mathgenerator
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A math problem generator, created for the purpose of giving self-studying students and teaching organizations the means to easily get access to high-quality, generated math problems to suit their need...
mathgenerator
A math problem generator, created for the purpose of giving self-studying students and teaching organizations the means to easily get access to random math problems to suit their needs.
To try out generators, go to https://lukew3.github.io/mathgenerator
See CONTRIBUTING.md for information about how to contribute.
Table of Contents
- Installation
-
Basic Usage
- More Complicated Usage
- Documentation
-
List of Generators
- algebra
- basic_math
- calculus
- computer_science
- geometry
- misc
- statistics
Installation
The project can be install via pip
pip install mathgenerator
Basic Usage
Here 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)
Creating a worksheet
If you wish to create a worksheet, you can use the worksheetgen package. Install this with pip install worksheetgen
. Here is an example of how a worksheet would be generated.
from mathgenerator import mathgen
from worksheetgen.wg import Worksheet
ws = Worksheet("Worksheet title")
with ws.section('Section 1', description='These are instructions')
# Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.
for _ in range(10):
ws.add_problem(mathgen.genById(1)[0])
ws.write_pdf()
This creates the pdf ws.pdf
in your current directory
Documentation
-
getGenList()
returns a list of all generators in the repository in the format[id, title, self, funcname, subjectname]
-
genById(id)
generates a problem, solution set with generator idid
in the format[problem, solution]
-
Pass the kwarg
format=latex
to return problem and solution set as latex. If latex is not available for that generator, the problem will return the string "Latex unavailable" -
Pass the kwarg
format=raw
to return just the raw data for each generator. An array of each variable necessary to the generator is returned.
List of Generators
algebra
Id | Skill | Example problem | Example Solution | Function Name | Kwargs | ||||||||||||||||||||||||||||||||
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11 | Basic Algebra | 5x + 5 = 7 | 2/5 | basic_algebra | maxVariable=10 |
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12 | Logarithm | log3(6561) | 8 | log | maxBase=3 maxVal=8 |
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17 | Integer Multiplication with 2x2 Matrix | 10 * [[10, 8], [9, 1]] = | [[100,80],[90,10]] | multiply_int_to_22_matrix | maxMatrixVal=10 maxRes=100 |
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20 | Midpoint of the two point | (-8,12),(8,-12)= | (0.0,0.0) | midpoint_of_two_points | maxValue=20 |
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21 | Factoring Quadratic | x^2-25 | (x+5)(x-5) | factoring | range_x1=10 range_x2=10 |
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23 | Solve a System of Equations in R^2 | 4x + 9y = -38, 3x + 8y = -36 | x = 4, y = -6 | 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 (-3, 21) and (17, 3) | sqrt(724) | distance_two_points | maxValXY=20 minValXY=-20 |
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26 | Linear Equations | 11x + -13y = -389, 16x + -11y = -463 | x = -20, y = 13 | 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 = 4/6x - 10 and y = 5x + 7 | (-51/13, -164/13) | 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 | [11, 8, 9] X [-20, 11, -12] = | [-195, -48, 281] | vector_cross | minVal=-20 maxVal=20 |
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45 | Simple Interest | Simple interest for a principle amount of 9453 dollars, 6% rate of interest and for a time period of 6 years is = | 3403.08 | simple_interest | maxPrinciple=10000 maxRate=10 maxTime=10 |
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46 | Multiplication of two matrices | Multiply
|
|
matrix_multiplication | maxVal=100 max_dim=10 |
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50 | Quadratic Equation | Zeros of the Quadratic Equation 38x^2+176x+57=0 | [-0.35, -4.28] | quadratic_equation | maxVal=100 |
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65 | Multiplication of 2 complex numbers | (13+14j) * (-20-11j) = | (-106-423j) | multiply_complex_numbers | minRealImaginaryNum=-20 maxRealImaginaryNum=20 |
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72 | Dot Product of 2 Vectors | [0, 18, -7] . [-11, -12, 14] = | -314 | vector_dot | minVal=-20 maxVal=20 |
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74 | Inverse of a Matrix | Inverse of Matrix Matrix([[69, 83, 21], [13, 46, 72], [53, 24, 42]]) is: | Matrix([[17/20070, -497/40140, 167/8028], [109/8028, 119/16056, -313/16056], [-1063/120420, 2743/240840, 419/48168]]) | invert_matrix | SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False |
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77 | Determinant to 2x2 Matrix | Det([[27, 0], [66, 78]]) = | 2106 | int_matrix_22_determinant | maxMatrixVal=100 |
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78 | Compound Interest | Compound interest for a principle amount of 9116 dollars, 6% rate of interest and for a time period of 7 year is = | 13707.09 | compound_interest | maxPrinciple=10000 maxRate=10 maxTime=10 |
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100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 2x^2 + 8x + 3 = 0 | simplified solution : ((-0.419, -3.581)), generalized solution : ((-8 + sqrt(40))/22, (-8 - sqrt(40))/22) | complex_quadratic | prob_type=0 max_range=10 |
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105 | Combine Like terms | 8x^5 + 5x^2 + 2x^5 + 5x^2 + 9x^2 + 7x^6 + 1x^5 | 19x^2 + 11x^5 + 7x^6 | combine_like_terms | maxCoef=10 maxExp=20 maxTerms=10 |
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111 | Expanding Factored Binomial | (-5x+10)(-5x-10) | 25x^2x-100 | expanding | range_x1=10 range_x2=10 range_a=10 range_b=10 |
basic_math
Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
---|---|---|---|---|---|
0 | Addition | 18+33= | 51 | addition | maxSum=99 maxAddend=50 |
1 | Subtraction | 51-4= | 47 | subtraction | maxMinuend=99 maxDiff=99 |
2 | Multiplication | 5*9= | 45 | multiplication | maxMulti=12 |
3 | Division | 209/11= | 19 | division | maxA=25 maxB=25 |
6 | Square Root | sqrt(9)= | 3 | square_root | minNo=1 maxNo=12 |
8 | Square | 10^2= | 100 | square | maxSquareNum=20 |
13 | Complex Division | 12/26= | 0.46 | complex_division | maxRes=99 maxDivid=99 |
16 | Fraction Division | (3/5)/(3/7) | 7/5 | divide_fractions | maxVal=10 |
28 | Fraction Multiplication | (7/5)*(7/9) | 49/45 | fraction_multiplication | maxVal=10 |
31 | Factorial | 0! = | 1 | factorial | maxInput=6 |
44 | Compare Fractions | Which symbol represents the comparison between 6/3 and 2/4? | > | compare_fractions | maxVal=10 |
47 | Cube Root | What is the cube root of 194 up to 2 decimal places? | 5.79 | cube_root | minNo=1 maxNo=1000 |
53 | Exponentiation | 4^10 = | 1048576 | exponentiation | maxBase=20 maxExpo=10 |
71 | Absolute difference between two numbers | -92--57 | = | 35 | |
80 | Percentage of a number | What is 14% of 14? | 1.96 | percentage | maxValue=99 maxpercentage=99 |
90 | isprime | Is 51 prime? | No | is_prime | max_num=100 |
97 | Power of Powers | Simplify 6^10^8= | 6^80 | power_of_powers | maxBase=50 maxPower=10 |
118 | Percentage difference | What is the percentage difference between 53 and 90? | 51.75% | percentage_difference | maxValue=200 minValue=0 |
119 | Percentage error | Find the percentage error when observed value equals 33 and exact value equals 61. | 45.9% | percentage_error | maxValue=100 minValue=-100 |
120 | Greatest Common Divisor of N Numbers | GCD(21465961,176654083)= | 1 | greatest_common_divisor | numbersCount=2 maximalNumberLimit=10**9 |
124 | Is Composite | Is 8 composite? | Yes | is_composite | maxNum=250 |
calculus
Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
---|---|---|---|---|---|
7 | Power Rule Differentiation | 8x^1 + 5x^2 + 3x^6 + 1x^8 | 8x^0 + 10x^1 + 18x^5 + 8x^7 | power_rule_differentiation | maxCoef=10 maxExp=10 maxTerms=5 |
48 | Power Rule Integration | 2x^7 + 2x^9 | (2/7)x^8 + (2/9)x^10 + c | power_rule_integration | maxCoef=10 maxExp=10 maxTerms=5 |
88 | Differentiation | differentiate w.r.t x : d(cos(x)+6*x^4)/dx | 24*x^3 - sin(x) | differentiation | diff_lvl=2 |
89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 70x^2 + 15x + 65 is = | 95.8333 | definite_integral | max_coeff=100 |
110 | Stationary Points | f(x)=4x^2 + 8x + 6 | (-1,2) | stationary_points | maxExp=3 maxCoef=10 |
computer_science
Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
---|---|---|---|---|---|
4 | Binary Complement 1s | 0= | 1 | binary_complement_1s | maxDigits=10 |
5 | Modulo Division | 53%8= | 5 | modulo_division | maxRes=99 maxModulo=99 |
14 | Decimal to Binary | Binary of 94= | 1011110 | decimal_to_binary | max_dec=99 |
15 | Binary to Decimal | 00 | 0 | binary_to_decimal | max_dig=10 |
56 | Fibonacci Series | The Fibonacci Series of the first 8 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13] | fibonacci_series | minNo=1 |
62 | nth Fibonacci number | What is the 69th Fibonacci number? | 117669030460994 | nth_fibonacci_number | maxN=100 |
64 | Binary to Hexidecimal | 11011101 | 0xdd | binary_to_hex | max_dig=10 |
73 | Binary 2's Complement | 2's complement of = | binary_2s_complement | maxDigits=10 |
|
79 | Decimal to Hexadecimal | Binary of 639= | 0x27f | decimal_to_hexadeci | max_dec=1000 |
84 | Converts decimal to octal | The decimal number 3882 in Octal is: | 0o7452 | decimal_to_octal | maxDecimal=4096 |
91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 9 is = | 38983 | bcd_to_decimal | maxNumber=10000 |
103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 3184 is = | 1270 | decimal_to_bcd | maxNumber=10000 |
geometry
Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
---|---|---|---|---|---|
18 | Area of Triangle | Area of triangle with side lengths: 13 5 11 = | 26.89 | area_of_triangle | maxA=20 maxB=20 |
19 | Triangle exists check | Does triangle with sides 19, 43 and 32 exist? | Yes | valid_triangle | maxSideLength=50 |
22 | Third Angle of Triangle | Third angle of triangle with angles 69 and 64 = | 47 | third_angle_of_triangle | maxAngle=89 |
25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 2 and 12 = | 12.17 | pythagorean_theorem | maxLength=20 |
29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 14 sides | 154.29 | angle_regular_polygon | minVal=3 maxVal=20 |
32 | Surface Area of Cube | Surface area of cube with side = 8m is | 384 m^2 | surface_area_cube | maxSide=20 unit='m' |
33 | Surface Area of Cuboid | Surface area of cuboid with sides = 5m, 2m, 17m is | 258 m^2 | surface_area_cuboid | maxSide=20 unit='m' |
34 | Surface Area of Cylinder | Surface area of cylinder with height = 8m and radius = 10m is | 1130 m^2 | surface_area_cylinder | maxRadius=20 maxHeight=50 unit='m' |
35 | Volume of Cube | Volume of cube with side = 13m is | 2197 m^3 | volume_cube | maxSide=20 unit='m' |
36 | Volume of Cuboid | Volume of cuboid with sides = 13m, 17m, 7m is | 1547 m^3 | volume_cuboid | maxSide=20 unit='m' |
37 | Volume of cylinder | Volume of cylinder with height = 34m and radius = 3m is | 961 m^3 | volume_cylinder | maxRadius=20 maxHeight=50 unit='m' |
38 | Surface Area of cone | Surface area of cone with height = 36m and radius = 20m is | 3844 m^2 | surface_area_cone | maxRadius=20 maxHeight=50 unit='m' |
39 | Volume of cone | Volume of cone with height = 37m and radius = 9m is | 3138 m^3 | volume_cone | maxRadius=20 maxHeight=50 unit='m' |
49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 43 , 171, 40 = | 106 | fourth_angle_of_quadrilateral | maxAngle=180 |
57 | Trigonometric Values | What is cos(90)? | 0 | basic_trigonometry | angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan'] |
58 | Sum of Angles of Polygon | Sum of angles of polygon with 8 sides = | 1080 | sum_of_polygon_angles | maxSides=12 |
60 | Surface Area of Sphere | Surface area of Sphere with radius = 11m is | 1520.5308443374597 m^2 | surface_area_sphere | maxSide=20 unit='m' |
61 | Volume of Sphere | Volume of sphere with radius 71 m = | 1499214.0909853019 m^3 | volume_sphere | maxRadius=100 |
70 | Angle between 2 vectors | angle between the vectors [313.53, 145.92, 865.52, 575.29, 397.71, 201.66, 322.34, 126.51, 899.2, 45.11, 230.29, 927.09, 354.67] and [663.26, 671.39, 637.09, 283.77, 846.59, 345.77, 127.24, 22.2, 287.33, 758.54, 141.04, 326.26, 986.76] is: | 0.84 radians | angle_btw_vectors | maxEltAmt=20 |
75 | Area of a Sector | Given radius, 44 and angle, 119. Find the area of the sector. | Area of sector = 2010.47967 | sector_area | maxRadius=49 maxAngle=359 |
86 | Degrees to Radians | Angle 241 in radians is = | 4.21 | degree_to_rad | max_deg=360 |
87 | Radians to Degrees | Angle 1 in degrees is = | 57.3 | radian_to_deg | max_rad=3 |
95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 12 and height, 17? | CSA of cylinder = 1281.77 | curved_surface_area_cylinder | maxRadius=49 maxHeight=99 |
96 | Perimeter of Polygons | The perimeter of a 9 sided polygon with lengths of [9, 38, 9, 30, 102, 64, 30, 91, 51]cm is: | 424 | perimeter_of_polygons | maxSides=12 maxLength=120 |
104 | Circumference | Circumference of circle with radius 65 | 408.4070449666731 | circumference | maxRadius=100 |
108 | Arc length of Angle | Given radius, 48 and angle, 129. Find the arc length of the angle. | Arc length of the angle = 108.07079 | arc_length | maxRadius=49 maxAngle=359 |
112 | Area of Circle | Area of circle with radius 67 | 14108.285714285714 | area_of_circle | maxRadius=100 |
113 | Volume of frustum | Volume of frustum with height = 29m and r1 = 1m is and r2 = 1m is | 941.0 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 (19,-1) and (15,-3) in slope-intercept form? | 2y = x -21 | 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 (4,0) and passing through (7.779999999999999, 5.89) is | 153.94 | area_of_circle_given_center_and_point | maxCoordinate = 10 maxRadius=10 |
117 | Volume of Hemisphere | Volume of hemisphere with radius 21 m = | 19396.193 m^3 | volume_hemisphere | maxRadius=100 |
122 | Volume of pyramid | Volume of pyramid with base length = 17 m, base width = 3 m and height = 2 m is | 34.0 m^3 | volume_pyramid | maxLength=20 maxWidth=20 maxHeight=50 unit='m' |
123 | Surface area of pyramid | Surface area of pyramid with base length = 52m, base width = 52m, and height = 24m | 3744 m^2 | surface_area_pyramid | unit='m' |
misc
Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
---|---|---|---|---|---|
9 | LCM (Least Common Multiple) | LCM of 17 and 10 = | 170 | lcm | maxVal=20 |
10 | GCD (Greatest Common Denominator) | GCD of 10 and 3 = | 1 | gcd | maxVal=20 |
27 | Prime Factorisation | Find prime factors of 72 | [2, 2, 2, 3, 3] | prime_factors | minVal=1 maxVal=200 |
40 | Common Factors | Common Factors of 24 and 36 = | [1, 2, 3, 4, 6, 12] | common_factors | maxVal=100 |
51 | HCF (Highest Common Factor) | HCF of 5 and 1 = | 1 | hcf | maxVal=20 |
55 | Comparing surds | Fill in the blanks 80^(1/4) _ 10^(1/7) | > | surds_comparison | maxValue=100 maxRoot=10 |
63 | Profit or Loss Percent | Profit percent when CP = 314 and SP = 358 is: | 14.012738853503185 | profit_loss_percent | maxCP=1000 maxSP=1000 |
66 | Geometric Progression | For the given GP [4, 28, 196, 1372, 9604, 67228] ,Find the value of a,common ratio,8th term value, sum upto 10th term | The value of a is 4, common ratio is 7 , 8th term is 3294172 , sum upto 10th term is 188316832.0 | 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 43 , 73 and 2 = | (43732)^(1/3) = 18.44762395255555 | geometric_mean | maxValue=100 maxNum=4 |
68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 80 , 79 , 74 , 78 = | 4/((1/80) + (1/79) + (1/74) + (1/78)) = 77.6815865518732 | harmonic_mean | maxValue=100 maxNum=4 |
69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[86.58156338792955, 165.0561703332688, 492.72813194295276, 781.1275671824076, 350.2592897058979, 595.3141574403849, 980.9590499170994, 765.0348165196015, 496.4518614259873, 834.8722353149475, 194.45844826499703] is: | 1973.223460988261 | euclidian_norm | maxEltAmt=20 |
81 | Celsius To Fahrenheit | Convert -14 degrees Celsius to degrees Fahrenheit = | 6.800000000000001 | celsius_to_fahrenheit | maxTemp=100 |
82 | AP Term Calculation | Find the term number 87 of the AP series: 14, -75, -164 ... | -7640 | arithmetic_progression_term | maxd=100 maxa=100 maxn=100 |
83 | AP Sum Calculation | Find the sum of first 49 terms of the AP series: 70, 166, 262 ... | 116326.0 | arithmetic_progression_sum | maxd=100 maxa=100 maxn=100 |
85 | Converts decimal to Roman Numerals | The number 0 in Roman Numerals is: | MCMXXXI | decimal_to_roman_numerals | maxDecimal=4000 |
92 | Complex To Polar Form | 16.76(-5.0theta + i-16.0theta) | -1.87 | complex_to_polar | minRealImaginaryNum=-20, maxRealImaginaryNum=20 |
93 | Union,Intersection,Difference of Two Sets | Given the two sets a={9, 3, 6, 1} ,b={8, 5, 6, 7}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 3, 5, 6, 7, 8, 9},Intersection is {6}, a-b is {9, 3, 1},b-a is {8, 5, 7}, Symmetric difference is {1, 3, 5, 7, 8, 9} | set_operation | minval=3 maxval=7 n_a=4 n_b=5 |
94 | Base Conversion | Convert 21421 from base 10 to base 7. | 116311 | base_conversion | maxNum=60000 maxBase=16 |
98 | Quotient of Powers with Same Base | The Quotient of 37^1 and 37^7 = 37^(1-7) = 37^-6 | 3.897531695087292e-10 | quotient_of_power_same_base | maxBase=50 maxPower=10 |
99 | Quotient of Powers with Same Power | The Quotient of 6^4 and 29^4 = (6/29)^4 = 0.20689655172413793^4 | 0.0018323693129039236 | quotient_of_power_same_power | maxBase=50 maxPower=10 |
101 | Leap Year or Not | Year 2073 | is not a leap year | is_leap_year | minNumber=1900 maxNumber=2099 |
102 | Minute to Hour conversion | Convert 905 minutes to Hours & Minutes | 15 hours and 5 minutes | minutes_to_hours | maxMinutes=999 |
106 | signum function | signum of 316 is = | 1 | signum_function | min=-999 max=999 |
109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 32.85% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 13 pistons will contain no more than 5 rejected pistons? | 77.05 | binomial_distribution | `` |
116 | Factors of a number | Factors of 860 = | [1, 2, 4, 5, 10, 20, 43, 86, 172, 215, 430, 860] | Factors | maxVal=1000 |
121 | Product of scientific notaions | Product of scientific notations 9.64x10^-53 and 6.53x10^-8 = | 6.29x10^-60 | product_of_scientific_notations | minExpVal=-100 maxExpVal=100 |
statistics
Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
---|---|---|---|---|---|
30 | Combinations of Objects | Number of combinations from 11 objects picked 8 at a time | 165 | combinations | maxlength=20 |
42 | Permutations | Number of Permutations from 15 objects picked 2 at a time = | 210 | 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 10 = | 3/36 | dice_sum_probability | maxDice=3 |
54 | Confidence interval For sample S | The confidence interval for sample [211, 207, 299, 261, 279, 291, 237, 288, 292, 268, 260, 290, 283, 213, 251, 209, 269, 266, 295, 232, 228, 224, 205, 235, 208, 214, 254, 255, 284, 267, 227, 241, 280, 233, 212] with 99% confidence is | (263.70301611669476, 237.32555531187666) | confidence_interval | `` |
59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[39, 39, 27, 18, 40, 27, 33, 41, 13, 50, 22, 5, 11, 15, 35] | The Mean is 27.666666666666668 , Standard Deviation is 164.0888888888889, Variance is 12.809718532773813 | data_summary | number_values=15 minval=5 maxval=50 |
76 | Mean and Median | Given the series of numbers [22, 27, 33, 35, 36, 42, 45, 47, 52, 83]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 42.2 and Arithmetic median of this series is 39.0 | mean_median | maxlen=10 |
107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.87% of population have. Test sensitivity (true positive) is equal to SN= 94.26% whereas test specificity (true negative) SP= 99.52%. What is the probability that this guy really has that disease? | 78.91% | conditional_probability | `` |