# Khan/khan-exercises

Fix up exercises that are too wide for tutorials

Reviewers: marcos, tom, desmond

1 parent 8183d56 commit 064281eac8e87bf5f48f3eb515ac382610c15004 beneater committed Sep 19, 2012
Showing with 327 additions and 258 deletions.
2. +1 −1 exercises/angle_types.html
3. +3 −3 exercises/angles_1.html
4. +3 −3 exercises/angles_2.html
5. +2 −2 exercises/completing_the_square_1.html
6. +1 −1 exercises/completing_the_square_2.html
7. +3 −2 exercises/compound_inequalities.html
8. +3 −3 exercises/conditional_statements_2.html
9. +1 −1 exercises/congruency_postulates.html
10. +4 −2 exercises/congruent_triangles_2.html
11. +4 −4 exercises/converting_between_point_slope_and_standard_form.html
12. +3 −3 exercises/counting_1_alternative.html
13. +1 −1 exercises/creating_bar_charts_1.html
14. +1 −0 exercises/creating_box_and_whisker_plots.html
15. +2 −2 exercises/decimals_on_the_number_line_2.html
16. +13 −7 exercises/dividing_complex_numbers.html
17. +5 −0 exercises/domain_and_range_0.5.html
18. +1 −1 exercises/empirical_rule.html
19. +1 −1 exercises/equation_of_a_circle_1.html
20. +1 −1 exercises/equation_of_a_circle_2.html
21. +5 −6 exercises/equation_of_a_hyperbola.html
22. +3 −3 exercises/equation_of_an_ellipse.html
23. +1 −1 exercises/exploring_mean_and_median.html
24. +2 −1 exercises/exploring_standard_deviation_1.html
25. +8 −4 exercises/factor_expressions_by_grouping.html
26. +3 −3 exercises/fractions_cut_and_copy_1.html
27. +8 −8 exercises/fractions_cut_and_copy_2.html
28. +1 −1 exercises/fractions_on_the_number_line_1.html
29. +1 −1 exercises/fractions_on_the_number_line_2.html
30. +18 −18 exercises/fractions_on_the_number_line_3.html
31. +7 −8 exercises/graphs_of_sine_and_cosine.html
32. +3 −2 exercises/identifying_points_1.html
33. +6 −1 exercises/midpoint_formula.html
34. +6 −7 exercises/multiplication_0.5.html
35. +6 −5 exercises/multiplication_1.html
36. +5 −0 exercises/multiplying_and_dividing_scientific_notation.html
37. +10 −10 exercises/multiplying_fractions_word_problems.html
38. +2 −2 exercises/ordering_negative_numbers.html
39. +3 −5 exercises/parabola_intuition_3.html
40. +1 −1 exercises/percentage_word_problems_2.html
41. +6 −6 exercises/point_slope_form.html
42. +2 −2 exercises/quotient_rule.html
43. +5 −0 exercises/range_of_a_function.html
49. +4 −4 exercises/rounding_numbers.html
50. +2 −2 exercises/rounding_whole_numbers.html
51. +2 −2 exercises/scientific_notation_intuition.html
53. +1 −1 exercises/signs_of_a_parabola.html
54. +2 −1 exercises/similar_triangles_1.html
55. +2 −1 exercises/similar_triangles_2.html
56. +1 −1 exercises/slope_intercept_form.html
57. +2 −2 exercises/slope_of_a_line.html
61. +2 −1 exercises/solving_similar_triangles_1.html
62. +7 −2 exercises/square_roots_2.html
63. +4 −4 exercises/standard_deviation.html
64. +1 −1 exercises/telling_time.html
65. +1 −1 exercises/telling_time_0.5.html
66. +5 −0 exercises/triangle_inequality_theorem.html
68. +2 −2 exercises/understanding_decimals_place_value.html
69. +3 −3 exercises/understanding_moving_the_decimal.html
70. +4 −4 exercises/variance.html
71. +4 −0 exercises/views_of_a_function.html
73. +2 −2 utils/derivative-intuition.js
74. +25 −25 utils/graphie-helpers-arithmetic.js
75. +4 −4 utils/graphie-helpers.js
76. +2 −1 utils/math.js
77. +1 −1 utils/slice-clone.js
 @@ -4,6 +4,11 @@ Adding vectors +
@@ -17,34 +22,32 @@
-
-
- graphInit({ - range: 10, - scale: 20, - tickStep: 1, - labelStep: 1, - unityLabels: false, - labelFormat: function( s ) { return "\\small{" + s + "}"; }, - axisArrows: "<->" - }); +

What is \vec a + \vec b?

- line( [0, 0], [AX, AY], { stroke: "#6495ed", arrows: "->" } ); - line( [0, 0], [BX, BY], { stroke: "#28ae7b", arrows: "->" } ); +

\begin{align*} + \vec a &= AX \hat\imath + AY \hat\jmath \\ + \vec b &= BX \hat\imath + BY \hat\jmath + \end{align*}

- var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY ); - label( [AF * AX, AF * AY], "\\vec a", { color: "#6495ed" } ); +
+ graphInit({ + range: 10, + scale: 20, + tickStep: 1, + labelStep: 1, + unityLabels: false, + labelFormat: function( s ) { return "\\small{" + s + "}"; }, + axisArrows: "<->" + }); - var BF = 1 + 0.8 / sqrt( BX * BX + BY * BY ); - label( [BF * BX, BF * BY], "\\vec b", { color: "#28ae7b" } ); -
+ line( [0, 0], [AX, AY], { stroke: "#6495ed", arrows: "->" } ); + line( [0, 0], [BX, BY], { stroke: "#28ae7b", arrows: "->" } ); -

What is \vec a + \vec b?

+ var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY ); + label( [AF * AX, AF * AY], "\\vec a", { color: "#6495ed" } ); -

\begin{align*} - \vec a &= AX \hat\imath + AY \hat\jmath \\ - \vec b &= BX \hat\imath + BY \hat\jmath - \end{align*}

+ var BF = 1 + 0.8 / sqrt( BX * BX + BY * BY ); + label( [BF * BX, BF * BY], "\\vec b", { color: "#28ae7b" } );
2 exercises/angle_types.html
 @@ -43,7 +43,7 @@ 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 ); addMouseLayer(); - graph.protractor = new Protractor( [22, 0] ); + graph.protractor = new Protractor( [14, -8] );
6 exercises/angles_1.html
 @@ -244,7 +244,7 @@
init({ range: [[-9, 6], [-3, 5]], - scale: [40, 40] + scale: [33, 33] }); style({ @@ -402,7 +402,7 @@
init( { range: [[-9, 9.5], [-5.7, 8]], - scale: [30, 30] + scale: [27, 27] }); style( { @@ -577,7 +577,7 @@
init( { range: [[-6, 8], [-5, 5]], - scale: [50, 50] + scale: [35, 35] } ); style( {
6 exercises/angles_2.html
 @@ -173,7 +173,7 @@
init({ - range: [[-7, 6], [-5, 5.2]], + range: [[-6.5, 6], [-5, 5.2]], scale: [40, 40] }); @@ -337,7 +337,7 @@
init({ range: [[-10, 10], [-7, 10]], - scale: [30, 30] + scale: [25, 25] }); @@ -482,7 +482,7 @@
init({ range: [[-10, 10], [-7, 10]], - scale: [30, 30] + scale: [25, 25] });
4 exercises/completing_the_square_1.html
 @@ -6,7 +6,7 @@ @@ -28,7 +28,7 @@
X1
X2
-

+

2 exercises/completing_the_square_2.html
 @@ -6,7 +6,7 @@
5 exercises/compound_inequalities.html
 @@ -137,7 +137,8 @@ var end = max( SOLUTION[0], SOLUTION[1] ) + randRange( 2, 5 ); init({ - range: [ [ start - 1, end + 1 ], [ -1, 1 ] ] + range: [ [ start - 1, end + 1 ], [ -1, 1 ] ], + scale: 28 }); numberLine( start, end, null, start ); @@ -148,7 +149,7 @@ style({ stroke: COLOR[i], fill: COLOR[i], strokeWidth: 3.5, arrows: "->" }); path([ [ SOLUTION[i] + 0.15 * ( LESS_THAN[i] ? -1 : 1 ), y_placement[i] ], [ LESS_THAN[i] ? start : end, y_placement[i] ] ]); style({ stroke: COLOR[i], fill: INCLUSIVE[i] ? COLOR[i] : null }); - circle( [ SOLUTION[i], y_placement[i] ], 0.15 ); + circle( [ SOLUTION[i], y_placement[i] ], 0.2 ); }
6 exercises/conditional_statements_2.html
 @@ -222,8 +222,8 @@ [["go to", "a birthday party", "eat", "cake"], - ["eat", "a sandwich", "turn into", "superman"], - ["turn into", "superman", "eat", "a sandwich"], + ["eat", "a sandwich", "turn into", "superman"], + ["turn into", "superman", "eat", "a sandwich"], ["watch", "a movie", "eat", "popcorn"], ["miss", "the bus", "ride with", "my dad"], ["go in", "the rain", "take", "my umbrella"], @@ -235,7 +235,7 @@ ["play", "basketball", "make", "a three point shot"], ["go to", "the Olympics", "win", "a gold medal"], ["go to", "the softball game", "hit", "a home run"], - ["finish", "my homework", "play", "on the computer"], + ["finish", "my homework", "play", "on the computer"], ["win", "a gold medal", "go to", "Disneyland"]] randFromArray(QUESTIONS)
2 exercises/congruency_postulates.html
 @@ -53,7 +53,7 @@ Your triangle can be anywhere. There is no need to line up the two triangles.
init({ - range: [ [ -7, 7 ], [ -7, 7 ] ] + range: [ [ -6.2, 6.2 ], [ -5.9, 6.5 ] ] }); addMouseLayer(); initCongruence({ triangle: TRIANGLE, type: TYPE, reflected: REFLECTED });
6 exercises/congruent_triangles_2.html
 @@ -44,7 +44,8 @@
init({ - range: [ [-1, 15 ], [ -7, 2.5 ] ] + range: [ [-1, 15 ], [ -7, 2.5 ] ], + scale: 31 }) TR_A.draw(); TR_A.drawLabels(); @@ -152,7 +153,8 @@
init({ - range: [ [-1, 15 ], [ -7, 2.5 ] ] + range: [ [-1, 15 ], [ -7, 2.5 ] ], + scale: 32 }) TR_A.draw(); TR_A.drawLabels();
8 exercises/converting_between_point_slope_and_standard_form.html
 @@ -6,7 +6,7 @@ @@ -32,7 +32,7 @@
-

+

y - {}{} = {}(x - {})

[ $( '#solution_x' ).val(),$( '#solution_y' ).val(), $( '#solution_m' ).val() ] @@ -128,8 +128,8 @@ - A\space x \space + \space - B\space y \quad = \quad + A\space x + {} + B\space y = {} C three integers to complete the standard form equation 6 exercises/counting_1_alternative.html  @@ -107,8 +107,8 @@ init({ - range: [ [ -1.5, 18.5 ], [ -4, -0.5 ] ], - scale: [ 30, 50 ] + range: [ [ -0.5, 17.5 ], [ -4, -0.5 ] ], + scale: [ 27, 50 ] }); graph.loaf = raphael.set(); @@ -200,7 +200,7 @@ init({ range: [ [ -1, LENGTH + 1 ], [ -2, 3.5 ] ], - scale: [ 600 / ( LENGTH + 2 ), 20 ] + scale: [ 475 / ( LENGTH + 2 ), 20 ] }); style({ stroke: null, fill: BLUE, opacity: 0.3 }, function() { 2 exercises/creating_bar_charts_1.html  @@ -41,7 +41,7 @@ init({ range: [ [ -2, 17 ], [ -3, 12 ] ], - scale: [ 30, 30 ] + scale: [ 26, 30 ] }); addMouseLayer(); 1 exercises/creating_box_and_whisker_plots.html  @@ -12,6 +12,7 @@ box-shadow: 0 0 0; -moz-box-shadow: 0 0 0; -webkit-box-shadow: 0 0 0; + padding-right: 0; } .sortable > ul > li { width: 28px; 4 exercises/decimals_on_the_number_line_2.html  @@ -25,8 +25,8 @@ Move the \color{orange}{\text{orange dot}} to \color{orange}{SOLUTION} on the number line. The distance between adjacent tick marks is 0.5. init({ - range: [ [LOWER_BOUND - 1, UPPER_BOUND + 1], [-1, 1] ], - scale: [120, 40] + range: [ [LOWER_BOUND - 0.3, UPPER_BOUND + 0.3], [-1, 1] ], + scale: [108, 40] }); style({arrows: ">"}); 20 exercises/dividing_complex_numbers.html  @@ -73,25 +73,31 @@ The squares in the denominator are evaluated and subtracted. - + \qquad \dfrac{(A_REP_COLORED) \cdot (CONJUGATE_COLORED)} {(B_REAL_COLORED)^2 - (B_IMAG_COLOREDi)^2} = - \dfrac{(A_REP_COLORED) \cdot (CONJUGATE_COLORED)} + + + \qquad \dfrac{(A_REP_COLORED) \cdot (CONJUGATE_COLORED)} {B_REAL * B_REAL + B_IMAG * B_IMAG} = - \dfrac{(A_REP_COLORED) \cdot (CONJUGATE_COLORED)} + + + \qquad \dfrac{(A_REP_COLORED) \cdot (CONJUGATE_COLORED)} {B_REAL * B_REAL + B_IMAG * B_IMAG} - + Afterwards, the numerator is multiplied using the distributive property. - + \qquad \dfrac{(A_REP_COLORED) \cdot (CONJUGATE_COLORED)} {DENOMINATOR} = - \dfrac{(A_REAL_COLORED \cdot \color{BLUE}{negParens( B_REAL )}) + (A_IMAG_COLORED \cdot \color{BLUE}{negParens( B_REAL )} i) + (A_REAL_COLORED \cdot \color{BLUE}{ B_CONJUGATE_IMAG_COLORED }i) + (A_IMAG_COLORED \cdot \color{BLUE}{ B_CONJUGATE_IMAG_COLORED } i^2)} + + + \qquad \dfrac{(A_REAL_COLORED \cdot \color{BLUE}{negParens( B_REAL )}) + (A_IMAG_COLORED \cdot \color{BLUE}{negParens( B_REAL )} i) + (A_REAL_COLORED \cdot \color{BLUE}{ B_CONJUGATE_IMAG_COLORED }i) + (A_IMAG_COLORED \cdot \color{BLUE}{ B_CONJUGATE_IMAG_COLORED } i^2)} {DENOMINATOR} - + All multiplications are evaluated. 5 exercises/domain_and_range_0.5.html  @@ -4,6 +4,11 @@ Domain and range of a function 0.5 + 2 exercises/empirical_rule.html  @@ -60,7 +60,7 @@ init({ range: [ [ MEAN - STDDEV * 3.5, MEAN + STDDEV * 3.5 ], [ -1.5, 4.3 ] ], - scale: [ 600 / ( STDDEV * 7 ), 40 ] + scale: [ 475 / ( STDDEV * 7 ), 40 ] }); style({ stroke: "#bbb" }, function() { 2 exercises/equation_of_a_circle_1.html  @@ -6,7 +6,7 @@ 2 exercises/equation_of_a_circle_2.html  @@ -6,7 +6,7 @@ 11 exercises/equation_of_a_hyperbola.html  @@ -6,8 +6,8 @@ @@ -39,10 +39,9 @@ - - y = \pm (B/A - )(x + -H - ) + K + + y = \pm B/A + (x + -H) + K enter integers, simplified fractions, or exact decimals for each term 6 exercises/equation_of_an_ellipse.html  @@ -6,7 +6,7 @@ @@ -37,8 +37,8 @@ (h, k) = (H, K) - Major radius = MAJ - Minor radius = MIN + Major radius = MAJ + Minor radius = MIN 2 exercises/exploring_mean_and_median.html  @@ -51,7 +51,7 @@ init({ range: [ - [LOWER_BOUND - 1, UPPER_BOUND + 1], + [LOWER_BOUND - 0.3, UPPER_BOUND + 0.2], [-3, 3]], scale: 35 }); 3 exercises/exploring_standard_deviation_1.html  @@ -25,7 +25,8 @@ graph.numPoints = POINTS; init({ - range: [ [LOWER_BOUND - 0.1, UPPER_BOUND + 0.1], [-2, 5] ] + range: [ [LOWER_BOUND - 0.3, UPPER_BOUND + 0.3], [-2, 5] ], + scale: 35 }); style({ stroke: "#bbb" }); 12 exercises/factor_expressions_by_grouping.html  @@ -6,7 +6,7 @@ @@ -47,9 +47,13 @@ - - (\space r + \space)(\space s + \space) - + + + (\space r + \space) + + (\space s + \space) + + enter an integer for each coefficient pay attention to the sign of each number you enter to be sure the entire equation is correct 6 exercises/fractions_cut_and_copy_1.html  @@ -33,21 +33,21 @@ initSliceClone(["current_block"]); - init({range: [[0, 1], [0, 1]], scale: [600, 25 ]}); + init({range: [[0, 1], [0, 1]], scale: [500, 25 ]}); rectchart([1, 0], ["#e00", "#999"]); Current Block: - init({ range: [[0, 1], [0, 1] ], scale: [600, 25]}); + init({ range: [[0, 1], [0, 1] ], scale: [500, 25]}); rectchart([1, 0], ["#e00", "#999"]); Goal Block: - init({range: [[0, 1], [0, 1]], scale: [600 * ANSWER, 25]}); + init({range: [[0, 1], [0, 1]], scale: [500 * ANSWER, 25]}); rectchart([1, 0], [BLUE, "#999"]); 16 exercises/fractions_cut_and_copy_2.html  @@ -36,56 +36,56 @@ initSliceClone(["current_block_1", "current_block_2"]); - init({range: [[0, 1], [0, 1]], scale: [ 600, 25]}); + init({range: [[0, 1], [0, 1]], scale: [ 500, 25]}); rectchart([1, 0], ["#e00", "#999"]); Current Block 1: - init({range: [[0, 1], [0, 1]], scale: [600, 25]}); + init({range: [[0, 1], [0, 1]], scale: [500, 25]}); rectchart([1, 0], ["#e00", "#999"]); Goal Block 1: - init({range: [[0, 1], [0, 1]], scale: [600 * ANSWER_1, 25]}); + init({range: [[0, 1], [0, 1]], scale: [500 * ANSWER_1, 25]}); rectchart([1, 0], [BLUE, "#999"]); Current Block 2: - init({range: [[0, 1], [0, 1]], scale: [600, 25]}); + init({range: [[0, 1], [0, 1]], scale: [500, 25]}); rectchart([1, 0], ["#e00", "#999"]); Goal Block 2: - init({range: [[0, 1], [0, 1]], scale: [600 * ANSWER_2, 25]}); + init({range: [[0, 1], [0, 1]], scale: [500 * ANSWER_2, 25]}); rectchart([1, 0], [ORANGE, "#999"]); - Cut Starting Block into + Cut Starting Block into 1 piece - Copy Current Block 1 + Copy Current Block 1 1 time - Copy Current Block 2 + Copy Current Block 2 1 time 2 exercises/fractions_on_the_number_line_1.html  @@ -31,7 +31,7 @@ init({ - range: [ [LOWER_BOUND - 0.3, UPPER_BOUND + 0.4], [-1, 1] ], + range: [ [LOWER_BOUND - 0.1, UPPER_BOUND + 0.1], [-1, 1] ], scale: [80*SCALE, 40] }); 2 exercises/fractions_on_the_number_line_2.html  @@ -32,7 +32,7 @@ init({ - range: [ [LOWER_BOUND - 1, UPPER_BOUND + 1], [-1, 1] ], + range: [ [LOWER_BOUND - 0.5, UPPER_BOUND + 0.5], [-1, 1] ], scale: [80 * SCALE, 40] }); 36 exercises/fractions_on_the_number_line_3.html  @@ -31,41 +31,41 @@ init({ - range: [ [LOWER_BOUND - 1, UPPER_BOUND + 1], [-1, 1] ], - scale: [80, 40] + range: [ [(LOWER_BOUND - 0.5) * abs(DENOMINATOR), (UPPER_BOUND + 0.5) * abs(DENOMINATOR)], [-1, 1] ], + scale: [70 / abs(DENOMINATOR), 40] }); style({arrows: ">"}); - line( [ 0, 0 ], [ UPPER_BOUND + 0.25, 0 ] ); + line( [ 0, 0 ], [ (UPPER_BOUND + 0.25) * abs(DENOMINATOR), 0 ] ); style({arrows: "->"}); - line( [ 0, 0 ], [ LOWER_BOUND - 0.25, 0 ] ); + line( [ 0, 0 ], [ (LOWER_BOUND - 0.25) * abs(DENOMINATOR), 0 ] ); style({arrows: ""}); for ( var x = LOWER_BOUND; x <= UPPER_BOUND; x++ ) { - line( [ x, -0.2 ], [ x, 0.2 ] ); + line( [ x * abs(DENOMINATOR), -0.2 ], [ x * abs(DENOMINATOR), 0.2 ] ); } style({ stroke: GREEN, strokeWidth: 3.5 }); - line( [ LOWER_BOUND, -0.2], [LOWER_BOUND, 0.2]); - label( [ LOWER_BOUND, -0.53 ], LOWER_BOUND, "center", { color: GREEN }); + line( [ LOWER_BOUND * abs(DENOMINATOR), -0.2], [LOWER_BOUND * abs(DENOMINATOR), 0.2]); + label( [ LOWER_BOUND * abs(DENOMINATOR), -0.53 ], LOWER_BOUND, "center", { color: GREEN }); - line( [ UPPER_BOUND, -0.2], [UPPER_BOUND, 0.2]); - label( [ UPPER_BOUND, -0.53 ], UPPER_BOUND, "center", { color: GREEN }); + line( [ UPPER_BOUND * abs(DENOMINATOR), -0.2], [UPPER_BOUND * abs(DENOMINATOR), 0.2]); + label( [ UPPER_BOUND * abs(DENOMINATOR), -0.53 ], UPPER_BOUND, "center", { color: GREEN }); line( [ 0, -0.2], [0, 0.2]); label( [ 0, -0.53 ], "0", "center", { color: GREEN }); addMouseLayer(); - graph.movablePoint = addMovablePoint({ constraints: { constrainY: true }, snapX: 1 / DENOMINATOR }); + graph.movablePoint = addMovablePoint({ constraints: { constrainY: true }, snapX: 1 }); graph.movablePoint.onMove = function( x, y ) { - return [ min( max( LOWER_BOUND, x ), UPPER_BOUND ), y ]; + return [ min( max( LOWER_BOUND * abs(DENOMINATOR), x ), UPPER_BOUND * abs(DENOMINATOR) ), y ]; }; Move the orange dot to select your answer. - graph.movablePoint.coord[0] + graph.movablePoint.coord[0] / abs(DENOMINATOR) if ( guess === 0 ) { return ""; @@ -92,8 +92,8 @@ and \color{green}{M_WHOLE + (SOLUTION > 1 ? 1 : -1)} on the number line. style({ stroke: "#FFA500", strokeWidth: 3.5 }); - line( [M_WHOLE, -0.2], [M_WHOLE, 0.2]); - line( [M_WHOLE + (SOLUTION > 0 ? 1 : -1), -0.2], [M_WHOLE + (SOLUTION > 0 ? 1 : -1), 0.2]); + line( [M_WHOLE * abs(DENOMINATOR), -0.2], [M_WHOLE * abs(DENOMINATOR), 0.2]); + line( [(M_WHOLE + (SOLUTION > 0 ? 1 : -1)) * abs(DENOMINATOR), -0.2], [(M_WHOLE + (SOLUTION > 0 ? 1 : -1)) * abs(DENOMINATOR), 0.2]); @@ -103,19 +103,19 @@ on the number line. style({ stroke: GREEN, fill: "#6495ED", strokeWidth: 3.5, arrows: "->" }); - line( [ M_WHOLE, 0 ], [ SOLUTION, 0 ] ); + line( [ M_WHOLE * abs(DENOMINATOR), 0 ], [ SOLUTION * abs(DENOMINATOR), 0 ] ); graph.movablePoint.visibleShape.toFront(); style({ stroke: "#FFA500", strokeWidth: 3.5, arrows: "" }); - line( [M_WHOLE, -0.2], [M_WHOLE, 0.2]); - line( [M_WHOLE + (SOLUTION > 0 ? 1 : -1), -0.2], [M_WHOLE + (SOLUTION > 0 ? 1 : -1), 0.2]); + line( [M_WHOLE * abs(DENOMINATOR), -0.2], [M_WHOLE * abs(DENOMINATOR), 0.2]); + line( [(M_WHOLE + (SOLUTION > 0 ? 1 : -1)) * abs(DENOMINATOR), -0.2], [(M_WHOLE + (SOLUTION > 0 ? 1 : -1)) * abs(DENOMINATOR), 0.2]); label( [ SOLUTION, -0.83 ], NUMBER, "center", { color: "#FFA500" }); - graph.movablePoint.moveTo( SOLUTION, 0 ); + graph.movablePoint.moveTo( SOLUTION * abs(DENOMINATOR), 0 ); The orange number shows where \color{orange}{NUMBER} is on the number line. 15 exercises/graphs_of_sine_and_cosine.html  @@ -14,7 +14,7 @@ @@ -28,10 +28,10 @@ 2 * PI * HSCALE 3.5 - 4.5 * PI * HSCALE + 3.5 * PI * HSCALE 150 / VRANGE - 300 / HRANGE + 250 / HRANGE VSCALE + "*" + FN + "(x/" + HSCALE + ")" @@ -80,14 +80,13 @@ What is f(x)? - f(x)= + + f(x)= VSCALE FN - (\ - 1 / HSCALE - \ x) - + (1 / HSCALEx) + 5 exercises/identifying_points_1.html  @@ -85,8 +85,9 @@ var point = POINTS[FORGOTTEN]; - label( point, PAIR( point ) + "\\text{ was not graphed.}", "above right" ); - circle( point, 0.15, { stroke: "red", fill: "red"} ); + label( point, PAIR( point ), "above right"); + label( point, "\\text{was not graphed.}", "right" ); + circle( point, 0.3, { stroke: "red" } ); 7 exercises/midpoint_formula.html  @@ -43,6 +43,11 @@ return pos; } + @@ -85,7 +90,7 @@ - (XM, YM) + \Large{(}XM, YM\Large{)} integers, like 6 simplified proper fractions, like 3/5 simplified improper fractions, like 7/4 13 exercises/multiplication_0.5.html  @@ -29,18 +29,17 @@ - label( [ 0, B - 1 ], "\\text{Draw " + plural( A, "circle" ) + ".}", "right" ); + label( [ 0, B - 1 ], "Draw " + plural( A, "circle" ) + ".", "right", false ); drawRow( A, B - 3, "#6495ED", 1 ); - label( [ 0, B - 2 ], "\\text{" - + "If there" + ( B === 1 ? " is " : " are " ) + plural( B, "row" ) - + " with " + plural( A, "circle" ) + ( B === 1 ? " " : " each " ) - + ", there is a total of how many circles?" - + "}", - "right" ); + label( [ 0, B - 2 ], + "If there" + ( B === 1 ? " is " : " are " ) + plural( B, "row" ) + + " with " + plural( A, "circle" ) + ( B === 1 ? "" : " each" ) + + ",<br>there are a total of how many circles?", + "right", false ); for ( var i = 1; i < B; i++ ) { drawRow( A, B - 3 - i, "#28AE7B", A * i + 1 ); } 11 exercises/multiplication_1.html  @@ -29,16 +29,17 @@ - label( [ 0, B - 1 ], "\\text{Draw " + plural( A, "circle" ) + ".}", "right" ); + label( [ 0, B - 1 ], "Draw " + plural( A, "circle" ) + ".", "right", false ); drawRow( A, B - 3, "#6495ED", 1 ); - label( [ 0, B - 2 ], "\\text{" - + "If there" + ( B === 1 ? " is " : " are " ) + plural( B, "row" ) - + " with " + plural( A, "circle" ) + ( B === 1 ? " " : " each " ) + ", there is a total of how many circles?" - + "}", "right" ); + label( [ 0, B - 2 ], + "If there" + ( B === 1 ? " is " : " are " ) + plural( B, "row" ) + + " with " + plural( A, "circle" ) + ( B === 1 ? "" : " each" ) + + ",<br>there are a total of how many circles?", + "right", false ); for ( var i = 1; i < B; i++ ) { drawRow( A, B - 3 - i, "#28AE7B", A * i + 1 ); } 5 exercises/multiplying_and_dividing_scientific_notation.html  @@ -4,6 +4,11 @@ Multiplying and dividing scientific notation + 20 exercises/multiplying_fractions_word_problems.html  @@ -58,10 +58,10 @@ INVITEES is SOLUTION: - init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 500, 30 ] }); + init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] }); rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 ); rectchart( [ INVITEES, 0 ], [ ORANGE, "#999" ], 1 ); - rectchart( [ SOLUTION, INVITEES - SOLUTION ], [ GREEN, "#fff" ], 0 ); + rectchart( [ SOLUTION, INVITEES - SOLUTION ], [ GREEN, BACKGROUND ], 0 ); style({ color: BLUE }, function() { label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" ); }); @@ -125,10 +125,10 @@ AMOUNT is SOLUTION: - init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 500, 30 ] }); + init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] }); rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 ); rectchart( [ AMOUNT, 0 ], [ ORANGE, "#999" ], 1 ); - rectchart( [ SOLUTION, AMOUNT - SOLUTION ], [ GREEN, "#fff" ], 0 ); + rectchart( [ SOLUTION, AMOUNT - SOLUTION ], [ GREEN, BACKGROUND ], 0 ); style({ color: BLUE }, function() { label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" ); }); @@ -192,10 +192,10 @@ AMOUNT is SOLUTION: - init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 500, 30 ] }); + init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] }); rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 ); rectchart( [ AMOUNT, 0 ], [ ORANGE, "#999" ], 1 ); - rectchart( [ SOLUTION, AMOUNT - SOLUTION ], [ GREEN, "#fff" ], 0 ); + rectchart( [ SOLUTION, AMOUNT - SOLUTION ], [ GREEN, BACKGROUND ], 0 ); style({ color: BLUE }, function() { label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" ); }); @@ -262,10 +262,10 @@ GALLONS is SOLUTION: - init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 500, 30 ] }); + init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] }); rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 ); rectchart( [ GALLONS, 0 ], [ ORANGE, "#999" ], 1 ); - rectchart( [ SOLUTION, GALLONS - SOLUTION ], [ GREEN, "#fff" ], 0 ); + rectchart( [ SOLUTION, GALLONS - SOLUTION ], [ GREEN, BACKGROUND ], 0 ); style({ color: BLUE }, function() { label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" ); }); @@ -330,10 +330,10 @@ ATTENDEES is SOLUTION: - init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 500, 30 ] }); + init({ range: [ [ -0.05, 1 ], [ 0, 3 ] ],scale: [ 450, 30 ] }); rectchart( [ N, D - N ], [ BLUE, "#ccc" ], 2 ); rectchart( [ ATTENDEES, 0 ], [ ORANGE, "#999" ], 1 ); - rectchart( [ SOLUTION, ATTENDEES - SOLUTION ], [ GREEN, "#fff" ], 0 ); + rectchart( [ SOLUTION, ATTENDEES - SOLUTION ], [ GREEN, BACKGROUND ], 0 ); style({ color: BLUE }, function() { label([ 0, 2.5 ], "\\frac{" + N + "}{" + D + "}", "left" ); }); 4 exercises/ordering_negative_numbers.html  @@ -95,7 +95,7 @@ init({ range: [ [-1, 101], [-1, 1] ], - scale: [ 7, 40 ] + scale: [ 4.5, 40 ] }); style({ @@ -109,7 +109,7 @@ var position = "above";$.each( NUMS_SORT, function( i, el ) { - ellipse( [ 100 + el[0], 0 ], [ 0.80, 0.14 ], { "stroke-width": 0, fill: el[1] } ); + ellipse( [ 100 + el[0], 0 ], [ 0.89, 0.1 ], { "stroke-width": 0, fill: el[1] } ); label( [ 100 + el[0], 0 ], "\\color{" + el[1] + "}{" + el[0] + "}", position, { labelDistance: 5 } ); position = ( position === "above" ? "below" : "above" ); } );
8 exercises/parabola_intuition_3.html
 @@ -7,7 +7,6 @@ @@ -104,10 +103,9 @@

Directrix: y = -1

Equation of the parabola:
- y - Y1 - = A - (x - X1 - )^2 + + y - Y1 = A(x - X1)^2 +

set the focus and directrix by moving them around the graph

2 exercises/percentage_word_problems_2.html
 @@ -24,7 +24,7 @@

x = \dfrac{$YEAR_THIS}{(100 + YEAR_PERCENT_MORE) / 100} x =$YEAR_LAST (rounding to the nearest penny in this step)

So, he(1) had $YEAR_LAST last year, but we want to know how much he(1) has made over the past year! - \text{money made over the past year} = \text{amount of money today} - \text{amount of money last year} + \text{money made over the past year} = \qquad \text{amount of money today} - \text{amount of money last year} \qquad =$YEAR_THIS-$YEAR_LAST \qquad \approx$round((YEAR_THIS - YEAR_LAST) * 100) / 100

So, the answer is \$round((YEAR_THIS - YEAR_LAST) * 100) / 100.

12 exercises/point_slope_form.html
 @@ -35,8 +35,8 @@ X1
-

- (y - \space) = \space(x - \space) +

+ (y - {}) = {}(x - {})

integers, like 6

@@ -82,8 +82,8 @@ X1
-

- (y - \space) = \space(x - \space) +

+ (y - {}) = {}(x - {})

integers, like 6

@@ -122,8 +122,8 @@ X1
-

- (y - \space) = \space(x - \space) +

+ (y - {}) = {}(x - {})

integers, like 6

4 exercises/quotient_rule.html
 @@ -8,8 +8,8 @@
- generateSpecialFunction("x") - generateSpecialFunction("x") + generateSpecialFunction("x") + generateSpecialFunction("x") FUNCN.fText FUNCN.ddxFText
5 exercises/range_of_a_function.html
 @@ -4,6 +4,11 @@ Range of a function +
 @@ -34,7 +34,7 @@
init({ range: [ [ -2, 17 ], [ -3, 11 ] ], - scale: [ 30, 30 ] + scale: [ 27, 30 ] }); for ( var y = 1; y <= 10; ++y ) {
 @@ -38,7 +38,7 @@
init({ range: [ [ -2, NUM_STUDENTS * 3 + 2 ], [ -3, 12 ] ], - scale: [ 26, 26 ] + scale: [ 24, 24 ] }); for ( var y = 1; y <= 10; ++y ) {
 @@ -6,16 +6,21 @@ +
 @@ -6,16 +6,21 @@ +
 @@ -81,33 +81,35 @@

- \left| \quad \begin{matrix} + \small{ + \left| \space \begin{matrix} \color{GREEN}{STEM} \vphantom{\Large{0}} \\ - \end{matrix} \quad \right| - \quad + \end{matrix} \space \right| + \space \begin{matrix} \color{BLUE}{LEAF}& \vphantom{\Large{0}} \\ \end{matrix} - \quad + \space \begin{matrix} \rightarrow \vphantom{\Large{0}} \\ \end{matrix} - \quad + \space \begin{matrix} \color{GREEN}{STEM}\color{BLUE}{LEAF}& \vphantom{\Large{0}} \\ \end{matrix} + }

8 exercises/rounding_numbers.html
 @@ -32,11 +32,11 @@
init({ range: [ [ -0.06 * pow( 10, -PLACE ) , 1.3 * pow( 10, -PLACE ) ], [-1, 1] ], - scale: [ 600 * pow( 10, PLACE ), 40 ] + scale: [ 450 * pow( 10, PLACE ), 40 ] }); numberLine( floorTo( PLACE , NUM ), ceilTo( PLACE , NUM ) + pow( 10, -( PLACE+2 )) , round( pow( 10, -(PLACE + 1 ))) ); style({ stroke: "#FFA500", fill: "#FFA500", strokeWidth: 3.5 }); - ellipse( [ 10 * pow( 10, -( PLACE+1 )) * (NUM - floorTo( PLACE , NUM ))/pow( 10,- (PLACE) ), 0 ], [pow( 10, -PLACE ) / 100, 0.15]); + ellipse( [ 10 * pow( 10, -( PLACE+1 )) * (NUM - floorTo( PLACE , NUM ))/pow( 10,- (PLACE) ), 0 ], [pow( 10, -PLACE ) / 115, 0.1]); label( [ 10 * pow(10, -( PLACE+1 )) * ( NUM - floorTo( PLACE , NUM ))/pow( 10,- (PLACE) )], NUM, "below"); style({ stroke: "#6495ED", "fill": "none", strokeWidth: 3.5 }); if( DIGITS[ 5 + PLACE ] >= 5 ) { @@ -71,11 +71,11 @@
init({ range: [ [ -0.06 * pow( 10, -PLACE ) , 10.3 * pow( 10, -PLACE ) ], [-1, 1] ], - scale: [ 600 * pow( 10, PLACE ), 40 ] + scale: [ 450 * pow( 10, PLACE ), 40 ] }); numberLine( floorTo( PLACE , NUM ), ceilTo( PLACE , NUM ) + pow( 10,- (PLACE+2 )) , pow( 10,- (PLACE+1) ) ); style({ stroke: "#FFA500", fill: "#FFA500", strokeWidth: 3.5 }); - ellipse( [ 10 * pow(10,- (PLACE+1)) * (NUM - floorTo( PLACE , NUM ))/pow(10,- (PLACE) ), 0 ], [pow(10, -PLACE) / 100, 0.15]); + ellipse( [ 10 * pow(10, -(PLACE+1)) * (NUM - floorTo( PLACE , NUM ))/pow(10,- (PLACE) ), 0 ], [pow(10, -PLACE) / 115, 0.1]); label( [ 10 * pow(10, -( PLACE+1 )) * ( NUM - floorTo( PLACE , NUM ))/pow(10, -(PLACE) )], NUM, "below"); style({ stroke: "#6495ED", "fill": "none", strokeWidth: 3.5 }); if ( DIGITS[ 2 + PLACE ] >= 5 ) {
4 exercises/rounding_whole_numbers.html
 @@ -49,11 +49,11 @@
init({ range: [ [ -0.06 * pow( 10, -PLACE ) , 1.3 * pow( 10, -PLACE ) ], [-1, 1] ], - scale: [ 600 * pow( 10, PLACE ), 40 ] + scale: [ 450 * pow( 10, PLACE ), 40 ] }); numberLine( floorTo( PLACE , NUM ), ceilTo( PLACE , NUM ) + pow( 10, -( PLACE+2 )) , round( pow( 10, -(PLACE + 1 ))) ); style({ stroke: "#FFA500", fill: "#FFA500", strokeWidth: 3.5 }); - ellipse( [ 10 * pow( 10, -( PLACE+1 )) * (NUM - floorTo( PLACE , NUM ))/pow( 10,- (PLACE) ), 0 ], [pow( 10, -PLACE ) / 100, 0.15]); + ellipse( [ 10 * pow( 10, -( PLACE+1 )) * (NUM - floorTo( PLACE , NUM ))/pow( 10,- (PLACE) ), 0 ], [pow( 10, -PLACE ) / 115, 0.1]); label( [ 10 * pow(10, -( PLACE+1 )) * ( NUM - floorTo( PLACE , NUM ))/pow( 10,- (PLACE) )], NUM, "below"); style({ stroke: "#6495ED", "fill": "none", strokeWidth: 3.5 }); if( DIGITS[ 5 + PLACE ] >= 5 ) {
4 exercises/scientific_notation_intuition.html
 @@ -39,7 +39,7 @@
init({ range: [ [ -8, 14 ], [ -1, 3 ] ], - scale: [30, 45] + scale: [23, 45] }); graph.decimalPlace = E; @@ -79,7 +79,7 @@ }); style({ stroke: null, fill: "black" }, function() { - ellipse( [ E, 1.7 ], [ 4 / 30, 4 / 45 ] ); + ellipse( [ E, 1.7 ], [ 4 / 23, 4 / 45 ] ); }); var setDecimal = function( place, exp ) {
 @@ -165,11 +165,11 @@ OUTER.drawShape(KhanUtil.currentGraph, { fill: BLUE, opacity: 0.5 }); -

\text{area of whole figure} = OUTER.hint() = PRETTY_OUTER_AREA

-

\text{area of inner region} = INNER.hint() = PRETTY_INNER_AREA

+

\text{area of whole figure} =

+

\text{area of inner region} =

Then subtract the inner region's area from the whole figure's area to find the area of the shaded region (the difference between the two areas).

- +
2 exercises/signs_of_a_parabola.html
 @@ -28,7 +28,7 @@
init({ range: [ [ -10, 10 ], [ -10, 10 ] ], - scale: [ 30, 30 ] + scale: [ 25, 25 ] }); grid( [ -10, 10 ], [ -10, 10 ], { stroke: "#e2e2e2" });
3 exercises/similar_triangles_1.html
 @@ -76,7 +76,8 @@
init({ - range: [ [-1, 13 ], [ -14, 2.5 ] ] + range: [ [-1, 13 ], [ -14, 2.5 ] ], + scale: 35 }) TR.draw();
3 exercises/similar_triangles_2.html
 @@ -114,7 +114,8 @@
init({ - range: [ [-1, 13 ], [ -14, 2.5 ] ] + range: [ [-1, 13 ], [ -14, 2.5 ] ], + scale: 35 }) TR.draw();
2 exercises/slope_intercept_form.html
 @@ -9,7 +9,7 @@ width: 40px; } #answer_area .short input[type=text] { - width: 60px; + width: 40px; }
4 exercises/slope_of_a_line.html
 @@ -138,7 +138,7 @@
graphInit({ range: 6, - scale: 20, + scale: 16.9, tickStep: 1, labelStep: 1, labelFormat: function( s ) { return "\\small{" + s + "}"; }, @@ -176,7 +176,7 @@ [ { value: M_INIT, display: M_INIT }, { value: 0, display: 0 }, - { value: 99999, display: "undefined" }, + { value: 999, display: "undefined" }, { value: 1 / M_INIT, display: "\\dfrac{1}{" + M_INIT + "}" } ] randRange( 1, 2 )
 @@ -6,7 +6,7 @@ @@ -35,9 +35,9 @@
A
B
-
-

-
+

+ x = {}\space \text{and}\space x = {} +

 @@ -6,7 +6,7 @@ @@ -35,9 +35,9 @@
A
B
-
-

-
+

+ x = {}\space \text{and} \space x = {} +

 @@ -6,7 +6,7 @@ @@ -27,9 +27,9 @@
H + CONSTANT
H - CONSTANT
-
-

-
+

+ x = {}\space \text{or} \space x = {} +

integers, like 6

simplified proper fractions, like 3/5

simplified improper fractions, like 7/4

3 exercises/solving_similar_triangles_1.html
 @@ -129,7 +129,8 @@ var maxY = Math.max(aBounding[1][1], bBounding[1][1]); init({ - range: [ [minX, maxX ], [ minY, maxY ] ] + range: [ [minX, maxX ], [ minY, maxY ] ], + scale: 500 / (maxX - minX) }) style({
9 exercises/square_roots_2.html
 @@ -3,6 +3,11 @@ Square roots 2 +
Estimating square roots as between two roots @@ -19,7 +24,7 @@

The value of \sqrt{Q} lies between which two consecutive integers?

- +
Integers that appear in order when counting, for example 2 and 3.
@@ -29,7 +34,7 @@

N < \sqrt{Q} < N + 1

two integers, like 6 - +

Consider the perfect squares near Q.

8 exercises/standard_deviation.html
 @@ -44,11 +44,11 @@

- Average age: + Average age:
\quad mean( DATA ) years old

- Standard deviation: + Standard deviation:

decimals, like 7.5
@@ -184,11 +184,11 @@

- Average age: + Average age:
\quad mean( DATA ) years old

- Standard deviation: + Standard deviation:

decimals, like 0.75
2 exercises/telling_time.html
 @@ -34,7 +34,7 @@
-

The time is HOUR : NICE_MINUTE AM_PM

+

The time is:
HOUR : NICE_MINUTE AM_PM

a 12-hour time in hours and minutes

2 exercises/telling_time_0.5.html
 @@ -34,7 +34,7 @@
-

The time is HOUR : NICE_MINUTE AM_PM

+

The time is:
HOUR : NICE_MINUTE AM_PM

a 12-hour time in hours and minutes

5 exercises/triangle_inequality_theorem.html
 @@ -19,6 +19,11 @@ return [ [ a, b, c] , [ sa.toFixed( 1 ), sb.toFixed( 1 ), sc.toFixed( 1 ) ] ]; } +