# Khan/khan-exercises

Run the exercise cleaner.

jeresig committed Apr 23, 2013
1 parent 254a029 commit ced362cd60836e873eec16fd4fc50230dfacfc5a
Showing with 1,928 additions and 1,983 deletions.
1. +5 −5 exercises/absolute_value.html
2. +5 −5 exercises/absolute_value_of_complex_numbers.html
22. +13 −14 exercises/age_word_problems.html
23. +13 −15 exercises/age_word_problems_alternative.html
25. +4 −4 exercises/angle_bisector_theorem.html
26. +118 −114 exercises/angles_1.html
27. +2 −2 exercises/areas_of_circles_and_sectors.html
28. +4 −4 exercises/arithmetic_sequences_2.html
29. +5 −5 exercises/arithmetic_series.html
30. +1 −1 exercises/axis_of_symmetry.html
31. +75 −77 exercises/balancing_chemical_equations.html
32. +5 −5 exercises/basic_set_notation.html
33. +2 −2 exercises/binomial_expansion.html
34. +1 −1 exercises/chain_rule_1.html
35. +2 −2 exercises/circles_and_arcs.html
36. +3 −3 exercises/coin_flip_sequences.html
37. +9 −10 exercises/combinations_1.html
38. +8 −8 exercises/combining_like_terms_1.html
39. +30 −30 exercises/combining_like_terms_2.html
40. +2 −2 exercises/comparing_fractions_2.html
41. +4 −5 exercises/comparing_improper_fractions_and_mixed_numbers.html
42. +3 −3 exercises/completing_the_square_1.html
43. +7 −7 exercises/completing_the_square_2.html
44. +7 −7 exercises/complex_number_polar_form_intuition.html
45. +11 −11 exercises/complex_plane_operations.html
46. +30 −30 exercises/compound_inequalities.html
47. +1 −1 exercises/conditional_statements_and_truth_value.html
48. +13 −13 exercises/congruency_postulates.html
49. +1 −1 exercises/congruent_angles.html
50. +3 −3 exercises/congruent_segments.html
51. +6 −6 exercises/congruent_triangles_1.html
52. +18 −27 exercises/constructions_1.html
53. +2 −2 exercises/converse_inverse_and_contrapositive.html
54. +6 −6 exercises/converting_between_point_slope_and_slope_intercept.html
55. +7 −7 exercises/converting_between_point_slope_and_standard_form.html
56. +3 −3 exercises/converting_between_slope_intercept_and_standard_form.html
57. +2 −2 exercises/converting_decimals_to_fractions_1.html
58. +2 −2 exercises/converting_decimals_to_fractions_2.html
59. +1 −1 exercises/converting_fractions_to_decimals.html
60. +2 −2 exercises/converting_mixed_numbers_and_improper_fractions.html
61. +4 −4 exercises/converting_repeating_decimals_to_fractions_1.html
62. +5 −5 exercises/converting_repeating_decimals_to_fractions_2.html
63. +33 −33 exercises/converting_temperatures.html
64. +11 −12 exercises/counting_1.html
65. +17 −18 exercises/counting_1_alternative.html
66. +8 −9 exercises/counting_2.html
67. +7 −7 exercises/creating_box_and_whisker_plots.html
68. +7 −7 exercises/cube_roots.html
69. +7 −7 exercises/decimals_on_the_number_line_2.html
70. +14 −14 exercises/defined_and_undefined_matrix_operations.html
72. +5 −5 exercises/derivative_intuition.html
73. +5 −5 exercises/derivatives_1.html
74. +4 −4 exercises/direct_and_inverse_variation.html
75. +12 −12 exercises/distance_between_point_and_line.html
76. +11 −13 exercises/distance_formula.html
77. +9 −10 exercises/dividing_complex_numbers.html
78. +1 −1 exercises/dividing_decimals.html
79. +2 −2 exercises/dividing_decimals_0.5.html
80. +1 −1 exercises/dividing_decimals_1.html
81. +1 −1 exercises/dividing_decimals_2.html
82. +2 −2 exercises/dividing_fractions.html
83. +2 −2 exercises/dividing_fractions_0.5.html
84. +4 −4 exercises/dividing_fractions_alternative.html
85. +4 −4 exercises/dividing_polynomials_by_binomials_3.html
86. +1 −1 exercises/divisibility.html
87. +2 −2 exercises/divisibility_0.5.html
88. +8 −11 exercises/divisibility_tests.html
89. +2 −2 exercises/division_0.5.html
90. +1 −1 exercises/division_1.5.html
91. +2 −2 exercises/division_1.html
92. +1 −1 exercises/division_2.html
93. +1 −1 exercises/division_3.html
94. +1 −1 exercises/division_4.html
95. +5 −5 exercises/domain_and_range_0.5.html
96. +29 −29 exercises/domain_of_a_function.html
97. +4 −4 exercises/equation_of_a_hyperbola.html
98. +1 −0 exercises/equation_of_a_line.html
99. +2 −2 exercises/equivalent_fractions.html
100. +5 −5 exercises/equivalent_fractions_2.html
101. +16 −16 exercises/equivalent_fractions_3.html
102. +1 −3 exercises/evaluating_expressions_1.html
103. +2 −8 exercises/evaluating_expressions_2.html
104. +12 −12 exercises/even_and_odd_functions.html
105. +7 −7 exercises/exploring_angle_pairs_1.html
106. +7 −9 exercises/exploring_mean_and_median.html
107. +4 −4 exercises/exploring_standard_deviation_1.html
108. +1 −1 exercises/exponent_rules.html
109. +5 −5 exercises/exponents_1.html
110. +3 −3 exercises/exponents_2.html
111. +10 −10 exercises/exponents_2_alternative.html
112. +3 −3 exercises/exponents_3.html
113. +8 −9 exercises/exponents_4.html
114. +1 −1 exercises/expressions_with_unknown_variables.html
115. +1 −1 exercises/expressions_with_unknown_variables_2.html
116. +1 −1 exercises/factoring_difference_of_squares_1.html
117. +1 −1 exercises/factoring_difference_of_squares_2.html
118. +1 −1 exercises/factoring_difference_of_squares_3.html
119. +4 −4 exercises/factoring_linear_binomials.html
120. +1 −1 exercises/factoring_polynomials_1_video_hint.html
121. +4 −4 exercises/factoring_polynomials_2.html
122. +9 −9 exercises/factoring_polynomials_by_grouping_1.html
123. +5 −5 exercises/factoring_polynomials_with_two_variables.html
124. +6 −6 exercises/fractions_cut_and_copy_1.html
125. +9 −9 exercises/fractions_cut_and_copy_2.html
126. +12 −12 exercises/fractions_on_the_number_line_2.html
127. +12 −12 exercises/fractions_on_the_number_line_3.html
128. +6 −6 exercises/functions_1.html
129. +1 −1 exercises/functions_2.html
130. +2 −2 exercises/functions_3.html
131. +4 −4 exercises/geometric_sequences_2.html
132. +5 −5 exercises/geometry_proofs_2.html
133. +9 −9 exercises/geometry_proofs_intro.html
134. +1 −2 exercises/graphing_circles.html
135. +7 −11 exercises/graphing_circles_2.html
136. +1 −1 exercises/graphing_parabolas_0.5.html
137. +4 −4 exercises/graphing_parabolas_1.html
138. +4 −4 exercises/graphing_parabolas_2.html
139. +6 −6 exercises/graphing_points.html
140. +12 −12 exercises/graphing_points_2.html
141. +10 −12 exercises/graphs_of_sine_and_cosine.html
142. +2 −2 exercises/greatest_common_divisor.html
143. +11 −11 exercises/greatest_common_divisor_alternative.html
144. +6 −6 exercises/identifying_points_1.html
145. +5 −5 exercises/identifying_points_2.html
146. +4 −3 exercises/imaginary_unit_powers.html
147. +10 −10 exercises/inequalities_on_a_number_line.html
148. +1 −1 exercises/inscribed_angles_2.html
149. +3 −3 exercises/integer_sums.html
150. +12 −14 exercises/interesting_perimeter_problems.html
151. +7 −7 exercises/inverse_trig_functions.html
152. +8 −8 exercises/inverses_of_functions.html
153. +35 −33 exercises/khan-exercise.html
154. +17 −17 exercises/khan-site.html
155. +14 −13 exercises/law_of_cosines.html
156. +11 −10 exercises/law_of_sines.html
157. +7 −4 exercises/lhopitals_rule.html
158. +22 −22 exercises/limits_1.html
159. +10 −10 exercises/line_graph_intuition.html
160. +16 −16 exercises/line_relationships.html
161. +1 −1 exercises/logarithms_1.html
162. +1 −1 exercises/logarithms_2.html
163. +8 −8 exercises/logical_arguments_deductive_reasoning.html
164. +9 −12 exercises/markup_and_commission_word_problems.html
166. +1 −1 exercises/matrix_determinant_2x2_video_hint.html
167. +1 −1 exercises/matrix_determinant_3x3_video_hint.html
168. +5 −5 exercises/matrix_dimensions.html
169. +3 −3 exercises/matrix_inverse_2x2.html
170. +3 −3 exercises/matrix_inverse_3x3.html
171. +3 −3 exercises/matrix_transpose.html
172. +4 −4 exercises/mean_median_and_mode.html
173. +5 −5 exercises/measuring_angles.html
174. +8 −8 exercises/midpoint_formula.html
175. +5 −5 exercises/midpoint_of_a_segment.html
176. +2 −2 exercises/multiplication_0.5.html
177. +1 −1 exercises/multiplication_1.5.html
178. +2 −2 exercises/multiplication_1.html
179. +1 −1 exercises/multiplication_2.html
180. +1 −1 exercises/multiplication_3.html
181. +1 −1 exercises/multiplication_4.html
182. +3 −3 exercises/multiplying_a_matrix_by_a_matrix.html
183. +3 −3 exercises/multiplying_a_matrix_by_a_vector.html
184. +17 −17 exercises/multiplying_and_dividing_complex_number_polar_forms.html
185. +7 −7 exercises/multiplying_and_dividing_negative_numbers.html
186. +4 −4 exercises/multiplying_and_dividing_rational_expressions_1.html
187. +3 −3 exercises/multiplying_and_dividing_scientific_notation.html
188. +3 −3 exercises/multiplying_complex_numbers.html
189. +2 −2 exercises/multiplying_decimals.html
190. +1 −1 exercises/multiplying_expressions_0.5.html
191. +1 −1 exercises/multiplying_expressions_1.html
192. +3 −3 exercises/multiplying_fractions.html
193. +3 −3 exercises/multiplying_fractions_0.5.html
194. +2 −3 exercises/multiplying_mixed_numbers_1.html
195. +7 −7 exercises/multiplying_polynomials.html
196. +2 −2 exercises/new_definitions_1.html
197. +1 −2 exercises/number_properties_terminology_1.html
198. +12 −20 exercises/one_step_equation_intuition.html
199. +16 −13 exercises/one_step_equations.html
200. +10 −10 exercises/one_step_inequalities.html
201. +1 −1 exercises/ordering_improper_fractions_and_mixed_numbers.html
202. +7 −7 exercises/parabola_intuition_1.html
203. +7 −7 exercises/parabola_intuition_2.html
204. +3 −3 exercises/parabola_intuition_3.html
205. +2 −2 exercises/partial_fraction_expansion_1.html
206. +12 −14 exercises/percentage_word_problems_1.html
207. +7 −8 exercises/percentage_word_problems_2.html
208. +2 −2 exercises/permutations_1.html
209. +1 −1 exercises/place_value.html
210. +6 −13 exercises/plotting_the_line_of_best_fit.html
211. +11 −11 exercises/plugging_in_values.html
212. +7 −7 exercises/point_slope_form.html
213. +2 −2 exercises/points_lines_and_planes.html
214. +1 −1 exercises/power_rule.html
215. +13 −13 exercises/powers_of_complex_numbers_1.html
216. +4 −4 exercises/prime_factorization.html
217. +1 −1 exercises/prime_numbers.html
218. +1 −1 exercises/product_rule.html
219. +1 −1 exercises/properties_of_numbers_2.html
220. +9 −9 exercises/proportions_1.html
221. +15 −15 exercises/proportions_2.html
222. +33 −33 exercises/pythagorean_identities.html
224. +5 −5 exercises/quotient_rule.html
225. +11 −12 exercises/rate_problems_0.5.html
226. +11 −12 exercises/rate_problems_2.html
227. +6 −6 exercises/ratio_word_problems.html
232. +4 −4 exercises/recognizing_conic_sections.html
233. +1 −1 exercises/recognizing_fractions.html
234. +5 −5 exercises/recognizing_rays_lines_and_line_segments.html
235. +6 −6 exercises/representing_numbers.html
236. +7 −7 exercises/rotation_of_polygons.html
237. +6 −6 exercises/rounding_numbers.html
238. +3 −3 exercises/rounding_whole_numbers.html
239. +3 −3 exercises/scalar_matrix_multiplication.html
240. +10 −10 exercises/scaling_vectors.html
243. +3 −3 exercises/significant_figures_1.html
244. +3 −3 exercises/similar_triangles_1.html
245. +5 −5 exercises/similar_triangles_2.html
246. +6 −3 exercises/simplifying_expressions_with_exponents.html
247. +2 −2 exercises/simplifying_fractions.html
249. +4 −4 exercises/simplifying_rational_expressions_1.html
250. +11 −11 exercises/simplifying_rational_expressions_2.html
251. +8 −8 exercises/simplifying_rational_expressions_3.html
252. +5 −5 exercises/slope_intercept_form.html
253. +8 −8 exercises/slope_of_a_line.html
254. +3 −5 exercises/solid_geometry.html
256. +16 −16 exercises/solutions_to_systems_of_equations.html
257. +29 −29 exercises/solving_for_a_variable.html
258. +2 −2 exercises/solving_for_the_x-intercept.html
259. +3 −3 exercises/solving_for_the_y-intercept.html
261. +1 −1 exercises/solving_similar_triangles_1.html
262. +8 −8 exercises/solving_similar_triangles_2.html
263. +1 −1 exercises/special_derivatives.html
264. +6 −6 exercises/square_roots.html
265. +1 −2 exercises/square_roots_2.html
266. +2 −0 exercises/standard_deviation.html
267. +2 −2 exercises/subtracting_decimals.html
268. +2 −2 exercises/subtracting_decimals_0.5.html
269. +1 −1 exercises/subtracting_fractions_with_common_denominators.html
270. +1 −1 exercises/subtraction_2.html
271. +1 −1 exercises/subtraction_3.html
272. +1 −1 exercises/subtraction_4.html
273. +10 −10 exercises/systems_of_equations_with_elimination.html
274. +4 −4 exercises/systems_of_equations_with_elimination_0.5.html
275. +4 −4 exercises/systems_of_equations_with_substitution.html
276. +23 −23 exercises/systems_of_equations_word_problems.html
277. +5 −5 exercises/telling_time.html
278. +5 −5 exercises/telling_time_2.html
279. +4 −4 exercises/the_complex_plane.html
280. +10 −10 exercises/translations_of_points_and_polygons.html
281. +5 −6 exercises/triangle_angles_1.html
282. +2 −2 exercises/triangle_inequality_theorem.html
283. +4 −4 exercises/triangle_types.html
284. +5 −5 exercises/trigonometry_0.5.html
285. +3 −3 exercises/trigonometry_1.5.html
286. +3 −3 exercises/trigonometry_1.html
287. +2 −2 exercises/trigonometry_2.html
288. +2 −2 exercises/unit_circle.html
289. +6 −6 exercises/units.html
290. +2 −0 exercises/variance.html
291. +1 −1 exercises/vertex_of_a_parabola.html
292. +19 −19 exercises/views_of_a_function.html
293. +4 −4 exercises/visualizing_derivatives.html
294. +5 −5 exercises/writing_expressions_1.html
295. +1 −1 exercises/writing_expressions_2.html
296. +7 −8 exercises/z_scores_2.html
297. +12 −12 exercises/z_scores_3.html
 @@ -7,9 +7,9 @@
-
- rand(5) > 0 ? randRange( 1, 9 ) : 0 - rand(3) > 0 ? "." + randRange(1, 9) : "" +
+ rand(5) > 0 ? randRange( 1, 9 ) : 0 + rand(3) > 0 ? "." + randRange(1, 9) : "" randFromArray(["", "-"])
@@ -40,13 +40,13 @@ numberLine( start, end ); style({ stroke: "#6495ED", fill: "#6495ED" }); graph.pt = circle( [ x, 0 ], 0.15 ); - style({ stroke: "#FFA500", fill: "#FFA500", strokeWidth: 3.5, arrows: "->" }); + style({ stroke: "#FFA500", fill: "#FFA500", strokeWidth: 3.5, arrows: "->" }); path( [ [ originX, 0 ], [ x, 0 ] ] ); circle( [ originX, 0 ], 0.10 ); graph.pt.toFront();

The distance from 0 to SIGN + INT + FRAC is INT + FRAC, which equals the absolute value.

-

In other words, INT + FRAC is the non-negative version of SIGN + INT + FRAC.

+

In other words, INT + FRAC is the non-negative version of SIGN + INT + FRAC.

 @@ -1,7 +1,7 @@ - + Absolute value of complex numbers @@ -77,8 +77,8 @@

- Substituting into the Pythagorean theorem:
- \qquad |REPRESENTATION|^2 = abs( REAL )^2 + abs( IMAG )^2, so
+ Substituting into the Pythagorean theorem:
+ \qquad |REPRESENTATION|^2 = abs( REAL )^2 + abs( IMAG )^2, so
\qquad |REPRESENTATION| = \sqrt{abs( REAL )^2 + abs( IMAG )^2}.

@@ -87,12 +87,12 @@

Simplifying the radical gives formattedSquareRootOf( ABS_SQUARE ). That is the absolute value of REPRESENTATION.

-

+

The radical cannot be simplified. The absolute value of REPRESENTATION is \sqrt{ABS_SQUARE}.

- +
 @@ -46,7 +46,7 @@
style({ stroke: "#28AE7B", - arrows: "->" + arrows: "->" }, function(){ path( [ [ 1 + A - START, -2 ], [ 1 + ANSWER - START, -2] ] ); }); @@ -96,7 +96,7 @@
style({ stroke: "#28AE7B", - arrows: "->" + arrows: "->" }, function(){ path( [ [ 1 + A - START, -2 ], [ 1 + ANSWER - START, -2] ] ); });
 @@ -40,7 +40,7 @@ [ BLUE, ORANGE, GREEN ] 7 randRangeUniqueNonZero( 0, MAX_DEGREE, randRange(2, 3) ).sort().reverse() - tabulate( function() { + tabulate( function() { var coefs = []; for ( var i = 0; i <= MAX_DEGREE; i++ ) { var value = 0; @@ -103,7 +103,7 @@

Identify like terms.

-

( POL.coefs[ index ] < 0 ) ? "-" : ( n === 0 && POL === POL_1 ) ? "" : "+"\color{COLORS[ n ]}{abs( POL.coefs[ index ] ) === 1 ? "" : abs( POL.coefs[ index ] )X^index}

+

( POL.coefs[ index ] < 0 ) ? "-" : ( n === 0 && POL === POL_1 ) ? "" : "+"\color{COLORS[ n ]}{abs( POL.coefs[ index ] ) === 1 ? "" : abs( POL.coefs[ index ] )X^index}

 @@ -84,8 +84,8 @@ pow( A_COEFF, 2 ) * NUM pow( B_COEFF, 2 ) * NUM pow( C_COEFF, 2 ) * NUM - B_COEFF > 0 ? "+" : "-" - C_COEFF > 0 ? "+" : "-" + B_COEFF > 0 ? "+" : "-" + C_COEFF > 0 ? "+" : "-"

Simplify the following expression:

\sqrt{A}B_SIGN\sqrt{B}C_SIGN\sqrt{C}

 @@ -70,8 +70,8 @@
-
+
-
Y = @@ -83,7 +83,7 @@ a
+ - +
 @@ -47,18 +47,18 @@
-
Y=
- +
Y= NUMERSOL.regex()
- DENOMSOL + DENOMSOL
+ - + @@ -77,8 +77,8 @@
-
Y=
- +
Y= NUMERSOL
+ @@ -88,7 +88,7 @@ DENOMSOL.regex() - + @@ -106,7 +106,7 @@

Y = \dfrac{NUMERATOR1 SIGN NUMERATOR2}{DENOMINATOR}

-
+

Y = \dfrac{NUMERATOR1 SIGN (NUMERATOR2)}{DENOMINATOR}

@@ -116,8 +116,8 @@

Simplify by dividing numerator and denominator by FACTOR:

-

Y = \dfrac{NUMERSOL}{DENOMSOL}

-

Y = NUMERSOL

+

Y = \dfrac{NUMERSOL}{DENOMSOL}

+

Y = NUMERSOL

 @@ -85,8 +85,8 @@
-
+
-
Y = @@ -98,7 +98,7 @@ a
+ - + @@ -114,7 +114,7 @@

Since the expressions have the same denominator we simply combine the numerators:

Y = \dfrac{NUMERATOR1 + NUMERATOR2}{DENOMINATOR}

-
+

Since the expressions have the same denominator we simply combine the numerators:

Y = \dfrac{NUMERATOR1 - (NUMERATOR2)}{DENOMINATOR}

 @@ -98,8 +98,8 @@
-
+
-
Y = @@ -111,13 +111,13 @@ a
+ - +
-

In order to addsubtract expressions, +

In order to addsubtract expressions, they must have a common denominator.

The smallest common denominator is the least common multiple of D1 and D2.

\lcm(D1, D2) = DENOMINATOR

+
+
+
 @@ -29,7 +29,7 @@

N1 / D1 + N2 / D2

-
+
1 2
 @@ -18,10 +18,10 @@

fraction( N1, D ) + fraction( N2, D ) = {?}

-
( N1 + N2 ) / D
+
( N1 + N2 ) / D
-
+
1 1
 @@ -46,7 +46,7 @@
style({ stroke: "#28AE7B", - arrows: "->" + arrows: "->" }, function(){ path( [ [ 1 + A - START, -3 ], [ 1 + ANSWER - START, -3] ] ); });
 @@ -16,11 +16,11 @@ randRange( 2, 19 ) ( PM === 1 ? randRange( 1, 19 ) : randRange( -W1 + 1, -1 )) -
+
randRange( 3, 20 ) randRange( 3, 20 )
-
+
randRange( 1, D1 - 1 ) randRange( 1, D2 - 1 )
@@ -53,12 +53,12 @@
-

+

=W1 + W2 + \blue{fraction( N1, D1 )} SIGN \pink{fraction( N2, D2 )}

-

+

= expr(["+", W1 + W2, fraction( N1 + PM * N2, D2 )])

@@ -67,7 +67,7 @@

= W1 + W2 + fraction( SIMP_N1 * LCM / SIMP_D1 + PM * SIMP_N2 * LCM / SIMP_D2, LCM )

-
+

Simplify to lowest terms:

= W1 + W2 + fractionReduce( SIMP_N1 * LCM / SIMP_D1 + PM * SIMP_N2 * LCM / SIMP_D2, LCM )

@@ -110,25 +110,24 @@

= \blue{W1} SIGN \pink{abs( W2 )} + \blue{fraction( N1, D1 )} SIGN \pink{fraction( N2, D2 )}

-

+

=W1 + W2 + \blue{fraction( N1, D1 )} SIGN \pink{fraction( N2, D2 )}

-

+

= expr(["+", W1 + W2, fraction( N1 + PM * N2, D2 )])

Combine the whole and fractional parts into a mixed number:

= W1 + W2 + fraction( N1 - N2, D2)

-
+

Simplify to lowest terms:

= W1 + W2 + fractionReduce( N1 - N2 , LCM )

-