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://todarith.ml/generate/

If you have an idea for a generator, please add it as an issue and tag it with the "New Generator" label.

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)

More Complicated Usage

import sys
from mathgenerator import mathgen

worksheet = mathgen.make_worksheet("2020-11-29")
mathgen.add_section_with_task_to_worksheet(worksheet, 105, 5)
mathgen.add_section_with_task_to_worksheet(worksheet, 2, 5)
mathgen.write_pdf(worksheet)

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]

• make_pdf(id, count) creates a printable pdf worksheet with count problems generated by the generator with id id.

List of Generators

algebra

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
11	Basic Algebra	9x + 6 = 6	0	basic_algebra	maxVariable=10
12	Logarithm	log2(256)	8	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	1 * 3, 1], [10, 1 =	3,1],[10,1	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	(-19,-5),(-10,-3)=	(-14.5,-4.0)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2-18x+81	(x-9)(x-9)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	-3x + 4y = -12, -x + 10y = 22	x = 8, y = 3	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (3, 7) and (-20, -18)	sqrt(1154)	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	6x + -13y = 111, 2x + -4y = 36	x = 12, y = -3	linear_equations	n=2 varRange=20 coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -8/4x - 7 and y = -7/3x + 4	(33, -73)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[1, 7, -1] X [-5, 8, 19] =	[141, -14, 43]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 5581 dollars, 1% rate of interest and for a time period of 8 years is =	446.48	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply 3 -7 -9 -9 -2 5 -4 10 and 9 -2 10 -8 -3 10 -9 1 5 3 0 3 0 3 -10 0	3 -130 183 -58 -53 72 -165 9	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 98x^2+108x+23=0	[-0.29, -0.81]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(8+10j) * (-7+4j) =	(-96-38j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[-3, -8, 2] . [15, 7, -6] =	-113	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix(60, 59, 5], [64, 13, 45], [54, 19, 35) is:	Matrix(20/511, 197/1022, -37/146], [-19/1022, -183/1022, 17/73], [-257/5110, -1023/5110, 107/365)	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det(38, 27], [91, 58) =	-253	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 5669 dollars, 4% rate of interest and for a time period of 8 year is =	7758.42	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 3x^2 + 9x + 4 = 0	simplified solution : ((-0.543, -2.457)), generalized solution : ((-9 + sqrt(33))/23, (-9 - sqrt(33))/23)	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	7x^1	7x^1	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(8x-5)(-3x-3)	-24x^2-9x+15	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	33+15=	48	addition	maxSum=99 maxAddend=50
1	Subtraction	5-5=	0	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	1*11=	11	multiplication	maxMulti=12
3	Division	384/16=	24	division	maxA=25 maxB=25
6	Square Root	sqrt(49)=	7	square_root	minNo=1 maxNo=12
8	Square	13^2=	169	square	maxSquareNum=20
13	Complex Division	89/11=	8.09	complex_division	maxRes=99 maxDivid=99
16	Fraction Division	(2/9)/(3/4)	8/27	divide_fractions	maxVal=10
28	Fraction Multiplication	(3/8)*(10/8)	15/32	fraction_multiplication	maxVal=10
31	Factorial	2! =	2	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 9/8 and 10/7?	<	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 183 up to 2 decimal places?	5.68	cube_root	minNo=1 maxNo=1000
53	Exponentiation	20^6 =	64000000	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers		-67--16	=	51
80	Percentage of a number	What is 24% of 74?	17.76	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 50 prime?	No	is_prime	max_num=100
97	Power of Powers	Simplify 48^7^6=	48^42	power_of_powers	maxBase=50 maxPower=10

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	7x^2 + 7x^3 + 5x^9 + 4x^1	14x^1 + 21x^2 + 45x^8 + 4x^0	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	4x^6 + 1x^9 + 8x^1 + 1x^8	(4/6)x^7 + (1/9)x^10 + (8/1)x^2 + (1/8)x^9 + c	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Differentiation	differentiate w.r.t x : d(sin(x)+8*x^3)/dx	24*x^2 + cos(x)	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 62x^2 + 93x + 81 is =	148.1667	definite_integral	max_coeff=100
110	Stationary Points	f(x)=9x^3 + 3x^2 + 4	(-2/9,328/81),(0,4)	stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	01000=	10111	binary_complement_1s	maxDigits=10
5	Modulo Division	64%42=	22	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 63=	111111	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 14 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233]	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 67th Fibonacci number?	44945570212853	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	0111111	0x3f	binary_to_hex	max_dig=10
73	Binary 2's Complement	2's complement of 10 =	10	binary_2s_complement	maxDigits=10
79	Decimal to Hexadecimal	Binary of 169=	0xa9	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 3744 in Octal is:	0o7240	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 1 is =	5924	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 3461 is =	1385	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 7 16 =	44.49719092257398	area_of_triangle	maxA=20 maxB=20 maxC=20
19	Triangle exists check	Does triangle with sides 32, 44 and 10 exist?	No	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 24 and 46 =	110	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 13 and 10 =	16.40	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 3 sides	60.0	angle_regular_polygon	minVal=3 maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 15m is	1350 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 6m, 11m, 3m is	234 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 38m and radius = 2m is	502 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volum of Cube	Volume of cube with side = 3m is	27 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 6m, 14m, 3m is	252 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 12m and radius = 16m is	9650 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 2m and radius = 5m is	163 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 31m and radius = 8m is	2077 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 166 , 68, 65 =	61	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is sin(0)?	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 10 sides =	1440	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 13m is	2123.7166338267 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 33 m =	150532.55358940852 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [373.03, 280.56, 51.12, 848.19, 914.96, 636.42, 936.04, 218.18, 727.01, 248.11] and [696.71, 8.09, 219.08, 466.57, 583.92, 152.82, 964.12, 686.21, 400.77, 343.46] is:	0.56 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 45 and angle, 145. Find the area of the sector.	Area of sector = 2562.36151	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 196 in radians is =	3.42	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, 16 and height, 21?	CSA of cylinder = 2111.15	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 5 sided polygon with lengths of [13, 84, 9, 97, 119]cm is:	322	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 48	301.59289474462014	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 16 and angle, 326. Find the arc length of the angle.	Arc length of the angle = 91.03637	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 44	6084.571428571428	area_of_circle	maxRadius=100

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 1 and 15 =	15	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 3 and 3 =	3	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 167	[167]	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 55 and 33 =	[1, 11]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 16 and 9 =	1	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 62^(1/7) _ 74^(1/6)	<	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Loss percent when CP = 704 and SP = 134 is:	80.9659090909091	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [8, 40, 200, 1000, 5000, 25000] ,Find the value of a,common ratio,8th term value, sum upto 11th term	The value of a is 8, common ratio is 5 , 8th term is 625000 , sum upto 11th term is 97656248.0	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 4 numbers 66 , 46 , 28 , 54 =	(664628*54)^(1/4) = 46.2874642463462	geometric_mean	maxValue=100 maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 4 numbers 74 , 59 , 47 , 36 =	4/((1/74) + (1/59) + (1/47) + (1/36)) = 50.30368360304657	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[118.69308620957398, 418.5316709436745, 529.1318417822414, 545.3215860464462, 387.999979078107, 298.1451264197782, 392.3895332994427, 833.7453539560848, 555.724882920332, 472.05768476591004, 214.55377537613495, 760.9785260761229, 448.91380437418314, 73.27333213603282, 791.8291233802007, 918.6577753538513] is:	2165.5845872381433	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert -12 degrees Celsius to degrees Fahrenheit =	10.399999999999999	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 29 of the AP series: -80, -71, -62 ...	172	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 64 terms of the AP series: -94, -6, 82 ...	171392.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 3026 in Roman Numerals is:	MMMXXVI	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	rexp(itheta) =	26.91exp(i-2.3)	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={1, 6, 7, 8, 9} ,b={1, 3, 4, 5, 10}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 3, 4, 5, 6, 7, 8, 9, 10},Intersection is {1}, a-b is {8, 9, 6, 7},b-a is {10, 3, 4, 5}, Symmetric difference is {3, 4, 5, 6, 7, 8, 9, 10}	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert A201 from base 14 to base 10.	27833	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 42^7 and 42^6 = 42^(7-6) = 42^1	42	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 31^10 and 37^10 = (31/37)^10 = 0.8378378378378378^10	0.17045105659000342	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Year 1999	is not a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 851 minutes to Hours & Minutes	14 hours and 11 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of 525 is =	1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 40.41% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 11 pistons will contain no more than 4 rejected pistons?	52.15	binomial_distribution	``

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 15 objects picked 1 at a time	15	combinations	maxlength=20
42	Permutations	Number of Permutations from 11 objects picked 8 at a time =	6652800	permutation	maxlength=20
52	Probability of a certain sum appearing on faces of dice	If 1 dice are rolled at the same time, the probability of getting a sum of 5 =	1/6	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [214, 235, 201, 238, 244, 219, 266, 234, 298, 258, 255, 254, 243, 220, 223, 215, 209, 225, 296, 252, 267, 248, 262, 226, 205, 211, 265] with 99% confidence is	(252.7166888228517, 227.50553339937053)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[31, 36, 35, 21, 38, 20, 19, 11, 37, 31, 24, 19, 18, 15, 17]	The Mean is 24.8 , Standard Deviation is 75.22666666666666, Variance is 8.673330771201261	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [32, 87, 22, 86, 92, 17, 57, 68, 82, 94]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 63.7 and Arithmetic median of this series is 75.0	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.78% of population have. Test sensitivity (true positive) is equal to SN= 96.47% whereas test specificity (true negative) SP= 92.86%. What is the probability that this guy really has that disease?	19.67%	conditional_probability	``