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

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	7x + 5 = 8	3/7	basic_algebra	maxVariable=10
12	Logarithm	log2(16)	4	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	12 * 6, 0], [5, 8 =	72,0],[60,96	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	(-13,12),(9,19)=	(-2.0,15.5)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2-6x-40	(x-10)(x+4)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	-5x + 2y = 40, -10x + 7y = 80	x = -8, y = 0	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (-8, -12) and (11, -8)	sqrt(377)	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	-5x + -19y = 155, 3x + -15y = 39	x = -12, y = -5	linear_equations	n=2 varRange=20 coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -7x + 9 and y = -10/2x + 6	(3/2, -3/2)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[14, 14, 17] X [-20, -1, 14] =	[213, -536, 266]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 2241 dollars, 8% rate of interest and for a time period of 6 years is =	1075.68	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply -10 1 8 2 4 7 -8 -2 3 7 5 -8 and -7 -2 0 10 4 10 -10 7	82 124 -40 -32 79 58	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 43x^2+171x+71=0	[-0.47, -3.51]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(-6+1j) * (15+20j) =	(-110-105j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[1, -3, 12] . [10, 18, 7] =	40	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix(63, 26, 31], [41, 88, 53], [23, 17, 73) is:	Matrix(1841/86896, -457/86896, -225/43448], [-887/130344, 1943/130344, -517/65172], [-1327/260688, -473/260688, 2239/130344)	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det(83, 6], [16, 95) =	7789	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 9301 dollars, 9% rate of interest and for a time period of 3 year is =	12045.06	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation x^2 + 7x + 2 = 0	simplified solution : ((-0.298, -6.702)), generalized solution : ((-7 + sqrt(41))/21, (-7 - sqrt(41))/21)	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	4x^3 + 4x^1 + 8x^1 + 9x^5 + 7x^4 + 9x^3 + 6x^5	12x^1 + 13x^3 + 7x^4 + 15x^5	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(-9x-1)(-10x-1)	90x^2+19x+1	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	27+42=	69	addition	maxSum=99 maxAddend=50
1	Subtraction	8-0=	8	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	12*4=	48	multiplication	maxMulti=12
3	Division	130/13=	10	division	maxA=25 maxB=25
6	Square Root	sqrt(36)=	6	square_root	minNo=1 maxNo=12
8	Square	10^2=	100	square	maxSquareNum=20
13	Complex Division	55/4=	13.75	complex_division	maxRes=99 maxDivid=99
16	Fraction Division	(9/8)/(8/10)	45/32	divide_fractions	maxVal=10
28	Fraction Multiplication	(4/1)*(10/2)	20	fraction_multiplication	maxVal=10
31	Factorial	6! =	720	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 4/5 and 7/9?	>	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 835 up to 2 decimal places?	9.42	cube_root	minNo=1 maxNo=1000
53	Exponentiation	2^5 =	32	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers		2--88	=	90
80	Percentage of a number	What is 65% of 80?	52.00	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 26 prime?	No	is_prime	max_num=100
97	Power of Powers	Simplify 34^9^10=	34^90	power_of_powers	maxBase=50 maxPower=10

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	8x^8 + 10x^7 + 1x^8 + 10x^6	64x^7 + 70x^6 + 8x^7 + 60x^5	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	1x^5 + 9x^4 + 3x^9 + 4x^8	(1/5)x^6 + (9/4)x^5 + (3/9)x^10 + (4/8)x^9 + c	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Differentiation	differentiate w.r.t x : d(cot(x)+7*x^(-3))/dx	-cot(x)^2 - 1 - 21/x^4	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 91x^2 + 2x + 25 is =	56.3333	definite_integral	max_coeff=100
110	Stationary Points	f(x)=7x^3 + 3x^2 + 4*x		stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	0010100=	1101011	binary_complement_1s	maxDigits=10
5	Modulo Division	34%7=	6	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 35=	100011	decimal_to_binary	max_dec=99
15	Binary to Decimal	1110	14	binary_to_decimal	max_dig=10
56	Fibonacci Series	The Fibonacci Series of the first 12 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 78th Fibonacci number?	8944394323791488	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 1 =	1	binary_2s_complement	maxDigits=10
79	Decimal to Hexadecimal	Binary of 406=	0x196	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 3398 in Octal is:	0o6506	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 5 is =	21877	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 8241 is =	2031	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: 7 5 8 =	17.320508075688775	area_of_triangle	maxA=20 maxB=20 maxC=20
19	Triangle exists check	Does triangle with sides 1, 10 and 7 exist?	No	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 41 and 4 =	135	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 18 and 9 =	20.12	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 18 sides	160.0	angle_regular_polygon	minVal=3 maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 1m is	6 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 11m, 9m, 14m is	758 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 32m and radius = 11m is	2971 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volum of Cube	Volume of cube with side = 2m is	8 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 16m, 20m, 16m is	5120 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 5m and radius = 3m is	141 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 7m and radius = 20m is	2588 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 11m and radius = 15m is	2591 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 154 , 53, 132 =	21	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is cos(60)?	1/2	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 = 3m is	113.09733552923255 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 78 m =	1987798.7692617911 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [997.76, 915.16, 886.73, 65.66, 59.48, 928.61, 268.24, 889.07, 302.53, 894.95] and [457.87, 988.95, 229.31, 312.49, 386.73, 822.4, 888.11, 849.72, 366.12, 582.06] is:	0.54 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 48 and angle, 145. Find the area of the sector.	Area of sector = 2915.39798	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 5 in radians is =	0.09	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, 22 and height, 58?	CSA of cylinder = 8017.34	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 12 sided polygon with lengths of [59, 37, 45, 116, 15, 97, 52, 45, 37, 89, 98, 71]cm is:	761	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 19	119.38052083641213	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 40 and angle, 74. Find the arc length of the angle.	Arc length of the angle = 51.66175	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 3	28.285714285714285	area_of_circle	maxRadius=100
113	Volume of frustum	Volume of frustum with height = 23m and r1 = 19m is and r2 = 19m is	15679.0 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,-11) and (-4,20) in slope-intercept form?	15y = 31x + 424	equation_of_line_from_two_points	maxCoordinate=20 minCoordinate=-20
115	Area of circle given center and a point on it	Area of circle with center (2,9) and passing through (12.0, 9.0) is?	314.16	area_of_circle_given_center_and_point	maxCoordinate=10 maxRadius=10

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 17 and 1 =	17	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 4 and 10 =	2	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 65	[5, 13]	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 2 and 96 =	[1, 2]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 3 and 3 =	3	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 10^(1/9) _ 81^(1/1)	<	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Loss percent when CP = 776 and SP = 765 is:	1.4175257731958764	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [11, 44, 176, 704, 2816, 11264] ,Find the value of a,common ratio,7th term value, sum upto 11th term	The value of a is 11, common ratio is 4 , 7th term is 45056 , sum upto 11th term is 15379111.0	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 81 , 86 and 10 =	(818610)^(1/3) = 41.14601910222523	geometric_mean	maxValue=100 maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 16 , 8 and 90 =	3/((1/16) + (1/8) + (1/90)) = 15.104895104895105	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[713.3697155960601, 113.23693566589287, 110.16552790278855, 394.36588841562923, 761.5268202733965, 323.174835097221, 636.0137791095572] is:	1333.5135737837843	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert -4 degrees Celsius to degrees Fahrenheit =	24.8	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 36 of the AP series: -59, -150, -241 ...	-3244	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 58 terms of the AP series: 60, 71, 82 ...	21663.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 0 in Roman Numerals is:	MMMCCI	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	16.28(-16.0theta + i3.0theta)	2.96	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={8, 10, 4} ,b={2, 3, 6, 7}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {2, 3, 4, 6, 7, 8, 10},Intersection is set(), a-b is {8, 10, 4},b-a is {2, 3, 6, 7}, Symmetric difference is {2, 3, 4, 6, 7, 8, 10}	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert 101743 from base 8 to base 16.	83E3	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 19^9 and 19^4 = 19^(9-4) = 19^5	2476099	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 1^5 and 11^5 = (1/11)^5 = 0.09090909090909091^5	6.209213230591552e-06	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Year 2084	is a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 525 minutes to Hours & Minutes	8 hours and 45 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of 17 is =	1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 32.13% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 14 pistons will contain no more than 1 rejected pistons?	3.36	binomial_distribution	``

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 16 objects picked 8 at a time	12870	combinations	maxlength=20
42	Permutations	Number of Permutations from 14 objects picked 0 at a time =	1	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 [297, 220, 227, 267, 249, 243, 258, 209, 203, 276, 239, 241, 283, 226, 246, 240, 273, 222, 254, 290, 244, 225, 286, 228, 296, 233, 238, 229, 264, 210, 235, 298, 256, 223, 242, 202] with 90% confidence is	(253.8057739042855, 239.0831149846034)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[17, 28, 12, 9, 29, 46, 19, 37, 49, 46, 7, 45, 8, 17, 9]	The Mean is 25.2 , Standard Deviation is 232.29333333333332, Variance is 15.241172308367009	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [4, 25, 30, 45, 46, 49, 69, 70, 71, 95]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 50.4 and Arithmetic median of this series is 47.5	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.46% of population have. Test sensitivity (true positive) is equal to SN= 95.64% whereas test specificity (true negative) SP= 97.97%. What is the probability that this guy really has that disease?	41.11%	conditional_probability	``