mathgenerator

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.

Table of Contents

• Installation
• Usage
• List of Generators
  • algebra
  • basic_math
  • calculus
  • computer_science
  • geometry
  • misc
  • statistics

Installation

The project can be install via pip

pip install mathgenerator

Usage

Here is an example of how you would generate an addition problem:

import mathgenerator

#generate an addition problem
problem, solution = mathgenerator.addition()

#another way to generate an addition problem using genById()
problem, solution = mathgenerator.genById(0)

You may prefer to use import mathgenerator as mg and run functions like mg.addition() so that you don't have to type as much.

Problem/solution pairs are generated with either:

• mathgenerator.<generator_name>() - generates a problem, solution set from the given generator name.
• mathgenerator.genById(id) - generates a problem, solution set with generator id provided by the id parameter

You can also use getGenList() to return a list of all generators included in the library in the format:

[id, title, gen_func, funcname, subjectname, kwargs]

List of Generators

algebra

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
11	Basic Algebra	9x + 9 = 9	0	basic_algebra	maxVariable=10
12	Logarithm	log_{2}(256)=	8	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	2 * \begin{bmatrix} 8 & 0 \\ 10 & 10 \end{bmatrix} =	\begin{bmatrix} 16 & 0 \\ 20 & 20 \end{bmatrix}	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	The midpoint of (7,5) and (-17,14) =	(-5.0,9.5)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2-2x	(x)(x-2)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	Given 4x - 6y = 36 and 9x - 2y = 12, solve for x and y.	x = 0, y = -6	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (7, -15) and (0, -1)	\sqrt{245}	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	Given the equations -3x + 10y = -140 and -3x + -4y = -28, solve for x and y	x = 20, y = -8	linear_equations	n=2 varRange=20 coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = 9/3x - 6 and y = 1/3x + 6	(9/2, 15/2)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[-18, 0, 20] \times [-16, -5, 0] =	[100, -320, 90]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 9080 dollars, $3$% rate of interest and for a time period of 6 years is =	1634.4	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply$\begin{bmatrix}0&-1&-9&1\-10&4&3&-10\end{bmatrix}$and$\begin{bmatrix}-4&-2&-4\8&-1&2\-2&6&-5\-10&7&5\end{bmatrix}$	\begin{bmatrix}0&-46&48\\166&-36&-17\end{bmatrix}	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	What are the zeros of the quadratic equation 24x^2+103x+26=0	{-0.27, -4.02}	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(17+1j) * (17-1j) =	(290+0j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[9, 14, -19]\cdot[-8, -9, 10]=	-388	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix \begin{bmatrix} 0 & 0 & 1 \\ 1 & 3 & 3 \\ 1 & 2 & 2 \end{bmatrix} is:	\begin{bmatrix} 0 & -2 & 3 \ -1 & 1 & -1 \ 1 & 0 & 0 \end{bmatrix}	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=True
77	Determinant to 2x2 Matrix	\det \begin{bmatrix} 24 & 94 \\ 21 & 29 \end{bmatrix}=	-1278	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 2004 dollars, $1$% rate of interest and for a time period of 5 years is =	2106.22	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 7x^2 + 7x + 1 = 0	((-0.173, -0.827)) = (\frac{-7 + \sqrt{21}}{2*7}, (\frac{-7 - \sqrt{21}}{2*7})	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	4x^{13} + 1x^{16}	4x^{13} + 1x^{16}	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(-10x-2)(-1x+6)	10x^2-58x-12	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	40+14=	54	addition	maxSum=99 maxAddend=50
1	Subtraction	12-2=	10	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	7\cdot8	56	multiplication	maxMulti=12
3	Division	92\div23=	4	division	maxA=25 maxB=25
6	Square Root	\sqrt{1}=	1	square_root	minNo=1 maxNo=12
8	Square	9^2=	81	square	maxSquareNum=20
13	Fraction to Decimal	84\div6=	14.0	fraction_to_decimal	maxRes=99 maxDivid=99
16	Fraction Division	\frac{6}{7}\div\frac{9}{5}=	\frac{10}{21}	divide_fractions	maxVal=10
28	Fraction Multiplication	\frac{3}{9}\cdot\frac{7}{6}=	\frac{7}{18}	fraction_multiplication	maxVal=10
31	Factorial	5! =	120	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between \frac{3}{5} and \frac{3}{9}?	>	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of: \sqrt[3]{30}= to 2 decimal places?	3.11	cube_root	minNo=1 maxNo=1000
53	Exponentiation	4^1 =	4	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers	$	22--59	=$	81
80	Percentage of a number	What is $5$% of 18?	0.90	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 73 prime?	Yes	is_prime	max_num=100
97	Power of Powers	Simplify 31^{8^{2}}	31^{16}	power_of_powers	maxBase=50 maxPower=10
118	Percentage difference	What is the percentage difference between 66 and 7?	$161.64$%	percentage_difference	maxValue=200 minValue=0
119	Percentage error	Find the percentage error when observed value equals -44 and exact value equals -26.	69.23\%	percentage_error	maxValue=100 minValue=-100
120	Greatest Common Divisor of N Numbers	GCD(860597057,541815762)=	1	greatest_common_divisor	numbersCount=2 maximalNumberLimit=10**9
124	Is Composite	Is 144 composite?	Yes	is_composite	maxNum=250

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	2x^{6} + 5x^{4} + 6x^{4} + 9x^{4}	12x^{5} + 20x^{3} + 24x^{3} + 36x^{3}	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	8x^{1} + 1x^{9} + 5x^{1}	\frac{8}{1}x^{2} + \frac{1}{9}x^{10} + \frac{5}{1}x^{2} + C	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Trigonometric Differentiation	\frac{d}{dx}(\sin)=	\cos	trig_differentiation
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 24x^2 + 93x + 13 =	67.5	definite_integral	max_coeff=100
110	Stationary Points	f(x)=10*x^3 + 8*x^2 + 2*x + 5	{- \frac{1}{3}, - \frac{1}{5}}	stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	010 =	101	binary_complement_1s	maxDigits=10
5	Modulo Division	84 % 20 =	4	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 49 =	110001	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 {n} numbers is ?	0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 74th Fibonacci number?	1304969544928660	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	11010100	0xd4	binary_to_hex	max_dig=10
73	Binary 2's Complement	2's complement of 1 =	1	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 {x} in Octal is:	0o5206	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 3 is =	12440	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 6981 =	11145	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: 5, 15 11 =	19.14	area_of_triangle	maxA=20 maxB=20
19	Triangle exists check	Does triangle with sides 20, 17 and 29 exist?	Yes	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 1 and 86 =	93	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	What is the hypotenuse of a right triangle given the other two sides have lengths 18 and 9?	20.12	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 7 sides	128.57	angle_regular_polygon	minVal=3 maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 17m is	1734 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides of lengths: 9m, 11m, 20m is	998 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 25m and radius = 18m is	4863 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volume of Cube	Volume of cube with a side length of 13m is	2197 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 2m, 6m, 18m is	216 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 28m and radius = 5m is	2199 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 37m and radius = 15m is	2588 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 17m and radius = 1m is	17 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 108 , 35, 117 =	100	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	\tan(0) =	0	basic_trigonometry	angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan']
58	Sum of Angles of Polygon	What is the sum of interior angles of a polygon with 5 sides?	540	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 14m is	2463.0086404143976 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 12 m =	7238.229473870882 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [90.18, 778.39, 6.95, 189.4, 402.86] and [937.62, 966.01, 986.87, 311.51, 725.29] is:	0.77 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	What is the area of a sector with radius 27 and angle 340 degrees?	2162.99	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 50 degrees in radians is:	0.87	degree_to_rad	max_deg=360
87	Radians to Degrees	Angle 1.14 radians in degrees is:	65.32	radian_to_deg	max_rad=6.28
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 42 and height, 28?	7389.03	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 11 sided polygon with lengths of $16, 109, 106, 37, 3, 59, 49, 1, 88, 43, 42$cm is:	553	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 37 =	232.48	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 49 and angle, 13. Find the arc length of the angle.	Arc length of the angle = 11.11775	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 92=	26590.44	area_of_circle	maxRadius=100
113	Volume of frustum	Volume of frustum with height = 33m and r1 = 7m is and r2 = 7m is	6669.0 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 (20,7) and (-12,12) in slope-intercept form?	32y = -5x + 324	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 (-8,9) and passing through (-4.0, 9.0) is	50.27	area_of_circle_given_center_and_point	maxCoordinate = 10 maxRadius=10
117	Volume of Hemisphere	Volume of hemisphere with radius 25 m =	32724.923 m^3	volume_hemisphere	maxRadius=100
122	Volume of pyramid	Volume of pyramid with base length = 3 m, base width = 1 m and height = 2 m is	2.0 m^3	volume_pyramid	maxLength=20 maxWidth=20 maxHeight=50 unit='m'
123	Surface area of pyramid	Surface area of pyramid with base length = 6m, base width = 6m, and height = 4m is	96 m^2	surface_area_pyramid	unit='m'
125	Complementary and Supplementary Angle	The supplementary angle of 48 =	132	complementary_and_supplementary_angle	maxSupp=180 maxComp=90

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 11 and 12 =	132	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 20 and 9 =	1	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 84	2, 2, 3, 7	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 7 and 44 =	[1]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 13 and 5 =	1	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 23^{\frac{1}{9}} _ 63^{\frac{1}{2}}	<	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Profit percent when CP = 145 and SP = 782 is:	439.31	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [3, 36, 432, 5184, 62208, 746496]. Find the value of a common ratio, 10th term value, sum upto 10th term	The value of a is 3, common ratio is 12 , 10th term is 15479341056, sum upto 10th term is 16886553879.0	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 [15, 90, 74] =	46.4	geometric_mean	maxValue=100 maxCount=4
68	Harmonic Mean of N Numbers	Harmonic mean of 4 numbers 4, 94, 70, 14 =	40.42123738481791	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector [667.6348977529038, 679.4272834518646, 255.59424823283462, 642.7158651607829, 619.0578738657584, 693.3434890856785, 107.39417747607006] is:	1503.75	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert 2 degrees Celsius to degrees Fahrenheit	35.6	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find term number 67 of the AP series: 56, 133, 210 ...	5138	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 54 terms of the AP series: 83, 42, 1 ...	-54189.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 0 in Roman Numerals is:	MMCCCLVI	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	17.12(2.0\theta + i17.0\theta)	1.45	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={2, 6, 8, 9, 10}, $b={8, 10, 4}. Find the Union, intersection, a-b, b-a, and symmetric difference	Union is {2, 4, 6, 8, 9, 10}. Intersection is {8, 10}, a-b is {9, 2, 6}, b-a is {4}. Symmetric difference is {2, 4, 6, 9}.	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert 56371 from base 10 to base 5.	3300441	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 17^{1} and $17^{9} = 17^{1-9} = 17^{-8}	1.4335360832968505e-10	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 33^{4} and 23^{4} = (33/23)^4 = 1.434782608695652^{4}	4.237838629793346	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Is 1906 a leap year?	1906 is not a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 381 minutes to hours & minutes	6 hours and 21 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of 985 is =	1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, $34.46$% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 10 pistons will contain no more than 8 rejected pistons?	99.95	binomial_distribution	``
116	Factors of a number	Factors of 949 =	[1, 13, 73, 949]	factors	maxVal=1000
121	Product of scientific notations	Product of scientific notations 7.83 \times 10^{-39} and 6.12 \times 10^{-95} =	4.79 \times 10^{-133}	product_of_scientific_notations	minExpVal=-100 maxExpVal=100

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Find the number of combinations from 14 objects picked 6 at a time.	3003	combinations	maxlength=20
42	Permutations	Number of Permutations from 17 objects picked 6 at a time is:	8910720	permutation	maxlength=20
52	Probability of a certain sum appearing on faces of dice	If 3 dice are rolled at the same time, the probability of getting a sum of 3 =	\frac{1}{216}	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [226, 260, 221, 245, 282, 274, 207, 299, 257, 211, 233, 239, 206, 208, 242, 224, 265, 287, 230, 276, 256, 237, 215, 291, 216, 251, 255, 229, 279, 275, 210, 203, 220, 292] with $95$% confidence is	(254.41804694839914, 235.052541286895)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data 48, 38, 10, 5, 24, 46, 50, 17, 20, 13, 17, 14, 5, 20, 34	The Mean is 24.066666666666666, Standard Deviation is 220.0622222222222, Variance is 14.834494336586678	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [6, 30, 32, 39, 42, 65, 72, 80, 84, 85]. Find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 53.5 and Arithmetic median of this series is 53.5	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.26\% of the population have. Test sensitivity (true positive) is equal to $SN=93.71$% whereas test specificity (true negative) SP=90.62\%. What is the probability that this guy really has that disease?	$11.31$%	conditional_probability	``