/mathgenerator

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 needs.

Primary LanguagePythonMIT LicenseMIT

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

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 id id 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
11 Basic Algebra 5x + 5 = 7 2/5 basic_algebra maxVariable=10
12 Logarithm log3(6561) 8 log maxBase=3 maxVal=8
17 Integer Multiplication with 2x2 Matrix 10 * [[10, 8], [9, 1]] = [[100,80],[90,10]] multiply_int_to_22_matrix maxMatrixVal=10 maxRes=100
20 Midpoint of the two point (-8,12),(8,-12)= (0.0,0.0) midpoint_of_two_points maxValue=20
21 Factoring Quadratic x^2-25 (x+5)(x-5) factoring range_x1=10 range_x2=10
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
24 Distance between 2 points Find the distance between (-3, 21) and (17, 3) sqrt(724) distance_two_points maxValXY=20 minValXY=-20
26 Linear Equations 11x + -13y = -389, 16x + -11y = -463 x = -20, y = 13 linear_equations n=2 varRange=20 coeffRange=20
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
43 Cross Product of 2 Vectors [11, 8, 9] X [-20, 11, -12] = [-195, -48, 281] vector_cross minVal=-20 maxVal=20
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
46 Multiplication of two matrices Multiply
-1-501
8-8109
-88-57
1-51-3
and
1-2
5-2
5-2
9-1
-1711
99-29
703
-469
 matrix_multiplication maxVal=100 max_dim=10
50 Quadratic Equation Zeros of the Quadratic Equation 38x^2+176x+57=0 [-0.35, -4.28] quadratic_equation maxVal=100
65 Multiplication of 2 complex numbers (13+14j) * (-20-11j) = (-106-423j) multiply_complex_numbers minRealImaginaryNum=-20 maxRealImaginaryNum=20
72 Dot Product of 2 Vectors [0, 18, -7] . [-11, -12, 14] = -314 vector_dot minVal=-20 maxVal=20
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
77 Determinant to 2x2 Matrix Det([[27, 0], [66, 78]]) = 2106 int_matrix_22_determinant maxMatrixVal=100
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
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
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
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 notations 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 ``