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	7x + 7 = 8	1/7	basic_algebra	maxVariable=10
12	Logarithm	log2(2)	1	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	4 * 2, 8], [2, 1 =	8,32],[8,4	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	(-11,18),(-9,12)=	(-10.0,15.0)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2-9x+20	(x-4)(x-5)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	-7x - y = -36, 9x + = 45	x = 5, y = 1	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (-6, 11) and (-10, -6)	sqrt(305)	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	-14x + 15y = -27, -5x + 7y = -31	x = -12, 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 = -2/6x - 3 and y = -9/5x + 1	(30/11, -43/11)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[-19, 0, 17] X [-14, 6, 12] =	[-102, -10, -114]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 6110 dollars, 1% rate of interest and for a time period of 8 years is =	488.8	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply 7 -3 -9 -2 -5 0 and 1 1 -3 4	16 -5 -3 -17 -5 -5	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 85x^2+103x+6=0	[-0.06, -1.15]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(-19-19j) * (-13+6j) =	(361+133j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[14, 16, 18] . [-18, -10, 8] =	-268	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix(89, 64, 55], [20, 41, 38], [33, 40, 2) is:	Matrix(1438/80701, -2072/80701, -177/80701], [-1214/80701, 1637/80701, 2282/80701], [553/80701, 1448/80701, -2369/80701)	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det(46, 64], [43, 43) =	-774	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 1345 dollars, 6% rate of interest and for a time period of 5 year is =	1799.91	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 5x^2 + 9x + 3 = 0	simplified solution : ((-0.442, -1.358)), generalized solution : ((-9 + sqrt(21))/25, (-9 - sqrt(21))/25)	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	8x^3 + 4x^4 + 2x^4 + 2x^2 + 4x^4 + 2x^2	4x^2 + 8x^3 + 10x^4	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(-6x)(+9x-2)	-54x^2+12x	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	24+4=	28	addition	maxSum=99 maxAddend=50
1	Subtraction	78-30=	48	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	8*2=	16	multiplication	maxMulti=12
3	Division	78/6=	13	division	maxA=25 maxB=25
6	Square Root	sqrt(36)=	6	square_root	minNo=1 maxNo=12
8	Square	11^2=	121	square	maxSquareNum=20
13	Complex Division	93/67=	1.39	complex_division	maxRes=99 maxDivid=99
16	Fraction Division	(6/9)/(3/8)	16/9	divide_fractions	maxVal=10
28	Fraction Multiplication	(9/4)*(3/5)	27/20	fraction_multiplication	maxVal=10
31	Factorial	6! =	720	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 4/5 and 7/2?	<	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 25 up to 2 decimal places?	2.92	cube_root	minNo=1 maxNo=1000
53	Exponentiation	13^8 =	815730721	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers		63--99	=	162
80	Percentage of a number	What is 38% of 45?	17.10	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 77 prime?	No	is_prime	max_num=100
97	Power of Powers	Simplify 29^1^5=	29^5	power_of_powers	maxBase=50 maxPower=10

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	10x^8 + 8x^3 + 8x^7 + 8x^1	80x^7 + 24x^2 + 56x^6 + 8x^0	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	10x^9 + 2x^4 + 4x^6 + 9x^5 + 2x^3	(10/9)x^10 + (2/4)x^5 + (4/6)x^7 + (9/5)x^6 + (2/3)x^4 + c	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Differentiation	differentiate w.r.t x : d(tan(x)+5*x^2)/dx	10*x + tan(x)^2 + 1	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 30x^2 + 51x + 45 is =	80.5	definite_integral	max_coeff=100
110	Stationary Points	f(x)=5x^3 + 9x^2 + 5*x + 2	(-3/5 - sqrt(6)/15,5*(-3/5 - sqrt(6)/15)*3 - 1 - sqrt(6)/3 + 9(-3/5 - sqrt(6)/15)*2),(-3/5 + sqrt(6)/15,-1 + 5(-3/5 + sqrt(6)/15)*3 + sqrt(6)/3 + 9(-3/5 + sqrt(6)/15)**2)	stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	000010=	111101	binary_complement_1s	maxDigits=10
5	Modulo Division	22%64=	22	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 26=	11010	decimal_to_binary	max_dec=99
15	Binary to Decimal	0	0	binary_to_decimal	max_dig=10
56	Fibonacci Series	The Fibonacci Series of the first 6 numbers is ?	[0, 1, 1, 2, 3, 5]	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 88th Fibonacci number?	1100087778366105088	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	000111	0x7	binary_to_hex	max_dig=10
73	Binary 2's Complement	2's complement of 1111 =	1	binary_2s_complement	maxDigits=10
79	Decimal to Hexadecimal	Binary of 266=	0x10a	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 1630 in Octal is:	0o3136	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 2 is =	10340	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 5665 is =	1621	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: 14 4 17 =	20.33316256758894	area_of_triangle	maxA=20 maxB=20 maxC=20
19	Triangle exists check	Does triangle with sides 42, 40 and 36 exist?	Yes	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 62 and 37 =	81	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 2 and 6 =	6.32	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 = 11m is	726 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 16m, 1m, 15m is	542 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 12m and radius = 1m is	81 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volum of Cube	Volume of cube with side = 14m is	2744 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 8m, 15m, 7m is	840 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 50m and radius = 14m is	30787 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 5m and radius = 12m is	942 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 50m and radius = 20m is	20943 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 42 , 52, 238 =	28	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is tan(30)?	1/√3	basic_trigonometry	angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan']
58	Sum of Angles of Polygon	Sum of angles of polygon with 9 sides =	1260	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 15m is	2827.4333882308138 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 69 m =	1376055.2813841724 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [10.33, 884.3] and [26.07, 699.58] is:	0.03 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 2 and angle, 38. Find the area of the sector.	Area of sector = 1.32645	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 252 in radians is =	4.4	degree_to_rad	max_deg=360
87	Radians to Degrees	Angle 2 in degrees is =	114.59	radian_to_deg	max_rad=3
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 25 and height, 26?	CSA of cylinder = 4084.07	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 7 sided polygon with lengths of [106, 2, 68, 76, 5, 33, 105]cm is:	395	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 12	75.39822368615503	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 26 and angle, 168. Find the arc length of the angle.	Arc length of the angle = 76.23598	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 48	7241.142857142857	area_of_circle	maxRadius=100

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 17 and 13 =	221	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 14 and 17 =	1	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 75	[3, 5, 5]	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 71 and 41 =	[1]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 11 and 15 =	1	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 33^(1/1) _ 82^(1/9)	>	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Loss percent when CP = 293 and SP = 37 is:	87.37201365187714	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [8, 48, 288, 1728, 10368, 62208] ,Find the value of a,common ratio,11th term value, sum upto 9th term	The value of a is 8, common ratio is 6 , 11th term is 483729408 , sum upto 9th term is 16124312.0	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 35 , 57 and 21 =	(355721)^(1/3) = 34.73127538750071	geometric_mean	maxValue=100 maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 28 , 49 and 54 =	3/((1/28) + (1/49) + (1/54)) = 40.19240506329114	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[40.30298267905974, 805.6944561248209, 276.21066847439425, 806.6064748556993, 957.8280112710016, 862.9140054943484, 480.03380665406024, 186.74042925660362, 197.7737844258112, 77.12282777074032, 137.67424706299215, 234.7784931085548] is:	1850.45164451948	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert 68 degrees Celsius to degrees Fahrenheit =	154.4	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 99 of the AP series: 27, 42, 57 ...	1497	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 90 terms of the AP series: -20, -73, -126 ...	-214065.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 3760 in Roman Numerals is:	MMMDCCLX	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	rexp(itheta) =	18.44exp(i-0.86)	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={5, 6, 8, 9, 10} ,b={8, 9, 2}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {2, 5, 6, 8, 9, 10},Intersection is {8, 9}, a-b is {10, 5, 6},b-a is {2}, Symmetric difference is {2, 5, 6, 10}	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert 49237 from base 10 to base 2.	1100000001010101	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 14^1 and 14^7 = 14^(1-7) = 14^-6	1.328103086299076e-07	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 1^1 and 18^1 = (1/18)^1 = 0.05555555555555555^1	0.05555555555555555	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Year 2068	is a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 429 minutes to Hours & Minutes	7 hours and 9 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of -301 is =	-1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 34.3% 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 2 rejected pistons?	27.7	binomial_distribution	``

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 20 objects picked 3 at a time	1140	combinations	maxlength=20
42	Permutations	Number of Permutations from 12 objects picked 1 at a time =	12	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 6 =	1/6	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [296, 281, 217, 204, 215, 219, 218, 245, 208, 274, 262, 213, 264, 225, 206, 248, 231, 259, 240, 226, 216, 255, 257, 249, 279, 251, 241, 287, 239, 200, 267, 288, 290, 246, 275] with 95% confidence is	(254.598134838323, 236.3161508759627)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[41, 36, 45, 15, 41, 26, 6, 39, 9, 22, 25, 40, 42, 5, 28]	The Mean is 28.0 , Standard Deviation is 182.93333333333334, Variance is 13.525284963110142	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [77, 79, 53, 12, 98, 65, 40, 44, 9, 19]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 49.6 and Arithmetic median of this series is 48.5	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 0.06% of population have. Test sensitivity (true positive) is equal to SN= 94.78% whereas test specificity (true negative) SP= 90.54%. What is the probability that this guy really has that disease?	0.6%	conditional_probability	``