A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.
To try out generators, go to https://lukew3.github.io/mathgenerator
See CONTRIBUTING.md for information about how to contribute.
The project can be install via pip
pip install mathgeneratorHere is an example of how you would generate an addition problem:
from mathgenerator import mathgen
#generate an addition problem
problem, solution = mathgen.addition()
#another way to generate an addition problem using genById()
problem, solution = mathgen.genById(0)Problem/solution pairs are generated with either:
mathgen.<generator_name>()- generates a problem, solution set from the given generator name.mathgen.genById(id)- generates a problem, solution set with generator id provided by theidparameter
You can also use getGenList() to return a list of all generators included in the library in the format:
[id, title, self, funcname, subjectname]
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 11 | Basic Algebra | 7x + 1 = 6 | 5/7 | basic_algebra | maxVariable=10 |
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| 12 | Logarithm | log2(16) | 4 | log | maxBase=3 maxVal=8 |
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| 17 | Integer Multiplication with 2x2 Matrix | 5 * [[0, 4], [3, 0]] = | [[0,20],[15,0]] | multiply_int_to_22_matrix | maxMatrixVal=10 maxRes=100 |
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| 20 | Midpoint of the two point | (3,-13),(-6,5)= | (-1.5,-4.0) | midpoint_of_two_points | maxValue=20 |
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| 21 | Factoring Quadratic | x^2+2x-48 | (x-6)(x+8) | factoring | range_x1=10 range_x2=10 |
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| 23 | Solve a System of Equations in R^2 | 5x + 2y = -9, -10x - y = -3 | x = 1, y = -7 | system_of_equations | range_x=10 range_y=10 coeff_mult_range=10 |
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| 24 | Distance between 2 points | Find the distance between (4, 18) and (-9, 4) | sqrt(365) | distance_two_points | maxValXY=20 minValXY=-20 |
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| 26 | Linear Equations | -18x + 11y = 445, 12x + -8y = -304 | x = -18, y = 11 | linear_equations | n=2 varRange=20 coeffRange=20 |
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| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -x + 1 and y = -1/6x + 1 | (0, 1) | intersection_of_two_lines | minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6 |
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| 43 | Cross Product of 2 Vectors | [9, 6, -6] X [-1, -4, -3] = | [-42, 33, -30] | vector_cross | minVal=-20 maxVal=20 |
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| 45 | Simple Interest | Simple interest for a principle amount of 5981 dollars, 9% rate of interest and for a time period of 4 years is = | 2153.16 | simple_interest | maxPrinciple=10000 maxRate=10 maxTime=10 |
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| 46 | Multiplication of two matrices | Multiply
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matrix_multiplication | maxVal=100 max_dim=10 |
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| 50 | Quadratic Equation | Zeros of the Quadratic Equation 47x^2+185x+57=0 | [-0.34, -3.6] | quadratic_equation | maxVal=100 |
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| 65 | Multiplication of 2 complex numbers | (8+0j) * (3-16j) = | (24-128j) | multiply_complex_numbers | minRealImaginaryNum=-20 maxRealImaginaryNum=20 |
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| 72 | Dot Product of 2 Vectors | [20, 15, -19] . [2, 6, 19] = | -231 | vector_dot | minVal=-20 maxVal=20 |
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| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[53, 37, 10], [19, 33, 67], [29, 74, 73]]) is: | Matrix([[2549/110035, 1961/110035, -2149/110035], [-556/110035, -3579/110035, 3361/110035], [-449/110035, 2849/110035, -1046/110035]]) | invert_matrix | SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False |
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| 77 | Determinant to 2x2 Matrix | Det([[55, 18], [12, 62]]) = | 3194 | int_matrix_22_determinant | maxMatrixVal=100 |
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| 78 | Compound Interest | Compound interest for a principle amount of 8346 dollars, 1% rate of interest and for a time period of 5 year is = | 8771.73 | compound_interest | maxPrinciple=10000 maxRate=10 maxTime=10 |
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| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 7x^2 + 8x + 1 = 0 | simplified solution : ((-0.143, -1.0)), generalized solution : ((-8 + 6)/27, (-8 - 6)/27) | complex_quadratic | prob_type=0 max_range=10 |
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| 105 | Combine Like terms | 5x^1 + 10x^2 | 5x^1 + 10x^2 | combine_like_terms | maxCoef=10 maxExp=20 maxTerms=10 |
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| 111 | Expanding Factored Binomial | (-9x+3)(-5x+10) | 45x^2-105x+30 | expanding | range_x1=10 range_x2=10 range_a=10 range_b=10 |
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|---|---|---|---|---|---|
| 0 | Addition | (25+2) | 27 | addition | maxSum=99 maxAddend=50 |
| 1 | Subtraction | 40-4= | 36 | subtraction | maxMinuend=99 maxDiff=99 |
| 2 | Multiplication | 7*0= | 0 | multiplication | maxMulti=12 |
| 3 | Division | 165/15= | 11 | division | maxA=25 maxB=25 |
| 6 | Square Root | sqrt(25)= | 5 | square_root | minNo=1 maxNo=12 |
| 8 | Square | 18^2= | 324 | square | maxSquareNum=20 |
| 13 | Complex Division | 10/10= | 1.0 | complex_division | maxRes=99 maxDivid=99 |
| 16 | Fraction Division | (8/9)/(1/2) | 16/9 | divide_fractions | maxVal=10 |
| 28 | Fraction Multiplication | (4/10)*(2/4) | 1/5 | fraction_multiplication | maxVal=10 |
| 31 | Factorial | 2! = | 2 | factorial | maxInput=6 |
| 44 | Compare Fractions | Which symbol represents the comparison between 8/3 and 3/7? | > | compare_fractions | maxVal=10 |
| 47 | Cube Root | What is the cube root of 962 up to 2 decimal places? | 9.87 | cube_root | minNo=1 maxNo=1000 |
| 53 | Exponentiation | 20^8 = | 25600000000 | exponentiation | maxBase=20 maxExpo=10 |
| 71 | Absolute difference between two numbers | 3--65 | = | 68 | |
| 80 | Percentage of a number | What is 16% of 57? | 9.12 | percentage | maxValue=99 maxpercentage=99 |
| 90 | isprime | Is 84 prime? | No | is_prime | max_num=100 |
| 97 | Power of Powers | Simplify 21^2^1= | 21^2 | power_of_powers | maxBase=50 maxPower=10 |
| 118 | Percentage difference | What is the percentage difference between 172 and 6? | 186.52% | percentage_difference | maxValue=200 minValue=0 |
| 119 | Percentage error | Find the percentage error when observed value equals -74 and exact value equals -30. | 146.67% | percentage_error | maxValue=100 minValue=-100 |
| 120 | Greatest Common Divisor of N Numbers | GCD(29525945,314084311)= | 1 | greatest_common_divisor | numbersCount=2 maximalNumberLimit=10**9 |
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|---|---|---|---|---|---|
| 7 | Power Rule Differentiation | 9x^9 + 6x^5 | 81x^8 + 30x^4 | power_rule_differentiation | maxCoef=10 maxExp=10 maxTerms=5 |
| 48 | Power Rule Integration | 3x^10 + 2x^10 | (3/10)x^11 + (2/10)x^11 + c | power_rule_integration | maxCoef=10 maxExp=10 maxTerms=5 |
| 88 | Differentiation | differentiate w.r.t x : d(tan(x)+3*x^3)/dx | 9*x^2 + tan(x)^2 + 1 | differentiation | diff_lvl=2 |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 91x^2 + 24x + 10 is = | 52.3333 | definite_integral | max_coeff=100 |
| 110 | Stationary Points | f(x)=10x^3 + 10x^2 + 2*x + 6 | (-1/3 - sqrt(10)/15,10*(-1/3 - sqrt(10)/15)**3 - 2sqrt(10)/15 + 10(-1/3 - sqrt(10)/15)*2 + 16/3),(-1/3 + sqrt(10)/15,10(-1/3 + sqrt(10)/15)*3 + 10(-1/3 + sqrt(10)/15)**2 + 2*sqrt(10)/15 + 16/3) | stationary_points | maxExp=3 maxCoef=10 |
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|---|---|---|---|---|---|
| 4 | Binary Complement 1s | 0110= | 1001 | binary_complement_1s | maxDigits=10 |
| 5 | Modulo Division | 82%80= | 2 | modulo_division | maxRes=99 maxModulo=99 |
| 14 | Decimal to Binary | Binary of 82= | 1010010 | decimal_to_binary | max_dec=99 |
| 15 | Binary to Decimal | 1010 | 10 | binary_to_decimal | max_dig=10 |
| 56 | Fibonacci Series | The Fibonacci Series of the first 3 numbers is ? | [0, 1, 1] | fibonacci_series | minNo=1 |
| 62 | nth Fibonacci number | What is the 31th Fibonacci number? | 1346269 | nth_fibonacci_number | maxN=100 |
| 64 | Binary to Hexidecimal | 00 | 0x0 | binary_to_hex | max_dig=10 |
| 73 | Binary 2's Complement | 2's complement of 1011111 = | 100001 | binary_2s_complement | maxDigits=10 |
| 79 | Decimal to Hexadecimal | Binary of 595= | 0x253 | decimal_to_hexadeci | max_dec=1000 |
| 84 | Converts decimal to octal | The decimal number 3335 in Octal is: | 0o6407 | decimal_to_octal | maxDecimal=4096 |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 2 is = | 8295 | bcd_to_decimal | maxNumber=10000 |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 3270 is = | 12126 | decimal_to_bcd | maxNumber=10000 |
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|---|---|---|---|---|---|
| 18 | Area of Triangle | Area of triangle with side lengths: 16 18 7 = | 55.8 | area_of_triangle | maxA=20 maxB=20 |
| 19 | Triangle exists check | Does triangle with sides 43, 29 and 45 exist? | Yes | valid_triangle | maxSideLength=50 |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 74 and 56 = | 50 | third_angle_of_triangle | maxAngle=89 |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 12 and 13 = | 17.69 | pythagorean_theorem | maxLength=20 |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 6 sides | 120.0 | angle_regular_polygon | minVal=3 maxVal=20 |
| 32 | Surface Area of Cube | Surface area of cube with side = 14m is | 1176 m^2 | surface_area_cube | maxSide=20 unit='m' |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 2m, 20m, 15m is | 740 m^2 | surface_area_cuboid | maxSide=20 unit='m' |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 5m and radius = 20m is | 3141 m^2 | surface_area_cylinder | maxRadius=20 maxHeight=50 unit='m' |
| 35 | Volume of Cube | Volume of cube with side = 3m is | 27 m^3 | volume_cube | maxSide=20 unit='m' |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 2m, 7m, 13m is | 182 m^3 | volume_cuboid | maxSide=20 unit='m' |
| 37 | Volume of cylinder | Volume of cylinder with height = 49m and radius = 9m is | 12468 m^3 | volume_cylinder | maxRadius=20 maxHeight=50 unit='m' |
| 38 | Surface Area of cone | Surface area of cone with height = 44m and radius = 7m is | 1133 m^2 | surface_area_cone | maxRadius=20 maxHeight=50 unit='m' |
| 39 | Volume of cone | Volume of cone with height = 5m and radius = 12m is | 753 m^3 | volume_cone | maxRadius=20 maxHeight=50 unit='m' |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 42 , 126, 95 = | 97 | fourth_angle_of_quadrilateral | maxAngle=180 |
| 57 | Trigonometric Values | What is tan(45)? | 1 | basic_trigonometry | angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan'] |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 9 sides = | 1260 | sum_of_polygon_angles | maxSides=12 |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 5m is | 314.1592653589793 m^2 | surface_area_sphere | maxSide=20 unit='m' |
| 61 | Volume of Sphere | Volume of sphere with radius 24 m = | 57905.83579096706 m^3 | volume_sphere | maxRadius=100 |
| 70 | Angle between 2 vectors | angle between the vectors [501.77, 761.2, 553.5, 411.41, 87.99, 695.99] and [329.3, 902.75, 451.75, 94.17, 457.01, 550.07] is: | 0.43 radians | angle_btw_vectors | maxEltAmt=20 |
| 75 | Area of a Sector | Given radius, 41 and angle, 214. Find the area of the sector. | Area of sector = 3139.27137 | sector_area | maxRadius=49 maxAngle=359 |
| 86 | Degrees to Radians | Angle 18 in radians is = | 0.31 | degree_to_rad | max_deg=360 |
| 87 | Radians to Degrees | Angle 3 in degrees is = | 171.89 | radian_to_deg | max_rad=3 |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 19 and height, 22? | CSA of cylinder = 2626.37 | curved_surface_area_cylinder | maxRadius=49 maxHeight=99 |
| 96 | Perimeter of Polygons | The perimeter of a 5 sided polygon with lengths of [85, 11, 110, 91, 52]cm is: | 349 | perimeter_of_polygons | maxSides=12 maxLength=120 |
| 104 | Circumference | Circumference of circle with radius 85 | 534.0707511102648 | circumference | maxRadius=100 |
| 108 | Arc length of Angle | Given radius, 49 and angle, 152. Find the arc length of the angle. | Arc length of the angle = 129.99212 | arc_length | maxRadius=49 maxAngle=359 |
| 112 | Area of Circle | Area of circle with radius 38 | 4538.285714285715 | area_of_circle | maxRadius=100 |
| 113 | Volume of frustum | Volume of frustum with height = 29m and r1 = 6m is and r2 = 6m is | 16885.0 m^3 | volume_frustum | maxR1=20 maxR2=20 maxHeight=50 unit='m' |
| 114 | Equation of line from two points | What is the equation of the line between points (2,19) and (-10,13) in slope-intercept form? | 2y = x + 36 | equation_of_line_from_two_points | maxCoordinate=20 minCoordinate=-20 |
| 115 | Area of Circle given center and a point on circle | Area of circle with center (4,4) and passing through (4.0, 4.0) is | 0.0 | area_of_circle_given_center_and_point | maxCoordinate = 10 maxRadius=10 |
| 117 | Volume of Hemisphere | Volume of hemisphere with radius 27 m = | 41223.979 m^3 | volume_hemisphere | maxRadius=100 |
| 122 | Volume of pyramid | Volume of pyramid with base length = 5 m, base width = 16 m and height = 42 m is | 1120.0 m^3 | volume_pyramid | maxLength=20 maxWidth=20 maxHeight=50 unit='m' |
| 123 | Surface area of pyramid | Surface area of pyramid with base length = 20m, base width = 50m, and height = 24m | 1870 m^2 | surface_area_pyramid | unit='m' |
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|---|---|---|---|---|---|
| 9 | LCM (Least Common Multiple) | LCM of 7 and 19 = | 133 | lcm | maxVal=20 |
| 10 | GCD (Greatest Common Denominator) | GCD of 16 and 11 = | 1 | gcd | maxVal=20 |
| 27 | Prime Factorisation | Find prime factors of 23 | [23] | prime_factors | minVal=1 maxVal=200 |
| 40 | Common Factors | Common Factors of 34 and 20 = | [1, 2] | common_factors | maxVal=100 |
| 51 | HCF (Highest Common Factor) | HCF of 10 and 20 = | 10 | hcf | maxVal=20 |
| 55 | Comparing surds | Fill in the blanks 67^(1/4) _ 15^(1/5) | > | surds_comparison | maxValue=100 maxRoot=10 |
| 63 | Profit or Loss Percent | Profit percent when CP = 116 and SP = 446 is: | 284.48275862068965 | profit_loss_percent | maxCP=1000 maxSP=1000 |
| 66 | Geometric Progression | For the given GP [7, 77, 847, 9317, 102487, 1127357] ,Find the value of a,common ratio,9th term value, sum upto 6th term | The value of a is 7, common ratio is 11 , 9th term is 1500512167 , sum upto 6th term is 1240092.0 | geometric_progression | number_values=6 min_value=2 max_value=12 n_term=7 sum_term=5 |
| 67 | Geometric Mean of N Numbers | Geometric mean of 3 numbers 24 , 17 and 8 = | (24178)^(1/3) = 14.833719077064755 | geometric_mean | maxValue=100 maxNum=4 |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 2 numbers 36 and 10 = | 2/((1/36) + (1/10)) = 15.65217391304348 | harmonic_mean | maxValue=100 maxNum=4 |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[662.188456830693, 258.9343100016411, 674.6373606909881, 145.42173783600865, 915.3419640001316, 532.3072720135815, 564.2351770581631, 108.13767884525704, 687.9402187703554, 874.3820025839659, 805.5736380024711, 941.7491419729342, 160.1472208023249, 174.14254996459778] is: | 2294.0573965748918 | euclidian_norm | maxEltAmt=20 |
| 81 | Celsius To Fahrenheit | Convert -25 degrees Celsius to degrees Fahrenheit = | -13.0 | celsius_to_fahrenheit | maxTemp=100 |
| 82 | AP Term Calculation | Find the term number 79 of the AP series: 27, -42, -111 ... | -5355 | arithmetic_progression_term | maxd=100 maxa=100 maxn=100 |
| 83 | AP Sum Calculation | Find the sum of first 72 terms of the AP series: -93, -114, -135 ... | -60372.0 | arithmetic_progression_sum | maxd=100 maxa=100 maxn=100 |
| 85 | Converts decimal to Roman Numerals | The number 0 in Roman Numerals is: | MDXXXVI | decimal_to_roman_numerals | maxDecimal=4000 |
| 92 | Complex To Polar Form | 8.54(-8.0theta + i-3.0theta) | -2.78 | complex_to_polar | minRealImaginaryNum=-20, maxRealImaginaryNum=20 |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={8, 9, 10, 7} ,b={3, 4, 5, 9, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {3, 4, 5, 7, 8, 9, 10},Intersection is {9, 10}, a-b is {8, 7},b-a is {3, 4, 5}, Symmetric difference is {3, 4, 5, 7, 8} | set_operation | minval=3 maxval=7 n_a=4 n_b=5 |
| 94 | Base Conversion | Convert 46132 from base 9 to base 16. | 7808 | base_conversion | maxNum=60000 maxBase=16 |
| 98 | Quotient of Powers with Same Base | The Quotient of 19^5 and 19^8 = 19^(5-8) = 19^-3 | 0.0001457938474996355 | quotient_of_power_same_base | maxBase=50 maxPower=10 |
| 99 | Quotient of Powers with Same Power | The Quotient of 48^8 and 42^8 = (48/42)^8 = 1.1428571428571428^8 | 2.910285368046528 | quotient_of_power_same_power | maxBase=50 maxPower=10 |
| 101 | Leap Year or Not | Year 1941 | is not a leap year | is_leap_year | minNumber=1900 maxNumber=2099 |
| 102 | Minute to Hour conversion | Convert 735 minutes to Hours & Minutes | 12 hours and 15 minutes | minutes_to_hours | maxMinutes=999 |
| 106 | signum function | signum of 46 is = | 1 | signum_function | min=-999 max=999 |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 31.39% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 11 pistons will contain no more than 2 rejected pistons? | 27.82 | binomial_distribution | `` |
| 116 | Factors of a number | Factors of 279 = | [1, 3, 9, 31, 93, 279] | Factors | maxVal=1000 |
| 121 | Product of scientific notaions | Product of scientific notations 5.18x10^48 and 5.01x10^16 = | 2.6x10^65 | product_of_scientific_notations | minExpVal=-100 maxExpVal=100 |
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|---|---|---|---|---|---|
| 30 | Combinations of Objects | Number of combinations from 20 objects picked 7 at a time | 77520 | combinations | maxlength=20 |
| 42 | Permutations | Number of Permutations from 15 objects picked 6 at a time = | 3603600 | permutation | maxlength=20 |
| 52 | Probability of a certain sum appearing on faces of dice | If 2 dice are rolled at the same time, the probability of getting a sum of 2 = | 1/36 | dice_sum_probability | maxDice=3 |
| 54 | Confidence interval For sample S | The confidence interval for sample [272, 236, 244, 247, 251, 209, 214, 207, 238, 204, 254, 258, 215, 218, 285, 274, 220, 235, 212, 271, 241, 222, 201, 237, 233, 246, 229, 287, 253, 208, 242, 299, 245] with 99% confidence is | (250.97182391664583, 228.24029729547536) | confidence_interval | `` |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[9, 26, 45, 37, 40, 13, 12, 18, 27, 5, 14, 25, 32, 28, 21] | The Mean is 23.466666666666665 , Standard Deviation is 130.11555555555555, Variance is 11.406820571726179 | data_summary | number_values=15 minval=5 maxval=50 |
| 76 | Mean and Median | Given the series of numbers [1, 4, 14, 21, 22, 30, 43, 44, 51, 63]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 29.3 and Arithmetic median of this series is 26.0 | mean_median | maxlen=10 |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 0.07% of population have. Test sensitivity (true positive) is equal to SN= 98.04% whereas test specificity (true negative) SP= 94.26%. What is the probability that this guy really has that disease? | 1.18% | conditional_probability | `` |