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:

frommathgeneratorimportmathgen#generate an addition problemproblem, 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
worksheet = Worksheet("Worksheet title")
worksheet.add_instruction("Instructions")
# Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.
for _ in range(10):
worksheet.add_problem(mathgen.genById(1)[0])
worksheet.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 + 10 = 10	0	basic_algebra	maxVariable=10
12	Logarithm	log3(6561)	8	log	maxBase=3maxVal=8
17	Integer Multiplication with 2x2 Matrix	8 * [[3, 2], [7, 2]] =	[[24,16],[56,16]]	multiply_int_to_22_matrix	maxMatrixVal=10maxRes=100
20	Midpoint of the two point	(20,9),(19,-14)=	(19.5,-2.5)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2+8x	(x)(x+8)	factoring	range_x1=10range_x2=10
23	Solve a System of Equations in R^2	-7x + 3y = 27, -7x - 6y = 72	x = -6, y = -5	system_of_equations	range_x=10range_y=10coeff_mult_range=10
24	Distance between 2 points	Find the distance between (2, -17) and (-3, 3)	sqrt(425)	distance_two_points	maxValXY=20minValXY=-20
26	Linear Equations	8x + -9y = 284, -1x + 8y = -173	x = 13, y = -20	linear_equations	n=2varRange=20coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -6/2x - 1 and y = -4/4x + 9	(-5, 14)	intersection_of_two_lines	minM=-10maxM=10minB=-10maxB=10minDenominator=1maxDenominator=6
43	Cross Product of 2 Vectors	[14, -13, 12] X [-19, -17, 13] =	[35, -410, -485]	vector_cross	minVal=-20maxVal=20
45	Simple Interest	Simple interest for a principle amount of 8091 dollars, 10% rate of interest and for a time period of 7 years is =	5663.7	simple_interest	maxPrinciple=10000maxRate=10maxTime=10
46	Multiplication of two matrices	Multiply -1 7 -8 -4 8 -9 -2 5 and 9 2 3 -5 5 -10 5 4 -6 3 -3 3	-96 13 -37 122 -52 141	matrix_multiplication	maxVal=100max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 7x^2+122x+94=0	[-0.81, -16.62]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(-16+20j) * (17+4j) =	(-352+276j)	multiply_complex_numbers	minRealImaginaryNum=-20maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[4, -3, -16] . [3, 13, 0] =	-27	vector_dot	minVal=-20maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix([[41, 99, 20], [79, 6, 68], [18, 53, 66]]) is:	Matrix([[1604/222479, 7/569, -3306/222479], [1995/222479, -3/569, 604/222479], [-4079/444958, 1/1138, 7575/444958]])	invert_matrix	SquareMatrixDimension=3MaxMatrixElement=99OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det([[96, 4], [87, 48]]) =	4260	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 2136 dollars, 10% rate of interest and for a time period of 6 year is =	3784.05	compound_interest	maxPrinciple=10000maxRate=10maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 4x^2 + 4x + 1 = 0	simplified solution : ((-0.5, -0.5)), generalized solution : ((-4 + 0)/24, (-4 - 0)/24)	complex_quadratic	prob_type=0max_range=10
105	Combine Like terms	9x^2 + 10x^6 + 6x^1 + 2x^5 + 1x^2 + 4x^5 + 3x^4	6x^1 + 10x^2 + 3x^4 + 6x^5 + 10x^6	combine_like_terms	maxCoef=10maxExp=20maxTerms=10
111	Expanding Factored Binomial	(-3x+10)(+6x-2)	-18x^2+66x-20	expanding	range_x1=10range_x2=10range_a=10range_b=10

basic_math

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
0	Addition	6+27=	33	addition	maxSum=99maxAddend=50
1	Subtraction	32-7=	25	subtraction	maxMinuend=99maxDiff=99
2	Multiplication	7*6=	42	multiplication	maxMulti=12
3	Division	40/4=	10	division	maxA=25maxB=25
6	Square Root	sqrt(64)=	8	square_root	minNo=1maxNo=12
8	Square	6^2=	36	square	maxSquareNum=20
13	Complex Division	13/81=	0.16	complex_division	maxRes=99maxDivid=99
16	Fraction Division	(3/10)/(3/10)	1	divide_fractions	maxVal=10
28	Fraction Multiplication	(6/2)*(5/4)	15/4	fraction_multiplication	maxVal=10
31	Factorial	4! =	24	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 2/10 and 9/6?	<	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 356 up to 2 decimal places?	7.09	cube_root	minNo=1maxNo=1000
53	Exponentiation	6^5 =	7776	exponentiation	maxBase=20maxExpo=10
71	Absolute difference between two numbers		87-65	=	22
80	Percentage of a number	What is 9% of 74?	6.66	percentage	maxValue=99maxpercentage=99
90	isprime	Is 52 prime?	No	is_prime	max_num=100
97	Power of Powers	Simplify 15^6^10=	15^60	power_of_powers	maxBase=50maxPower=10
118	Percentage difference	What is the percentage difference between 111 and 173?	43.66%	percentage_difference	maxValue=200minValue=0
119	Percentage error	Find the percentage error when observed value equals -64 and exact value equals -14.	357.14%	percentage_error	maxValue=100minValue=-100
120	Greatest Common Divisor of N Numbers	GCD(326471423,856701641)=	1	greatest_common_divisor	numbersCount=2maximalNumberLimit=10**9

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	7x^7 + 3x^7 + 9x^6 + 6x^1	49x^6 + 21x^6 + 54x^5 + 6x^0	power_rule_differentiation	maxCoef=10maxExp=10maxTerms=5
48	Power Rule Integration	9x^8	(9/8)x^9 + c	power_rule_integration	maxCoef=10maxExp=10maxTerms=5
88	Differentiation	differentiate w.r.t x : d(sin(x)+9*x^(-2))/dx	cos(x) - 18/x^3	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 68x^2 + 64x + 30 is =	84.6667	definite_integral	max_coeff=100
110	Stationary Points	f(x)=5*x^3 + x^2 + 8	(-2/15,5404/675),(0,8)	stationary_points	maxExp=3maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	1110=	0001	binary_complement_1s	maxDigits=10
5	Modulo Division	4%90=	4	modulo_division	maxRes=99maxModulo=99
14	Decimal to Binary	Binary of 76=	1001100	decimal_to_binary	max_dec=99
15	Binary to Decimal	101	5	binary_to_decimal	max_dig=10
56	Fibonacci Series	The Fibonacci Series of the first 10 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13, 21, 34]	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 80th Fibonacci number?	23416728348467744	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	0111011	0x3b	binary_to_hex	max_dig=10
73	Binary 2's Complement	2's complement of 111001 =	111	binary_2s_complement	maxDigits=10
79	Decimal to Hexadecimal	Binary of 162=	0xa2	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 1566 in Octal is:	0o3036	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 8 is =	33143	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 6225 is =	1851	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: 4 18 17 =	33.67	area_of_triangle	maxA=20maxB=20
19	Triangle exists check	Does triangle with sides 6, 23 and 24 exist?	Yes	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 23 and 47 =	110	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 6 and 6 =	8.49	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 8 sides	135.0	angle_regular_polygon	minVal=3maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 2m is	24 m^2	surface_area_cube	maxSide=20unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 19m, 16m, 17m is	1798 m^2	surface_area_cuboid	maxSide=20unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 19m and radius = 7m is	1143 m^2	surface_area_cylinder	maxRadius=20maxHeight=50unit='m'
35	Volum of Cube	Volume of cube with side = 2m is	8 m^3	volume_cube	maxSide=20unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 13m, 17m, 9m is	1989 m^3	volume_cuboid	maxSide=20unit='m'
37	Volume of cylinder	Volume of cylinder with height = 11m and radius = 2m is	138 m^3	volume_cylinder	maxRadius=20maxHeight=50unit='m'
38	Surface Area of cone	Surface area of cone with height = 31m and radius = 9m is	1167 m^2	surface_area_cone	maxRadius=20maxHeight=50unit='m'
39	Volume of cone	Volume of cone with height = 10m and radius = 18m is	3392 m^3	volume_cone	maxRadius=20maxHeight=50unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 51 , 181, 49 =	79	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is tan(90)?	∞	basic_trigonometry	angles=[0, 30, 45, 60, 90]functions=['sin', 'cos', 'tan']
58	Sum of Angles of Polygon	Sum of angles of polygon with 12 sides =	1800	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 20m is	5026.548245743669 m^2	surface_area_sphere	maxSide=20unit='m'
61	Volume of Sphere	Volume of sphere with radius 56 m =	735618.5806037667 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [358.33, 666.13, 650.06, 264.35, 50.1, 338.6, 155.98, 262.18, 470.17, 681.63, 862.29, 561.78, 341.26, 551.94, 484.91, 166.68] and [721.12, 986.28, 667.31, 927.66, 834.74, 48.76, 623.8, 975.84, 466.86, 263.3, 963.54, 653.39, 313.28, 92.3, 218.0, 40.74] is:	0.67 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 39 and angle, 10. Find the area of the sector.	Area of sector = 132.73229	sector_area	maxRadius=49maxAngle=359
86	Degrees to Radians	Angle 227 in radians is =	3.96	degree_to_rad	max_deg=360
87	Radians to Degrees	Angle 0 in degrees is =	0.0	radian_to_deg	max_rad=3
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 10 and height, 21?	CSA of cylinder = 1319.47	curved_surface_area_cylinder	maxRadius=49maxHeight=99
96	Perimeter of Polygons	The perimeter of a 10 sided polygon with lengths of [109, 77, 116, 47, 36, 80, 87, 8, 117, 111]cm is:	788	perimeter_of_polygons	maxSides=12maxLength=120
104	Circumference	Circumference of circle with radius 8	50.26548245743669	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 4 and angle, 323. Find the arc length of the angle.	Arc length of the angle = 22.54965	arc_length	maxRadius=49maxAngle=359
112	Area of Circle	Area of circle with radius 62	12081.142857142857	area_of_circle	maxRadius=100
113	Volume of frustum	Volume of frustum with height = 44m and r1 = 19m is and r2 = 19m is	29995.0 m^3	volume_frustum	maxR1=20maxR2=20maxHeight=50unit='m'
114	Equation of line from two points	What is the equation of the line between points (-12,4) and (8,0) in slope-intercept form?	5y = -x + 8	equation_of_line_from_two_points	maxCoordinate=20minCoordinate=-20
115	Area of Circle given center and a point on circle	Area of circle with center (3,1) and passing through (2.35, 0.24) is	3.14	area_of_circle_given_center_and_point	maxCoordinate = 10maxRadius=10
117	Volume of Hemisphere	Volume of hemisphere with radius 22 m =	22301.119 m^3	volume_hemisphere	maxRadius=100

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 3 and 5 =	15	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 3 and 19 =	1	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 185	[5, 37]	prime_factors	minVal=1maxVal=200
40	Common Factors	Common Factors of 19 and 11 =	[1]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 16 and 13 =	1	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 41^(1/3) _ 11^(1/4)	>	surds_comparison	maxValue=100maxRoot=10
63	Profit or Loss Percent	Loss percent when CP = 769 and SP = 460 is:	40.18205461638492	profit_loss_percent	maxCP=1000maxSP=1000
66	Geometric Progression	For the given GP [12, 72, 432, 2592, 15552, 93312] ,Find the value of a,common ratio,10th term value, sum upto 7th term	The value of a is 12, common ratio is 6 , 10th term is 120932352 , sum upto 7th term is 671844.0	geometric_progression	number_values=6min_value=2max_value=12n_term=7sum_term=5
67	Geometric Mean of N Numbers	Geometric mean of 3 numbers 23 , 42 and 80 =	(234280)^(1/3) = 42.59471379666575	geometric_mean	maxValue=100maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 2 numbers 19 and 53 =	2/((1/19) + (1/53)) = 27.972222222222225	harmonic_mean	maxValue=100maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[628.9497984743637, 413.7025276967905, 55.08325175633222, 543.4734094406972, 407.4510705587269, 568.7990971658147, 407.9155106455502, 474.20039089590216, 720.3486866530783, 514.2113795291383, 273.3258978495645, 488.8393919190255, 897.4344293916904, 541.0117215640587] is:	1985.1961648306578	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert 89 degrees Celsius to degrees Fahrenheit =	192.20000000000002	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 81 of the AP series: 24, 104, 184 ...	6424	arithmetic_progression_term	maxd=100maxa=100maxn=100
83	AP Sum Calculation	Find the sum of first 73 terms of the AP series: -98, -140, -182 ...	-117530.0	arithmetic_progression_sum	maxd=100maxa=100maxn=100
85	Converts decimal to Roman Numerals	The number 0 in Roman Numerals is:	MMMDXXXIX	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	5.1(-1.0theta + i5.0theta)	1.77	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={1, 4, 5, 6, 9} ,b={2, 3, 5, 6, 7, 8}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 3, 4, 5, 6, 7, 8, 9},Intersection is {5, 6}, a-b is {1, 4, 9},b-a is {8, 2, 3, 7}, Symmetric difference is {1, 2, 3, 4, 7, 8, 9}	set_operation	minval=3maxval=7n_a=4n_b=5
94	Base Conversion	Convert 40122 from base 5 to base 15.	B42	base_conversion	maxNum=60000maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 43^10 and 43^1 = 43^(10-1) = 43^9	502592611936843	quotient_of_power_same_base	maxBase=50maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 1^7 and 1^7 = (1/1)^7 = 1.0^7	1.0	quotient_of_power_same_power	maxBase=50maxPower=10
101	Leap Year or Not	Year 1986	is not a leap year	is_leap_year	minNumber=1900maxNumber=2099
102	Minute to Hour conversion	Convert 446 minutes to Hours & Minutes	7 hours and 26 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of 941 is =	1	signum_function	min=-999max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 37.08% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 15 pistons will contain no more than 5 rejected pistons?	49.63	binomial_distribution	``
116	Factors of a number	Factors of 661 =	[1, 661]	Factors	maxVal=1000
121	Product of scientific notaions	Product of scientific notations 7.65x10^-75 and 5.51x10^-50 =	4.22x10^-124	product_of_scientific_notations	minExpVal=-100maxExpVal=100

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 15 objects picked 3 at a time	455	combinations	maxlength=20
42	Permutations	Number of Permutations from 16 objects picked 9 at a time =	4151347200	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 12 =	1/36	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [234, 254, 283, 218, 205, 251, 282, 228, 280, 202, 268, 220, 273, 277, 267, 249, 285, 208, 225, 266, 274, 235, 223, 226, 245, 200, 213, 221, 298, 236, 288, 231, 222, 299, 243, 242, 255] with 90% confidence is	(254.32591454896394, 238.97138274833335)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[23, 20, 35, 38, 24, 41, 6, 7, 26, 37, 49, 12, 15, 31, 12]	The Mean is 25.066666666666666 , Standard Deviation is 162.32888888888888, Variance is 12.740835486297156	data_summary	number_values=15minval=5maxval=50
76	Mean and Median	Given the series of numbers [2, 8, 9, 14, 16, 17, 35, 47, 55, 74]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 27.7 and Arithmetic median of this series is 16.5	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 0.90% of population have. Test sensitivity (true positive) is equal to SN= 98.84% whereas test specificity (true negative) SP= 90.89%. What is the probability that this guy really has that disease?	8.97%	conditional_probability	``