Khan/khan-exercises

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 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 1 baf3e43 Simplifying simplifying exercises petercollingridge authored Aug 19, 2013 2 cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 3 0f0c630 Clean up the exercise files using the new cleaning utility. (II) cbhl authored Apr 16, 2013 4 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 5 Simplifying rational expressions 2 ac1415e Use requirejs for module loading spicyj authored Mar 5, 2014 6 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 7 45 46 47
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57067cf ensure that NUMERATOR is not divisible by DENOMINATOR, fix #160476 mauk81 authored Jan 25, 2014 50
baf3e43 Simplifying simplifying exercises petercollingridge authored Aug 19, 2013 51 randVar() 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 52
e56e60b Fix hints (nearly) petercollingridge authored Feb 27, 2013 53 randRangeWeighted(-10, 10, 0, 0.15) 54 randRangeWeighted(-10, 10, 0, 0.15) 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 55
baf3e43 Simplifying simplifying exercises petercollingridge authored Aug 19, 2013 56 randRangeWeighted(-10, 10, 0, 0.15) 4469124 Add a statement to assume x != 0 for simplifying rational expressions beneater authored Mar 14, 2013 57 5721a0c Ensure terms in the answer do not have a common factor petercollingridge authored Mar 3, 2013 58 (function() { e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 59 if (getGCD(COEFFICIENT1, CONSTANT1) !== 1 && getGCD(COEFFICIENT2, CONSTANT1) !== 1) { 5721a0c Ensure terms in the answer do not have a common factor petercollingridge authored Mar 3, 2013 60 // Ensure there are no common factors 61 return randFromArray([-13, -11, -1, 1, 11, 13]); 62 } else { 63 if (COEFFICIENT2 !== 0) { 64 return randRangeWeighted(-10, 10, 0, 0.15); 65 } else { 66 return randRangeExclude(-10, 10, [0]); 67 } 68 } 69 })() 70 baf3e43 Simplifying simplifying exercises petercollingridge authored Aug 19, 2013 71 randRange(2, 12) 1154d38 Expand questions to include factor with powers of a variable petercollingridge authored Feb 27, 2013 72 randRangeWeighted(0, 2, 0, 0.5) baf3e43 Simplifying simplifying exercises petercollingridge authored Aug 19, 2013 73 (function() { 74 var d = {}; 75 d[X] = DEGREE; 76 return new Term(FACTOR, d); 77426f4 No longer accept answers with a negative denominator petercollingridge authored Mar 19, 2013 77 })() 78 e7728e1 Allow answers to ignore the denominator when it's 1 petercollingridge authored Nov 13, 2014 79 new RationalExpression([[COEFFICIENT1, X], CONSTANT1]) 80 new RationalExpression([[COEFFICIENT2, X], CONSTANT2]) 81 NUMERSOL.multiply(FACTORDEGREE) 82 DENOMSOL.multiply(FACTORDEGREE) 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 83
84 e7728e1 Allow answers to ignore the denominator when it's 1 petercollingridge authored Nov 13, 2014 85

Simplify the following expression:

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\dfrac{NUMERATOR}{DENOMINATOR}

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You can assume X \neq 0.

8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 88 cdb9df4 Convert lots of exercises that use regex to use expression entry beneater authored Aug 8, 2014 89
0bd6737 Allow expression answer type to take a set of answers petercollingridge authored Oct 2, 2014 90
e7728e1 Allow answers to ignore the denominator when it's 1 petercollingridge authored Nov 13, 2014 91
(NUMERSOL.toString())/(DENOMSOL.toString())
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(NUMERSOL.toString())/(DENOMSOL.toStringFactored())
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(NUMERSOL.toStringFactored())/(DENOMSOL.toString())
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(NUMERSOL.toStringFactored())/(DENOMSOL.toStringFactored())
baf3e43 Simplifying simplifying exercises petercollingridge authored Aug 19, 2013 95
8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 96
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e56e60b Fix hints (nearly) petercollingridge authored Feb 27, 2013 99

Find the greatest common factor of the numerator and denominator.

8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 100 9622a5a Fix regex petercollingridge authored Feb 27, 2013 101
45a9373 Improve hint layout petercollingridge authored Feb 27, 2013 102

e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 103

The numerator can be factored:
ce13849 Additional hint petercollingridge authored Feb 27, 2013 104
NUMERATOR = getFactoredExpression(FACTOR, COEFFICIENT1, X, DEGREE, CONSTANT1)
e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 105

45a9373 Improve hint layout petercollingridge authored Feb 27, 2013 106

e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 107

The denominator can be factored:
ce13849 Additional hint petercollingridge authored Feb 27, 2013 108
DENOMINATOR = getFactoredExpression(FACTOR, COEFFICIENT2, X, DEGREE, CONSTANT2)
e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 109

9622a5a Fix regex petercollingridge authored Feb 27, 2013 110
111 1154d38 Expand questions to include factor with powers of a variable petercollingridge authored Feb 27, 2013 112

The greatest common factor of all the terms is FACTORDEGREE.

8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 113 114
ce13849 Additional hint petercollingridge authored Feb 27, 2013 115

Factoring out FACTORDEGREE gives us:

e7728e1 Allow answers to ignore the denominator when it's 1 petercollingridge authored Nov 13, 2014 116
117 \qquad \dfrac{(FACTORDEGREE)(NUMERSOL)} 118 {(FACTORDEGREE)(DENOMSOL)} 119
ce13849 Additional hint petercollingridge authored Feb 27, 2013 120
121 122
1154d38 Expand questions to include factor with powers of a variable petercollingridge authored Feb 27, 2013 123

Dividing both the numerator and denominator by FACTORDEGREE gives:

e7728e1 Allow answers to ignore the denominator when it's 1 petercollingridge authored Nov 13, 2014 124
125 \qquad \dfrac{NUMERSOL}{DENOMSOL} or more simply, 126 NUMERSOL 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 127
e9807ff Clean up the exercise files using the new cleaning utility. jeresig authored Apr 16, 2013 128
e7728e1 Allow answers to ignore the denominator when it's 1 petercollingridge authored Nov 13, 2014 129 \qquad \dfrac{NUMERSOL}{DENOMSOL} 8443c79 Start simplifying rational expressions 2 petercollingridge authored Feb 27, 2013 130
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cde9e9f Re-run the exercises through the updated cleaner. jeresig authored Apr 24, 2013 136 137
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