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

• Usage
• Basic 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)

Documentation

getGenList() returns a list of all generators in the repository in the format [id, title, self, funcname]

genById(id) generates a problem, solution set with generator id id in the form of a list in the format [problem, solution]

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

More complicated worksheets

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)

List of Generators

algebra

Id	Skill	Example problem	Example Solution	Function Name
11	Basic Algebra	1x + 7 = 8	1	basic_algebra
12	Logarithm	log3(243)	5	log
17	Integer Multiplication with 2x2 Matrix	1 * 1, 10], [4, 7 =	1,10],[4,7	multiply_int_to_22_matrix
20	Midpoint of the two point	(2,2),(9,-20)=	(5.5,-9.0)	midpoint_of_two_points
21	Factoring Quadratic	x^2-11x+30	(x-5)(x-6)	factoring
23	Solve a System of Equations in R^2	5x - 2y = -22, x + 3y = 16	x = -2, y = 6	system_of_equations
24	Distance between 2 points	Find the distance between (1, 17) and (3, -13)	sqrt(904)	distance_two_points
26	Linear Equations	11x + 1y = 110, 20x + 14y = 200	x = 10, y = 0	linear_equations
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = 9/5x - 10 and y = -2/3x + 4	(210/37, 8/37)	intersection_of_two_lines
43	Cross Product of 2 Vectors	[3, -13, -15] X [-7, -17, -2] =	[-229, 111, -142]	vector_cross
45	Simple Interest	Simple interest for a principle amount of 5720 dollars, 1% rate of interest and for a time period of 6 years is =	343.2	simple_interest
46	Multiplication of two matrices	Multiply 1 0 -2 2 -8 8 -10 9 and -8 -9 0 -2 -7 -7 -10 9	-8 -9 0 -2 2 4 -20 22 8 16 -80 88 17 27 -90 101	matrix_multiplication
50	Quadratic Equation	Zeros of the Quadratic Equation 95x^2+151x+54=0	[-0.54, -1.05]	quadratic_equation
65	Multiplication of 2 complex numbers	(-16+18j) * (20-9j) =	(-158+504j)	multiply_complex_numbers
72	Dot Product of 2 Vectors	[-8, 19, -7] . [13, 12, 16] =	12	vector_dot
74	Inverse of a Matrix	Inverse of Matrix Matrix(23, 40, 67], [72, 41, 63], [71, 75, 27) is:	Matrix(-3618/184709, 3945/184709, -227/184709], [2529/184709, -4136/184709, 3375/184709], [2489/184709, 1115/184709, -1937/184709)	invert_matrix
77	Determinant to 2x2 Matrix	Det(92, 39], [87, 30) =	-633	int_matrix_22_determinant
78	Compound Interest	Compound interest for a principle amount of 3384 dollars, 10% rate of interest and for a time period of 5 year is =	5449.97	compound_interest
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 2x^2 + 6x + 3 = 0	simplified solution : ((-0.634, -2.366)), generalized solution : ((-6 + sqrt(12))/22, (-6 - sqrt(12))/22)	complex_quadratic
105	Combine Like terms	2x^3 + 2x^2 + 9x^2 + 10x^2 + 1x^4	21x^2 + 2x^3 + 1x^4	combine_like_terms
111	Expanding Factored Binomial	(2x-5)(+4x-2)	8x^2-24x+10	expanding

basic_math

Id	Skill	Example problem	Example Solution	Function Name
0	Addition	46+18=	64	addition
1	Subtraction	46-35=	11	subtraction
2	Multiplication	38*0=	0	multiplication
3	Division	192/16=	12	division
6	Square Root	sqrt(16)=	4	square_root
8	Square	4^2=	16	square
13	Complex Division	26/40=	0.65	complex_division
16	Fraction Division	(4/3)/(8/10)	5/3	divide_fractions
28	Fraction Multiplication	(7/3)*(2/5)	14/15	fraction_multiplication
31	Factorial	3! =	6	factorial
44	Compare Fractions	Which symbol represents the comparison between 4/5 and 7/1?	<	compare_fractions
47	Cube Root	cuberoot of 718 upto 2 decimal places is:	8.95	cube_root
53	Exponentiation	17^6 =	24137569	exponentiation
71	Absolute difference between two numbers	Absolute difference between numbers -27 and 96 =	123	absolute_difference
80	Percentage of a number	What is 55% of 82?	Required percentage = 45.10%	percentage
90	isprime	61	True	is_prime
97	Power of Powers	The 42^1^2 = 42^(1*2) = 42^2	1764	power_of_powers

calculus

Id	Skill	Example problem	Example Solution	Function Name
7	Power Rule Differentiation	1x^2 + 3x^5 + 6x^7	2x^1 + 15x^4 + 42x^6	power_rule_differentiation
48	Power Rule Integration	9x^1 + 10x^4 + 5x^6	(9/1)x^2 + (10/4)x^5 + (5/6)x^7 + c	power_rule_integration
88	Differentiation	differentiate w.r.t x : d(tan(x)+5*x^(-2))/dx	tan(x)^2 + 1 - 10/x^3	differentiation
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 20x^2 + 27x + 41 is =	61.1667	definite_integral
110	Stationary Points	f(x)=7x^3 + 2x^2 + 6	(-4/21,7970/1323),(0,6)	stationary_points

computer_science

Id	Skill	Example problem	Example Solution	Function Name
4	Binary Complement 1s	00011=	11100	binary_complement_1s
5	Modulo Division	0%10=	0	modulo_division
14	Decimal to Binary	Binary of 62=	111110	decimal_to_binary
15	Binary to Decimal	0101101	45	binary_to_decimal
56	Fibonacci Series	The Fibonacci Series of the first 13 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144]	fibonacci_series
62	nth Fibonacci number	What is the 63th Fibonacci number?	6557470319842	nth_fibonacci_number
64	Binary to Hexidecimal	110010100	0x194	binary_to_hex
73	Binary 2's Complement	2's complement of 10 =	10	binary_2s_complement
79	Decimal to Hexadecimal	Binary of 797=	0x31d	decimal_to_hexadeci
84	Converts decimal to octal	The decimal number 3704 in Octal is:	0o7170	decimal_to_octal
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 7 is =	30104	bcd_to_decimal
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 2037 is =	7155	decimal_to_bcd

geometry

Id	Skill	Example problem	Example Solution	Function Name
18	Area of Triangle	Area of triangle with side lengths: 7 4 7 =	13.416407864998739	area_of_triangle
19	Triangle exists check	Does triangle with sides 7, 31 and 16 exist?	No	valid_triangle
22	Third Angle of Triangle	Third angle of triangle with angles 73 and 76 =	31	third_angle_of_triangle
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 16 and 5 =	16.76	pythagorean_theorem
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 12 sides	150.0	angle_regular_polygon
32	Surface Area of Cube	Surface area of cube with side = 1m is	6 m^2	surface_area_cube
33	Surface Area of Cuboid	Surface area of cuboid with sides = 1m, 18m, 12m is	492 m^2	surface_area_cuboid
34	Surface Area of Cylinder	Surface area of cylinder with height = 11m and radius = 17m is	2990 m^2	surface_area_cylinder
35	Volum of Cube	Volume of cube with side = 5m is	125 m^3	volume_cube
36	Volume of Cuboid	Volume of cuboid with sides = 16m, 18m, 10m is	2880 m^3	volume_cuboid
37	Volume of cylinder	Volume of cylinder with height = 13m and radius = 4m is	653 m^3	volume_cylinder
38	Surface Area of cone	Surface area of cone with height = 30m and radius = 16m is	2513 m^2	surface_area_cone
39	Volume of cone	Volume of cone with height = 14m and radius = 20m is	5864 m^3	volume_cone
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 25 , 183, 109 =	43	fourth_angle_of_quadrilateral
57	Trigonometric Values	What is sin(30)?	1/2	basic_trigonometry
58	Sum of Angles of Polygon	Sum of angles of polygon with 12 sides =	1800	sum_of_polygon_angles
60	Surface Area of Sphere	Surface area of Sphere with radius = 10m is	1256.6370614359173 m^2	surface_area_sphere
61	Volume of Sphere	Volume of sphere with radius 61 m =	950775.7894726198 m^3	volume_sphere
70	Angle between 2 vectors	angle between the vectors [437.0, 613.71, 778.37, 977.11, 617.14, 527.38, 196.94, 993.88, 186.86, 937.36, 323.15, 896.54, 646.74] and [753.99, 971.66, 175.71, 81.48, 178.5, 671.53, 624.94, 662.16, 533.37, 974.47, 598.63, 690.91, 743.68] is:	0.62 radians	angle_btw_vectors
75	Area of a Sector	Given radius, 2 and angle, 324. Find the area of the sector.	Area of sector = 11.30973	sector_area
86	Degrees to Radians	Angle 47 in radians is =	0.82	degree_to_rad
87	Radians to Degrees	Angle 0 in degrees is =	0.0	radian_to_deg
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 19 and height, 88?	CSA of cylinder = 10505.49	curved_surface_area_cylinder
96	Perimeter of Polygons	The perimeter of a 3 sided polygon with lengths of [27, 98, 14]cm is:	139	perimeter_of_polygons
104	Circumference	Circumference of circle with radius 90	565.4866776461628	circumference
108	Arc length of Angle	Given radius, 2 and angle, 37. Find the arc length of the angle.	Arc length of the angle = 1.29154	arc_length
112	Area of Circle	Area of circle with radius 0	0.0	area_of_circle

misc

Id	Skill	Example problem	Example Solution	Function Name
9	LCM (Least Common Multiple)	LCM of 16 and 10 =	80	lcm
10	GCD (Greatest Common Denominator)	GCD of 13 and 1 =	1	gcd
27	Prime Factorisation	Find prime factors of 11	[11]	prime_factors
40	Common Factors	Common Factors of 65 and 19 =	[1]	common_factors
51	HCF (Highest Common Factor)	HCF of 20 and 14 =	2	hcf
55	Comparing surds	Fill in the blanks 78^(1/7) _ 52^(1/9)	>	surds_comparison
63	Profit or Loss Percent	Loss percent when CP = 431 and SP = 150 is:	65.19721577726219	profit_loss_percent
66	Geometric Progression	For the given GP [3, 12, 48, 192, 768, 3072] ,Find the value of a,common ratio,11th term value, sum upto 11th term	The value of a is 3, common ratio is 4 , 11th term is 3145728 , sum upto 11th term is 4194303.0	geometric_progression
67	Geometric Mean of N Numbers	Geometric mean of 4 numbers 40 , 63 , 65 , 24 =	(406365*24)^(1/4) = 44.52780476312522	geometric_mean
68	Harmonic Mean of N Numbers	Harmonic mean of 4 numbers 48 , 59 , 75 , 80 =	4/((1/48) + (1/59) + (1/75) + (1/80)) = 62.87744227353463	harmonic_mean
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[249.0015460376116, 867.8122114074212, 4.2765473742734095, 450.4653172064377, 435.0307355906793, 628.6207356296137, 313.9369656743921, 290.1828788563886, 716.1780160982277, 29.88164461825127] is:	1516.2517107189344	euclidian_norm
81	Celsius To Fahrenheit	Convert 22 degrees Celsius to degrees Fahrenheit =	71.6	celsius_to_fahrenheit
82	AP Term Calculation	Find the term number 93 of the AP series: 54, 33, 12 ...	-1878	arithmetic_progression_term
83	AP Sum Calculation	Find the sum of first 21 terms of the AP series: -96, -65, -34 ...	4494.0	arithmetic_progression_sum
85	Converts decimal to Roman Numerals	The number 3999 in Roman Numerals is:	MMMCMXCIX	decimal_to_roman_numerals
92	Complex To Polar Form	rexp(itheta) =	13.04exp(i-3.06)	complex_to_polar
93	Union,Intersection,Difference of Two Sets	Given the two sets a={8, 10, 3, 5} ,b={1, 3, 6}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 3, 5, 6, 8, 10},Intersection is {3}, a-b is {8, 10, 5},b-a is {1, 6}, Symmetric difference is {1, 5, 6, 8, 10}	set_operation
94	Base Conversion	Convert 7959 from base 16 to base 9.	46546	base_conversion
98	Quotient of Powers with Same Base	The Quotient of 40^4 and 40^4 = 40^(4-4) = 40^0	1	quotient_of_power_same_base
99	Quotient of Powers with Same Power	The Quotient of 26^7 and 33^7 = (26/33)^7 = 0.7878787878787878^7	0.1884585549109465	quotient_of_power_same_power
101	Leap Year or Not	Year 1975	is not a leap year	is_leap_year
102	Minute to Hour conversion	Convert 151 minutes to Hours & Minutes	2 hours and 31 minutes	minutes_to_hours
106	signum function	signum of -252 is =	-1	signum_function
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 39.81% 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?	40.91	binomial_distribution

statistics

Id	Skill	Example problem	Example Solution	Function Name
30	Combinations of Objects	Number of combinations from 11 objects picked 8 at a time	165	combinations
42	Permutations	Number of Permutations from 17 objects picked 1 at a time =	17	permutation
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 14 =	15/216	dice_sum_probability
54	Confidence interval For sample S	The confidence interval for sample [270, 291, 266, 239, 273, 283, 243, 288, 289, 214, 226, 209, 258, 256, 249, 202, 220, 253, 208, 236, 245, 221, 271, 264, 240, 293] with 90% confidence is	(259.0741428605511, 241.46431867791048)	confidence_interval
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[46, 25, 24, 23, 49, 22, 17, 8, 24, 28, 37, 31, 31, 23, 8]	The Mean is 26.4 , Standard Deviation is 124.90666666666668, Variance is 11.17616511450447	data_summary
76	Mean and Median	Given the series of numbers [21, 85, 4, 40, 42, 50, 69, 75, 91, 71]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 54.8 and Arithmetic median of this series is 59.5	mean_median
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.68% of population have. Test sensitivity (true positive) is equal to SN= 94.32% whereas test specificity (true negative) SP= 99.09%. What is the probability that this guy really has that disease?	63.91%	conditional_probability