}", "below" ); arc( [-5.07, 1.75], 1, 260, 325, {stroke: "orange"} );

- \color{orange}{\angle{AJK}} = \color{green}{\angle{AHI}}, - because they are corresponding angles formed by 2 parallel lines and + \color{orange}{\angle{AJK}} = \color{green}{\angle{AHI}}, + because they are corresponding angles formed by 2 parallel lines and a transversal line. Corresponding angles are congruent (equal). - label( [-4.00, 4.25], "\\color{orange}{Tri_Z°}", + label( [-4.00, 4.25], "\\color{orange}{Tri_Z°}", "below" ); arc( [-4.47, 5.25], 1, 257, 325, {stroke: "orange"} ); @@ -510,43 +510,43 @@

- \color{blue}{\angle{AIH}} = - 180° - \color{orange}{\angle{AHI}} - \color{purple}{\angle{BAC}} = - 180 - Tri_X - Tri_Z° + \color{blue}{\angle{AIH}} = + 180° - \color{orange}{\angle{AHI}} - \color{purple}{\angle{BAC}} = + 180 - Tri_X - Tri_Z° , - because the 3 angles are contained in \triangle{AHI}. + because the 3 angles are contained in \triangle{AHI}. Angles inside a triangle add up to 180°. ORIGINAL_LABEL.remove(); - label( [0, -2.50], - "\\color{blue}{\\angle{AIH}} = 180 - Tri_X - Tri_Z°", - "left" ); + label( [0, -2.50], + "\\color{blue}{\\angle{AIH}} = 180 - Tri_X - Tri_Z°", + "left" );

- ORIGINAL_LABEL.remove(); + ORIGINAL_LABEL.remove(); if ( RAND3 === 1 ) { - label( [3.3, -2.6], - "\\color{blue}{\\angle{AKJ}} = Tri_Y°", + label( [3.3, -2.6], + "\\color{blue}{\\angle{AKJ}} = Tri_Y°", "above" ); } else { - label( [-5.5, -3.5], - "\\color{blue}{\\angle{BAC}} = Tri_X°", + label( [-5.5, -3.5], + "\\color{blue}{\\angle{BAC}} = Tri_X°", "above right" ); } - \color{blue}{\angle{AKJ}} = - 180° - \color{orange}{\angle{AJK}} - \color{purple}{\angle{BAC}} = - Tri_Y° + \color{blue}{\angle{AKJ}} = + 180° - \color{orange}{\angle{AJK}} - \color{purple}{\angle{BAC}} = + Tri_Y° - \color{blue}{\angle{BAC}} = - 180° - \color{orange}{\angle{AJK}} - \color{purple}{\angle{AKJ}} = + \color{blue}{\angle{BAC}} = + 180° - \color{orange}{\angle{AJK}} - \color{purple}{\angle{AKJ}} = Tri_X° - , - because the 3 angles are contained in \triangle{AJK}. + , + because the 3 angles are contained in \triangle{AJK}. Angles inside a triangle add up to 180°.

@@ -574,7 +574,7 @@ \color{blue}{\angle{GCJ}} = {?} -
+
init( { range: [[-6, 8], [-5, 5]], scale: [50, 50] @@ -613,23 +613,23 @@ // Label given angles if( RAND2 == 0 ) { - ORIGINAL_LABEL = label( [0, 3.5], + ORIGINAL_LABEL = label( [0, 3.5], "\\color{blue}{\\angle{IAK}} = {?}", "above left" ); arc( [0, 2], 1, 90, 135, {stroke:"blue"} ); - label( [4.75, -2], "\\color{green}{Tri_Y°}", + label( [4.75, -2], "\\color{green}{Tri_Y°}", "below right" ); arc( [4, -2], .75, 315, 360, {stroke: "green"} ); } else { label( [0, 3], "\\color{green}{Tri_Y°}", "above left" ); arc( [0, 2], 1, 90, 135, {stroke:"green"} ); - ORIGINAL_LABEL = label( [4.75, -2], + ORIGINAL_LABEL = label( [4.75, -2], "\\color{blue}{\\angle{GCJ} = {?}}", "below right" ); arc( [4, -2], .75, 315, 360, {stroke: "blue"} ) }
-

NOTE: +

NOTE: Angles not necessarily drawn to scale.

@@ -638,30 +638,30 @@

- \color{orange}{\angle{DAI}} = \color{green}{\angle{GCJ}} = - Tri_Y°, - because they are alternate exterior angles, formed by 2 parallel lines + \color{orange}{\angle{DAI}} = \color{green}{\angle{GCJ}} = + Tri_Y°, + because they are alternate exterior angles, formed by 2 parallel lines and a transversal line, they are congruent (equal). - label( [-.80, 2], "\\color{orange}{Tri_Y°}", + label( [-.80, 2], "\\color{orange}{Tri_Y°}", "above left" ); arc( [0, 2], 1, 135, 180, {stroke: "orange"} ); Alternatively, you can pair up using opposite angles and alternate interior - angles to achieve the same result (as seen using + angles to achieve the same result (as seen using \color{pink}{pink}). - label( [1, 2], "\\color{pink}{Tri_Y°}", + label( [1, 2], "\\color{pink}{Tri_Y°}", "below right" ); arc( [0, 2], 1, 315, 360, {stroke: "pink"} ); - label( [3, -2], "\\color{pink}{Tri_Y°}", + label( [3, -2], "\\color{pink}{Tri_Y°}", "above left" ); arc( [4, -2], 1, 135, 180, {stroke: "pink"} );

- \color{purple}{\angle{DAK}} = 90°, + \color{purple}{\angle{DAK}} = 90°, because angles formed by perpendicular lines are equal to 90°. label( [-1.68, 2], "\\color{purple}{90°}", "above left" ); @@ -670,52 +670,52 @@

- \color{blue}{\angle{IAK}} = 90° - \color{orange}{\angle{DAI}} = - 90 - Tri_Y°, - because angles \color{blue}{\angle{IAK}} - and \color{orange}{\angle{DAI}} make up angle + \color{blue}{\angle{IAK}} = 90° - \color{orange}{\angle{DAI}} = + 90 - Tri_Y°, + because angles \color{blue}{\angle{IAK}} + and \color{orange}{\angle{DAI}} make up angle \color{purple}{\angle{DAK}}. ORIGINAL_LABEL.remove(); - label( [0, 3.5], - "\\color{blue}{\\angle{IAK}} = 90 - Tri_Y°", - "above left" ); + label( [0, 3.5], + "\\color{blue}{\\angle{IAK}} = 90 - Tri_Y°", + "above left" );

- \color{orange}{\angle{IAK}} = 90° - \color{green}{\angle{IAK}} = - 90 - Tri_Y°, - because angles \color{green}{\angle{IAK}} - and \color{orange}{\angle{DAI}}, make up angle + \color{orange}{\angle{IAK}} = 90° - \color{green}{\angle{IAK}} = + 90 - Tri_Y°, + because angles \color{green}{\angle{IAK}} + and \color{orange}{\angle{DAI}}, make up angle \color{purple}{\angle{DAK}}. - label( [-.80, 2], "\\color{orange}{90-Tri_Y°}", + label( [-.80, 2], "\\color{orange}{90-Tri_Y°}", "above left" ); arc( [0, 2], 1, 135, 180, {stroke: "orange"} ); - +

- \color{blue}{\angle{GCJ}} = \color{orange}{\angle{DAI}} = - 90 - Tri_Y°, - because they are alternate exterior angles formed by 2 parallel lines + \color{blue}{\angle{GCJ}} = \color{orange}{\angle{DAI}} = + 90 - Tri_Y°, + because they are alternate exterior angles formed by 2 parallel lines and a transversal line, they are congruent (equal). Alternatively, you can pair up using opposite angles and alternate interior - angles to achieve the same result (as seen using + angles to achieve the same result (as seen using \color{pink}{pink}). - label( [1, 2], "\\color{pink}{90-Tri_Y°}", + label( [1, 2], "\\color{pink}{90-Tri_Y°}", "below right" ); arc( [0, 2], 1, 315, 360, {stroke: "pink"} ); - label( [3, -2], "\\color{pink}{90-Tri_Y°}", + label( [3, -2], "\\color{pink}{90-Tri_Y°}", "above left" ); arc( [4, -2], 1, 135, 180, {stroke: "pink"} ); - + ORIGINAL_LABEL.remove(); - label( [4.75, -2], - "\\color{blue}{\\angle{GCJ} = 90-Tri_Y°}", + label( [4.75, -2], + "\\color{blue}{\\angle{GCJ} = 90-Tri_Y°}", "below right" );

2  exercises/angles_of_a_polygon.html
 @@ -73,7 +73,7 @@
360 degrees
- +

The exterior angles are shown above.

6 exercises/arithmetic_word_problems_2.html
 @@ -24,7 +24,7 @@ How much does the color(2) clothing(2) cost?

TOTAL
- +

The cost of the color(2) clothing(2) @@ -67,7 +67,7 @@

An( color( 2 ) ) clothing( 2 ) costs $NUM1. - + An( color(1) ) clothing(1) costs$TOTAL, @@ -155,7 +155,7 @@

- person(1) has biked(1) his(1) bike(1) for a total of plural( TOTAL, distance(1) ) + person(1) has biked(1) his(1) bike(1) for a total of plural( TOTAL, distance(1) ) since he(1) started biking(1) daily. He(1) has been biking(1) plural( NUM2, distance(1) ) each day.

4 exercises/changing_decimals_to_percents.html
 @@ -16,7 +16,7 @@

Express DECIMAL as a percent.

SOLN %

-
+

To convert a decimal to a fraction, we need to multiply by 100 and add the \% symbol.

@@ -28,4 +28,4 @@
- +
4 exercises/changing_fractions_to_decimals_1.html
 @@ -3,7 +3,7 @@ Changing fractions to decimals 1 - +
2  exercises/changing_percents_to_decimals.html
 @@ -27,4 +27,4 @@ - +
4 exercises/changing_percents_to_fractions.html
 @@ -14,7 +14,7 @@ randRangeExclude( 1 , 299 , [ 100 ] )

Express A\% as a fraction. Reduce to lowest terms.

-

A / 100

+

A / 100

A\% literally means A per 100

Putting this in fraction form: fraction( A , 100 )

@@ -41,4 +41,4 @@
- +
34 exercises/circles_1.html
 @@ -9,42 +9,42 @@ var D_COLOR = "green"; var C_COLOR = "blue"; var K_COLOR = "red"; - + function initCircle( R ) { var graph = KhanUtil.currentGraph; - + graph.init({ range: [ [-1.1, 1.1], [-1.1, 1.1] ], scale: 100 }); - + graph.circle( [0, 0], 1, { "fill-opacity": 0 } ); } function drawRadius( R ) { var graph = KhanUtil.currentGraph; - + graph.line( [0, 0], [1, 0], { "fill": "none", "stroke": R_COLOR } ); graph.label( [1/2, 0], "\\color{" + R_COLOR + "}{r = " + R + "}", "below" ); } function drawDiameter( R ) { var graph = KhanUtil.currentGraph; - + graph.line( [-1, 0], [1, 0], { "stroke": D_COLOR } ); graph.label( [0, 0], "\\color{" + D_COLOR + "}{d = " + 2 * R + "}", "above" ); } function drawCircumference( R ) { var graph = KhanUtil.currentGraph; - + graph.circle( [0, 0], 1, { "stroke": C_COLOR } ); graph.label( [0, -1], "\\color{" + C_COLOR + "}{c = " + 2 * R + "\\pi}", "below" ); } function drawArea( R ) { var graph = KhanUtil.currentGraph; - + var c = graph.circle( [0, 0], 1, { "fill": "#ffcccc", "stroke-width": 0 } ); jQuery(c.node).insertBefore(jQuery(graph.raphael.canvas).find("ellipse")[0]); @@ -69,7 +69,7 @@
initCircle( R ); - + drawRadius( R );
@@ -123,7 +123,7 @@
initCircle( R ); - + drawRadius( R );
@@ -177,7 +177,7 @@
initCircle( R ); - + drawDiameter( R );
@@ -231,7 +231,7 @@
initCircle( R ); - + drawRadius( R );
@@ -258,7 +258,7 @@
initCircle( R ); - + drawArea( R );
@@ -285,13 +285,13 @@
initCircle( R ); - + drawDiameter( R );

First, find the radius: r = d/2 = \color{D_COLOR}{2 * R}/2 = \color{R_COLOR}{R}.

Now find the area: K = \pi r^2, so K = \pi \cdot \color{R_COLOR}{R}^2 = \color{K_COLOR}{R * R\pi}.

- +
drawArea( R );
@@ -313,13 +313,13 @@
initCircle( R ); - + drawArea( R );

First, find the radius: K = \pi r^2, so r = \sqrt{K / \pi} = \sqrt{\color{K_COLOR}{R * R\pi} / \pi} = \color{R_COLOR}{R}.

Now find the diameter: d = 2r = 2\cdot \color{R_COLOR}{R} = \color{D_COLOR}{2*R}.

- +
drawDiameter( R );
@@ -369,7 +369,7 @@
initCircle( R ); - + drawArea( R );

First, find the radius: K = \pi r^2, so r = \sqrt{K / \pi} = \sqrt{\color{K_COLOR}{R * R\pi} / \pi} = \color{R_COLOR}{R}.

 @@ -27,8 +27,8 @@ init({ range: [ [-1, 12 ], [ -7, 2.5 ] ] }) - var trA = new Triangle( [ 3, -4 ], [ 60, 60, 60 ] , 16 , {} ); - var pointD = findIntersection( bisectAngle( trA.sides[ 0 ], reverseLine( trA.sides[ 2 ] ), 1 ), trA.sides[ 1 ] ); + var trA = new Triangle( [ 3, -4 ], [ 60, 60, 60 ] , 16 , {} ); + var pointD = findIntersection( bisectAngle( trA.sides[ 0 ], reverseLine( trA.sides[ 2 ] ), 1 ), trA.sides[ 1 ] ); trA.draw() trA.labels = { "sides" : trA.niceSideLengths, "points": [ "A", "B", "C" ] }; trA.drawLabels(); @@ -43,7 +43,7 @@

Because side DAB and DAC are equal.

ThatAngles DAB and DAC are equal.

-
+
4 exercises/comparing_absolute_values.html
 @@ -4,10 +4,10 @@ Comparing absolute values -
2  exercises/complementary_angles.html
 @@ -31,7 +31,7 @@ range: [ [-2, 7], [-2, 6] ], scale: 40 }); - + var DISP_ANGLE = Math.min( Math.max( 10, ANGLE ), 80 ); if ( ANGLE_ONE !== ANGLE_BOT ) { DISP_ANGLE = 90 - DISP_ANGLE;
2  exercises/completing_the_square_1.html
 @@ -78,4 +78,4 @@ - +
2  exercises/completing_the_square_2.html
 @@ -91,4 +91,4 @@ - +
24 exercises/compound_inequalities.html
 @@ -22,25 +22,25 @@
- tabulate( function() { + tabulate( function() { return randRange( 2, 9 ) * ( rand( 3 ) > 0 ? 1 : -1 ); } , 2 ) - tabulate( function(i) { - return fraction( 1, COEF[i] ); + tabulate( function(i) { + return fraction( 1, COEF[i] ); }, 2 ) randFromArray( [ "-", "+" ], 2) - tabulate( function() { + tabulate( function() { return rand( 3 ) > 0 ? randRange( 2, 9 ) : 0; }, 2 ) - tabulate( function(i) { + tabulate( function(i) { return LEFT_INT[i] * ( SIGN[i] === "+" ? -1 : 1 ); }, 2 ) randFromArray( [ "<", ">", "≤", "≥" ], 2 ) - tabulate( function(i) { + tabulate( function(i) { return randRange( 1, 6 ) * abs( COEF[i] ) + ( SIGN[i] === "+" ? 1 : -1 ) * LEFT_INT[i]; }, 2 ) randFromArray([ "a", "b", "c", "x", "y", "z" ]) - tabulate( function(i) { + tabulate( function(i) { return getComp( COEF[i], COMP[i] ); }, 2 ) tabulate( function(i) { @@ -133,8 +133,8 @@
- var start = min( SOLUTION[0], SOLUTION[1] ) - randRange( 2, 5 ); - var end = max( SOLUTION[0], SOLUTION[1] ) + randRange( 2, 5 ); + var start = min( SOLUTION[0], SOLUTION[1] ) - randRange( 2, 5 ); + var end = max( SOLUTION[0], SOLUTION[1] ) + randRange( 2, 5 ); init({ range: [ [ start - 1, end + 1 ], [ -1, 1 ] ] @@ -161,8 +161,8 @@

Therefore, since the graphs of the equalities do not intersect, the solution is:

- \color{COLOR[0]}{VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0]} or - \color{COLOR[1]}{VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]} + \color{COLOR[0]}{VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0]} or + \color{COLOR[1]}{VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]}

@@ -181,7 +181,7 @@

Therefore, the solution is:

\color{COLOR[0]}{VARIABLE_NAME + COMP_SOLUTION[0] + SOLUTION[0]} and - \color{COLOR[1]}{VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]} + \color{COLOR[1]}{VARIABLE_NAME + COMP_SOLUTION[1] + SOLUTION[1]}

20 exercises/congruent_triangles_1.html
 @@ -23,7 +23,7 @@ function(){ var t = new Triangle( [ 3, -2 ], MAIN, MAIN_SIZE, {} ); - t.labels = { "name": "A", "angles" : clearArray( t.niceAngles, A_ANGLES ), "sides" : clearArray( t.niceSideLengths, A_SIDES ) }; + t.labels = { "name": "A", "angles" : clearArray( t.niceAngles, A_ANGLES ), "sides" : clearArray( t.niceSideLengths, A_SIDES ) }; return t; }() @@ -38,7 +38,7 @@

Triangles are congruent when all corresponding sides and interior angles are congruent.

However, we do not need to know all the values in order to determine whether two triangles are congruent.

-

The rules we use for determining congruency are SSS, ASA, SAS and AAS

+

The rules we use for determining congruency are SSS, ASA, SAS and AAS

Are these two triangles congruent? @@ -51,7 +51,7 @@ TR_A.rotate( randRange( 0, 360 ) ); TR_A.draw(); TR_A.drawLabels(); - + TR_B.rotate( randRange( 0, 360 ) ); TR_B.draw(); TR_B.drawLabels(); @@ -81,19 +81,19 @@
[ 1 ] - [ 0, 1 ] + [ 0, 1 ]

In this problem we are given two sides and an angle between them, so we can use the SAS rule.

Triangle B has those two sides and the angle the same as triangle A, so they are congruent.

Because the sides and the angle do not match, triangle A is not congruent with triangle B.

-
+
[ 0, 1 ] - [ 1 ] + [ 1 ]

In this problem we are given two angles and as side between them, so we can use the ASA rule.

@@ -105,7 +105,7 @@
[ 0, 1 ] - randRange( 0, 1 ) === 1 ? [ 2 ] : [ 1 ] + randRange( 0, 1 ) === 1 ? [ 2 ] : [ 1 ]

In this problem we are given two angles and another side so we can use the AAS rule.

@@ -116,14 +116,14 @@
[ 0, 1, 2 ] - [ ] - IS_B ? "There is not enough information to say" : "No" + [ ] + IS_B ? "There is not enough information to say" : "No"

In this problem we know all three triangle angles.

However, having all three angles the same is not a property we can use to conclude that two triangles are congruent. We can only say that they are similar. They are not congruent because they might be different size, yet have same angles.

Because the angles do not match, triangle A is not congruent with triangle B.

-
+
8 exercises/congruent_triangles_2.html
 @@ -26,11 +26,11 @@ function(){ - var trA = new Triangle( [ 3, -5 ], ANGLES ,6, {} ); + var trA = new Triangle( [ 3, -5 ], ANGLES ,6, {} ); trA.labels = { "points" : [ "A", "B", "C" ], "sides" : clearArray( trA.niceSideLengths, SIDES_A ), "angles" : clearArray( trA.niceAngles, ANGLES_A ) }; return trA; }() - + function(){ var trB = new Triangle( [ TR_A.centroid[ 0 ], TR_A.centroid[ 1 ] ], ANGLES, 6, {} ); @@ -131,13 +131,13 @@ ANGLES[ 0 ] / 2 function(){ - var trA = new Triangle( [ 7, -3 ], ANGLES ,6, {} ); + var trA = new Triangle( [ 7, -3 ], ANGLES ,6, {} ); trA.rotationCenter = trA.points[ 0 ]; trA.rotate( ANG ); trA.labels = { "points" : [ "", "B", "C" ], "sides" : clearArray( trA.niceSideLengths, SIDES_A ), "angles" : clearArray( trA.niceAngles, ANGLES_A ) }; return trA; }() - + function(){ var trB = new Triangle( [ 7 - cos( ANG * PI / 180 ) * TR_A.sideLengths[ 0 ], -3 - sin( ANG * PI / 180 ) * TR_A.sideLengths[ 0 ] ], [ ANGLES[ 1 ], ANGLES[ 0 ], ANGLES[ 2 ] ] , 6, {} );
4 exercises/converting_decimals_to_fractions_1.html
 @@ -28,7 +28,7 @@ floor( ( D * 100 ) % 10 )

Express D.toFixed( 2 ) as a fraction.

-

D

+

D

The number T is in the tenths place, so we have cardinal( T ) tenths.

Cardinal( T ) tenths can be written as fraction( T, 10 ).

@@ -51,4 +51,4 @@
- +
2  exercises/converting_decimals_to_fractions_2.html
 @@ -60,4 +60,4 @@ - +
2  exercises/converting_decimals_to_percents.html
 @@ -31,4 +31,4 @@ - +
6 exercises/converting_mixed_numbers_and_improper_fractions.html
 @@ -8,13 +8,13 @@
randRange( 1, 10 ) - + randRange( 1, 30 ) randRange( 1, 30 ) M_NUM / getGCD( M_NUM, M_DENOM ) M_DENOM / getGCD( M_NUM, M_DENOM ) - + WHOLE * M_REDUCED_DENOM + M_REDUCED_NUM M_REDUCED_DENOM
@@ -64,7 +64,7 @@

Note that if we add up the two pieces of our mixed fraction, \color{#28AE7B}{fraction( I_DENOM * WHOLE, I_DENOM, false, false )} + \color{purple}{fraction( M_NUM, M_DENOM, false, true )}, we get the original improper fraction fraction( I_NUM, I_DENOM, false, true ).

- +

Convert WHOLE\ fraction( M_NUM, M_DENOM, false, true ) to an improper fraction.

2  exercises/converting_percents_to_decimals.html
 @@ -30,4 +30,4 @@ - +
2  exercises/converting_repeating_decimals_to_fractions_1.html
 @@ -43,4 +43,4 @@ - +