mathgenerator/README.md

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]

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.

List of Generators

algebra

Id	Skill	Example problem	Example Solution	Function Name
11	Basic Algebra	10x + 4 = 8	2/5	basic_algebra
12	Logarithm	log2(16)	4	log
17	Integer Multiplication with 2x2 Matrix	5 * 9, 7], [8, 7 =	45,35],[40,35	multiply_int_to_22_matrix
20	Midpoint of the two point	(-2,-6),(8,-10)=	(3.0,-8.0)	midpoint_of_two_points
21	Factoring Quadratic	x^2-7x-8	(x+1)(x-8)	factoring
23	Solve a System of Equations in R^2	4x + 8y = 40, -2x - 4y = -20	x = 8, y = 1	system_of_equations
24	Distance between 2 points	Find the distance between (14, -2) and (17, 4)	sqrt(45)	distance_two_points
26	Linear Equations	7x + 4y = -144, -19x + 15y = 365	x = -20, y = -1	linear_equations
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = 4x - 9 and y = -2x + 1	(5/3, -7/3)	intersection_of_two_lines
43	Cross Product of 2 Vectors	[-14, 15, -1] X [-7, 1, 6] =	[91, 91, 91]	vector_cross
45	Simple Interest	Simple interest for a principle amount of 2349 dollars, 4% rate of interest and for a time period of 9 years is =	845.64	simple_interest
46	Multiplication of two matrices	Multiply 8 6 -8 9 2 3 10 -1 and -8 -10 -1 -4 -1 -1	-88 -86 -14 28 71 -1 -28 -23 -5 -76 -99 -9	matrix_multiplication
50	Quadratic Equation	Zeros of the Quadratic Equation 4x^2+120x+5=0	[-0.04, -29.96]	quadratic_equation
65	Multiplication of 2 complex numbers	(-7-9j) * (19+8j) =	(-61-227j)	multiply_complex_numbers
72	Dot Product of 2 Vectors	[11, -4, 2] . [-1, 1, 19] =	23	vector_dot
74	Inverse of a Matrix	Inverse of Matrix Matrix(43, 67, 81], [23, 71, 79], [70, 96, 7) is:	Matrix(7087/168740, -7307/168740, 229/84370], [-7/220, 7/220, 1/110], [1381/84370, -281/84370, -378/42185)	invert_matrix
77	Determinant to 2x2 Matrix	Det(31, 16], [92, 93) =	1411	int_matrix_22_determinant
78	Compound Interest	Compound interest for a principle amount of 6310 dollars, 1% rate of interest and for a time period of 2 year is =	6436.83	compound_interest
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 2x^2 + 6x + 4 = 0	simplified solution : ((-1.0, -2.0)), generalized solution : ((-6 + 2)/22, (-6 - 2)/22)	complex_quadratic
105	Combine Like terms	3x^2 + 3x^1 + 1x^2	3x^1 + 4x^2	combine_like_terms
111	Expanding Factored Binomial	(-7x)(-4x-1)	28x^2+7x	expanding

basic_math

Id	Skill	Example problem	Example Solution	Function Name
0	Addition	21+24=	45	addition
1	Subtraction	17-4=	13	subtraction
2	Multiplication	87*0=	0	multiplication
3	Division	136/17=	8	division
6	Square Root	sqrt(16)=	4	square_root
8	Square	14^2=	196	square
13	Complex Division	76/53=	1.43	complex_division
16	Fraction Division	(9/10)/(2/7)	63/20	divide_fractions
28	Fraction Multiplication	(3/9)*(1/3)	1/9	fraction_multiplication
31	Factorial	1! =	1	factorial
44	Compare Fractions	Which symbol represents the comparison between 3/5 and 4/10?	>	compare_fractions
47	Cube Root	cuberoot of 127 upto 2 decimal places is:	5.03	cube_root
53	Exponentiation	8^4 =	4096	exponentiation
71	Absolute difference between two numbers	Absolute difference between numbers -67 and 11 =	78	absolute_difference
80	Percentage of a number	What is 51% of 89?	Required percentage = 45.39%	percentage
90	isprime	32	False	is_prime
97	Power of Powers	The 23^7^4 = 23^(7*4) = 23^28	134393854047545109686936775588697536481	power_of_powers

calculus

Id	Skill	Example problem	Example Solution	Function Name
7	Power Rule Differentiation	4x^10 + 1x^7 + 9x^8 + 2x^9	40x^9 + 7x^6 + 72x^7 + 18x^8	power_rule_differentiation
48	Power Rule Integration	9x^1 + 3x^2 + 1x^7	(9/1)x^2 + (3/2)x^3 + (1/7)x^8 + c	power_rule_integration
88	Differentiation	differentiate w.r.t x : d(cot(x)+3*x^(-2))/dx	-cot(x)^2 - 1 - 6/x^3	differentiation
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 72x^2 + 6x + 55 is =	82.0	definite_integral
110	Stationary Points	f(x)=x^3 + 9x^2 + 3x + 3	(-3 - 2sqrt(2),(-3 - 2sqrt(2))**3 - 6sqrt(2) - 6 + 9(-3 - 2sqrt(2))**2),(-3 + 2sqrt(2),-6 + (-3 + 2sqrt(2))*3 + 9(-3 + 2sqrt(2))**2 + 6*sqrt(2))	stationary_points

computer_science

Id	Skill	Example problem	Example Solution	Function Name
4	Binary Complement 1s	011=	100	binary_complement_1s
5	Modulo Division	79%59=	20	modulo_division
14	Decimal to Binary	Binary of 3=	11	decimal_to_binary
15	Binary to Decimal	111100	60	binary_to_decimal
56	Fibonacci Series	The Fibonacci Series of the first 15 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377]	fibonacci_series
62	nth Fibonacci number	What is the 80th Fibonacci number?	23416728348467744	nth_fibonacci_number
64	Binary to Hexidecimal	11	0x3	binary_to_hex
73	Binary 2's Complement	2's complement of =		binary_2s_complement
79	Decimal to Hexadecimal	Binary of 308=	0x134	decimal_to_hexadeci
84	Converts decimal to octal	The decimal number 4031 in Octal is:	0o7677	decimal_to_octal
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 1 is =	5416	bcd_to_decimal
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 4889 is =	1319	decimal_to_bcd

geometry

Id	Skill	Example problem	Example Solution	Function Name
18	Area of Triangle	Area of triangle with side lengths: 6 8 19 =	(3.715326154880634e-15+60.675880710542636j)	area_of_triangle
19	Triangle exists check	Does triangle with sides 8, 30 and 7 exist?	No	valid_triangle
22	Third Angle of Triangle	Third angle of triangle with angles 30 and 54 =	96	third_angle_of_triangle
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 20 and 4 =	20.40	pythagorean_theorem
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 14 sides	154.29	angle_regular_polygon
32	Surface Area of Cube	Surface area of cube with side = 7m is	294 m^2	surface_area_cube
33	Surface Area of Cuboid	Surface area of cuboid with sides = 3m, 1m, 15m is	126 m^2	surface_area_cuboid
34	Surface Area of Cylinder	Surface area of cylinder with height = 27m and radius = 9m is	2035 m^2	surface_area_cylinder
35	Volum of Cube	Volume of cube with side = 7m is	343 m^3	volume_cube
36	Volume of Cuboid	Volume of cuboid with sides = 11m, 6m, 3m is	198 m^3	volume_cuboid
37	Volume of cylinder	Volume of cylinder with height = 34m and radius = 20m is	42725 m^3	volume_cylinder
38	Surface Area of cone	Surface area of cone with height = 31m and radius = 14m is	2111 m^2	surface_area_cone
39	Volume of cone	Volume of cone with height = 23m and radius = 1m is	24 m^3	volume_cone
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 117 , 34, 65 =	144	fourth_angle_of_quadrilateral
57	Trigonometric Values	What is sin(60)?	√3/2	basic_trigonometry
58	Sum of Angles of Polygon	Sum of angles of polygon with 4 sides =	360	sum_of_polygon_angles
60	Surface Area of Sphere	Surface area of Sphere with radius = 13m is	2123.7166338267 m^2	surface_area_sphere
61	Volume of Sphere	Volume of sphere with radius 9 m =	3053.628059289279 m^3	volume_sphere
70	Angle between 2 vectors	angle between the vectors [125.74, 310.83] and [290.27, 233.14] is:	0.51 radians	angle_btw_vectors
75	Area of a Sector	Given radius, 41 and angle, 1. Find the area of the sector.	Area of sector = 14.66949	sector_area
86	Degrees to Radians	Angle 244 in radians is =	4.26	degree_to_rad
87	Radians to Degrees	Angle 3 in degrees is =	171.89	radian_to_deg
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 16 and height, 41?	CSA of cylinder = 4121.77	curved_surface_area_cylinder
96	Perimeter of Polygons	The perimeter of a 3 sided polygon with lengths of [117, 20, 100]cm is:	237	perimeter_of_polygons
104	Circumference	Circumference of circle with radius 22	138.23007675795088	circumference
108	Arc length of Angle	Given radius, 15 and angle, 88. Find the arc length of the angle.	Arc length of the angle = 23.03835	arc_length
112	Area of Circle	Area of circle with radius 9	254.57142857142856	area_of_circle

misc

Id	Skill	Example problem	Example Solution	Function Name
9	LCM (Least Common Multiple)	LCM of 6 and 13 =	78	lcm
10	GCD (Greatest Common Denominator)	GCD of 6 and 19 =	1	gcd
27	Prime Factorisation	Find prime factors of 88	[2, 2, 2, 11]	prime_factors
40	Common Factors	Common Factors of 5 and 1 =	[1]	common_factors
51	HCF (Highest Common Factor)	HCF of 12 and 16 =	4	hcf
55	Comparing surds	Fill in the blanks 38^(1/3) _ 72^(1/7)	>	surds_comparison
63	Profit or Loss Percent	Loss percent when CP = 890 and SP = 392 is:	55.955056179775276	profit_loss_percent
66	Geometric Progression	For the given GP [3, 27, 243, 2187, 19683, 177147] ,Find the value of a,common ratio,8th term value, sum upto 8th term	The value of a is 3, common ratio is 9 , 8th term is 14348907 , sum upto 8th term is 16142520.0	geometric_progression
67	Geometric Mean of N Numbers	Geometric mean of 4 numbers 68 , 99 , 69 , 94 =	(689969*94)^(1/4) = 81.28871585461766	geometric_mean
68	Harmonic Mean of N Numbers	Harmonic mean of 2 numbers 36 and 89 =	2/((1/36) + (1/89)) = 51.264	harmonic_mean
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[500.9951948616654, 42.203693843008814, 503.055665827151, 997.8018016538981, 720.8110612915443, 219.71485715574812, 445.67377783903027] is:	1505.9611867978413	euclidian_norm
81	Celsius To Fahrenheit	Convert -40 degrees Celsius to degrees Fahrenheit =	-40.0	celsius_to_fahrenheit
82	AP Term Calculation	Find the term number 82 of the AP series: -86, -93, -100 ...	-653	arithmetic_progression_term
83	AP Sum Calculation	Find the sum of first 71 terms of the AP series: -62, -8, 46 ...	129788.0	arithmetic_progression_sum
85	Converts decimal to Roman Numerals	The number 1282 in Roman Numerals is:	MCCLXXXII	decimal_to_roman_numerals
92	Complex To Polar Form	rexp(itheta) =	16.12exp(i-1.05)	complex_to_polar
93	Union,Intersection,Difference of Two Sets	Given the two sets a={10, 2, 5, 7} ,b={2, 3, 6, 8, 10}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {2, 3, 5, 6, 7, 8, 10},Intersection is {10, 2}, a-b is {5, 7},b-a is {8, 3, 6}, Symmetric difference is {3, 5, 6, 7, 8}	set_operation
94	Base Conversion	Convert E079 from base 16 to base 2.	1110000001111001	base_conversion
98	Quotient of Powers with Same Base	The Quotient of 48^6 and 48^7 = 48^(6-7) = 48^-1	0.020833333333333332	quotient_of_power_same_base
99	Quotient of Powers with Same Power	The Quotient of 2^3 and 17^3 = (2/17)^3 = 0.11764705882352941^3	0.001628332994097293	quotient_of_power_same_power
101	Leap Year or Not	Year 2016	is a leap year	is_leap_year
102	Minute to Hour conversion	Convert 509 minutes to Hours & Minutes	8 hours and 29 minutes	minutes_to_hours
106	signum function	signum of 750 is =	1	signum_function
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 39.24% 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 7 rejected pistons?	80.44	binomial_distribution

statistics

Id	Skill	Example problem	Example Solution	Function Name
30	Combinations of Objects	Number of combinations from 12 objects picked 3 at a time	220	combinations
42	Permutations	Number of Permutations from 13 objects picked 1 at a time =	13	permutation
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 6 =	5/36	dice_sum_probability
54	Confidence interval For sample S	The confidence interval for sample [270, 279, 280, 228, 245, 203, 254, 207, 218, 243, 205, 258, 244, 288, 278, 269, 216, 297, 215, 277, 296, 282, 257, 242, 246, 274, 224, 299, 239, 230, 225, 295, 284] with 99% confidence is	(266.76150517633465, 240.3294039145744)	confidence_interval
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[44, 7, 14, 15, 20, 43, 46, 29, 13, 15, 22, 45, 6, 24, 25]	The Mean is 24.533333333333335 , Standard Deviation is 181.58222222222224, Variance is 13.475244792664148	data_summary
76	Mean and Median	Given the series of numbers [76, 34, 10, 78, 55, 74, 54, 91, 19, 39]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 53.0 and Arithmetic median of this series is 54.5	mean_median
107	Conditional Probability	Someone tested positive for a nasty disease which only 0.47% of population have. Test sensitivity (true positive) is equal to SN= 93.50% whereas test specificity (true negative) SP= 98.52%. What is the probability that this guy really has that disease?	22.98%	conditional_probability