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 + 5 = 5	0	basic_algebra
12	Logarithm	log3(3)	1	log
17	Integer Multiplication with 2x2 Matrix	8 * 10, 5], [3, 9 =	80,40],[24,72	multiply_int_to_22_matrix
20	Midpoint of the two point	(-14,1),(-2,2)=	(-8.0,1.5)	midpoint_of_two_points
21	Factoring Quadratic	x^2-2x-15	(x-5)(x+3)	factoring
23	Solve a System of Equations in R^2	-8x - 3y = -31, 4x - 6y = 38	x = 5, y = -3	system_of_equations
24	Distance between 2 points	Find the distance between (-4, -6) and (-4, 15)	sqrt(441)	distance_two_points
26	Linear Equations	8x + 9y = -202, 5x + -7y = 0	x = -14, y = -10	linear_equations
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = 7/2x + 3 and y = 2/5x + 10	(70/31, 338/31)	intersection_of_two_lines
43	Cross Product of 2 Vectors	[-18, 12, 1] X [-12, -19, 1] =	[31, 6, 486]	vector_cross
45	Simple Interest	Simple interest for a principle amount of 4200 dollars, 5% rate of interest and for a time period of 8 years is =	1680.0	simple_interest
46	Multiplication of two matrices	Multiply -8 7 0 -5 -3 0 7 2 and -7 -4 6 -4	98 4 -30 20 21 12 -37 -36	matrix_multiplication
50	Quadratic Equation	Zeros of the Quadratic Equation 33x^2+199x+22=0	[-0.11, -5.92]	quadratic_equation
65	Multiplication of 2 complex numbers	(-4-10j) * (4-18j) =	(-196+32j)	multiply_complex_numbers
72	Dot Product of 2 Vectors	[7, -2, 14] . [14, -17, -16] =	-92	vector_dot
74	Inverse of a Matrix	Inverse of Matrix Matrix(81, 23, 19], [73, 75, 49], [7, 71, 93) is:	Matrix(874/55855, -79/22342, -149/111710], [-3223/111710, 370/11171, -1291/111710], [2329/111710, -559/22342, 1099/55855)	invert_matrix
77	Determinant to 2x2 Matrix	Det(9, 31], [5, 30) =	115	int_matrix_22_determinant
78	Compound Interest	Compound interest for a principle amount of 8699 dollars, 9% rate of interest and for a time period of 9 year is =	18893.3	compound_interest
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 8x^2 + 8x + 1 = 0	simplified solution : ((-0.146, -0.854)), generalized solution : ((-8 + sqrt(32))/28, (-8 - sqrt(32))/28)	complex_quadratic
105	Combine Like terms	6x^1 + 5x^1 + 2x^2	11x^1 + 2x^2	combine_like_terms
111	Expanding Factored Binomial	(3x-1)(+4x-7)	12x^2-25x+7	expanding

basic_math

Id	Skill	Example problem	Example Solution	Function Name
0	Addition	46+24=	70	addition
1	Subtraction	17-10=	7	subtraction
2	Multiplication	28*0=	0	multiplication
3	Division	150/6=	25	division
6	Square Root	sqrt(144)=	12	square_root
8	Square	9^2=	81	square
13	Complex Division	3/39=	0.08	complex_division
16	Fraction Division	(4/1)/(10/1)	2/5	divide_fractions
28	Fraction Multiplication	(9/7)*(9/6)	27/14	fraction_multiplication
31	Factorial	0! =	1	factorial
44	Compare Fractions	Which symbol represents the comparison between 4/10 and 8/9?	<	compare_fractions
47	Cube Root	cuberoot of 685 upto 2 decimal places is:	8.82	cube_root
53	Exponentiation	2^7 =	128	exponentiation
71	Absolute difference between two numbers	Absolute difference between numbers -43 and 99 =	142	absolute_difference
80	Percentage of a number	What is 58% of 84?	Required percentage = 48.72%	percentage
90	isprime	32	False	is_prime
97	Power of Powers	The 34^2^9 =	34^18	power_of_powers

calculus

Id	Skill	Example problem	Example Solution	Function Name
7	Power Rule Differentiation	6x^10 + 4x^7 + 6x^4 + 2x^2 + 7x^8	60x^9 + 28x^6 + 24x^3 + 4x^1 + 56x^7	power_rule_differentiation
48	Power Rule Integration	1x^2 + 8x^8	(1/2)x^3 + (8/8)x^9 + c	power_rule_integration
88	Differentiation	differentiate w.r.t x : d(exp(x)+9*x^(-2))/dx	exp(x) - 18/x^3	differentiation
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 16x^2 + 29x + 67 is =	86.8333	definite_integral
110	Stationary Points	f(x)=6x^3 + 8x^2 + 3*x + 2	(-4/9 - sqrt(10)/18,6*(-4/9 - sqrt(10)/18)*3 - sqrt(10)/6 + 2/3 + 8(-4/9 - sqrt(10)/18)*2),(-4/9 + sqrt(10)/18,6(-4/9 + sqrt(10)/18)*3 + sqrt(10)/6 + 8(-4/9 + sqrt(10)/18)**2 + 2/3)	stationary_points

computer_science

Id	Skill	Example problem	Example Solution	Function Name
4	Binary Complement 1s	000=	111	binary_complement_1s
5	Modulo Division	3%97=	3	modulo_division
14	Decimal to Binary	Binary of 35=	100011	decimal_to_binary
15	Binary to Decimal	0001100	12	binary_to_decimal
56	Fibonacci Series	The Fibonacci Series of the first 3 numbers is ?	[0, 1, 1]	fibonacci_series
62	nth Fibonacci number	What is the 28th Fibonacci number?	317811	nth_fibonacci_number
64	Binary to Hexidecimal	110101	0x35	binary_to_hex
73	Binary 2's Complement	2's complement of 11101010 =	10110	binary_2s_complement
79	Decimal to Hexadecimal	Binary of 858=	0x35a	decimal_to_hexadeci
84	Converts decimal to octal	The decimal number 1377 in Octal is:	0o2541	decimal_to_octal
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 3 is =	12386	bcd_to_decimal
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 4841 is =	12149	decimal_to_bcd

geometry

Id	Skill	Example problem	Example Solution	Function Name
18	Area of Triangle	Area of triangle with side lengths: 20 16 14 =	111.24297730643494	area_of_triangle
19	Triangle exists check	Does triangle with sides 44, 29 and 14 exist?	No	valid_triangle
22	Third Angle of Triangle	Third angle of triangle with angles 26 and 79 =	75	third_angle_of_triangle
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 9 and 20 =	21.93	pythagorean_theorem
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 15 sides	156.0	angle_regular_polygon
32	Surface Area of Cube	Surface area of cube with side = 6m is	216 m^2	surface_area_cube
33	Surface Area of Cuboid	Surface area of cuboid with sides = 9m, 13m, 1m is	278 m^2	surface_area_cuboid
34	Surface Area of Cylinder	Surface area of cylinder with height = 44m and radius = 2m is	578 m^2	surface_area_cylinder
35	Volum of Cube	Volume of cube with side = 6m is	216 m^3	volume_cube
36	Volume of Cuboid	Volume of cuboid with sides = 9m, 10m, 17m is	1530 m^3	volume_cuboid
37	Volume of cylinder	Volume of cylinder with height = 46m and radius = 3m is	1300 m^3	volume_cylinder
38	Surface Area of cone	Surface area of cone with height = 15m and radius = 6m is	417 m^2	surface_area_cone
39	Volume of cone	Volume of cone with height = 2m and radius = 4m is	33 m^3	volume_cone
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 16 , 182, 51 =	111	fourth_angle_of_quadrilateral
57	Trigonometric Values	What is cos(0)?	1	basic_trigonometry
58	Sum of Angles of Polygon	Sum of angles of polygon with 7 sides =	900	sum_of_polygon_angles
60	Surface Area of Sphere	Surface area of Sphere with radius = 4m is	201.06192982974676 m^2	surface_area_sphere
61	Volume of Sphere	Volume of sphere with radius 95 m =	3591364.0018287315 m^3	volume_sphere
70	Angle between 2 vectors	angle between the vectors [971.6, 661.5, 319.66, 602.97, 423.53, 190.72, 120.07, 795.33] and [448.68, 587.18, 139.74, 198.63, 570.02, 430.49, 735.04, 51.89] is:	0.82 radians	angle_btw_vectors
75	Area of a Sector	Given radius, 12 and angle, 292. Find the area of the sector.	Area of sector = 366.93802	sector_area
86	Degrees to Radians	Angle 182 in radians is =	3.18	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, 2 and height, 30?	CSA of cylinder = 376.99	curved_surface_area_cylinder
96	Perimeter of Polygons	The perimeter of a 10 sided polygon with lengths of [64, 97, 94, 42, 33, 71, 98, 104, 50, 47]cm is:	700	perimeter_of_polygons
104	Circumference	Circumference of circle with radius 24	150.79644737231007	circumference
108	Arc length of Angle	Given radius, 39 and angle, 318. Find the arc length of the angle.	Arc length of the angle = 216.45573	arc_length
112	Area of Circle	Area of circle with radius 11	380.2857142857143	area_of_circle

misc

Id	Skill	Example problem	Example Solution	Function Name
9	LCM (Least Common Multiple)	LCM of 1 and 5 =	5	lcm
10	GCD (Greatest Common Denominator)	GCD of 3 and 18 =	3	gcd
27	Prime Factorisation	Find prime factors of 52	[2, 2, 13]	prime_factors
40	Common Factors	Common Factors of 13 and 11 =	[1]	common_factors
51	HCF (Highest Common Factor)	HCF of 4 and 14 =	2	hcf
55	Comparing surds	Fill in the blanks 27^(1/5) _ 4^(1/3)	>	surds_comparison
63	Profit or Loss Percent	Profit percent when CP = 198 and SP = 209 is:	5.555555555555555	profit_loss_percent
66	Geometric Progression	For the given GP [6, 66, 726, 7986, 87846, 966306] ,Find the value of a,common ratio,8th term value, sum upto 9th term	The value of a is 6, common ratio is 11 , 8th term is 116923026 , sum upto 9th term is 1414768614.0	geometric_progression
67	Geometric Mean of N Numbers	Geometric mean of 2 numbers 79 and 94 =	(79*94)^(1/2) = 86.17424209124209	geometric_mean
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 40 , 14 and 88 =	3/((1/40) + (1/14) + (1/88)) = 27.83132530120482	harmonic_mean
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[261.42719124755655, 829.8065702712056, 82.49007842320133, 333.03044204454835, 102.77960652154705, 201.9111176608831, 309.0507046659713, 610.4565223359361, 41.43497441732025, 690.4630475041106, 925.7944414219104, 349.37781230105634, 204.28488944053746, 377.3045460430586, 370.27260172442533, 215.3422861061215, 881.7450792783372, 736.7449607302535, 186.25288081152647, 512.2187637065] is:	2199.237457798086	euclidian_norm
81	Celsius To Fahrenheit	Convert 55 degrees Celsius to degrees Fahrenheit =	131.0	celsius_to_fahrenheit
82	AP Term Calculation	Find the term number 94 of the AP series: -72, -115, -158 ...	-4071	arithmetic_progression_term
83	AP Sum Calculation	Find the sum of first 48 terms of the AP series: 57, -36, -129 ...	-102168.0	arithmetic_progression_sum
85	Converts decimal to Roman Numerals	The number 3762 in Roman Numerals is:	MMMDCCLXII	decimal_to_roman_numerals
92	Complex To Polar Form	rexp(itheta) =	17.46exp(i1.98)	complex_to_polar
93	Union,Intersection,Difference of Two Sets	Given the two sets a={1, 2, 5, 6, 7} ,b={1, 2, 5, 7, 8}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 5, 6, 7, 8},Intersection is {1, 2, 5, 7}, a-b is {6},b-a is {8}, Symmetric difference is {6, 8}	set_operation
94	Base Conversion	Convert 1011000110100000 from base 2 to base 10.	45472	base_conversion
98	Quotient of Powers with Same Base	The Quotient of 7^6 and 7^10 = 7^(6-10) = 7^-4	0.00041649312786339027	quotient_of_power_same_base
99	Quotient of Powers with Same Power	The Quotient of 49^7 and 10^7 = (49/10)^7 = 4.9^7	67822.30728490003	quotient_of_power_same_power
101	Leap Year or Not	Year 2051	is not a leap year	is_leap_year
102	Minute to Hour conversion	Convert 86 minutes to Hours & Minutes	1 hours and 26 minutes	minutes_to_hours
106	signum function	signum of -742 is =	-1	signum_function
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 39.96% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 16 pistons will contain no more than 3 rejected pistons?	6.56	binomial_distribution

statistics

Id	Skill	Example problem	Example Solution	Function Name
30	Combinations of Objects	Number of combinations from 12 objects picked 7 at a time	792	combinations
42	Permutations	Number of Permutations from 11 objects picked 6 at a time =	332640	permutation
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
54	Confidence interval For sample S	The confidence interval for sample [270, 268, 245, 251, 295, 291, 257, 276, 284, 283, 282, 279, 211, 258, 277, 290, 265, 271, 208, 219, 247, 260, 259, 273, 244, 207, 281, 294, 293, 216, 212, 248, 231, 254, 233, 289, 263, 249, 298, 201] with 95% confidence is	(266.9073350347248, 249.69266496527527)	confidence_interval
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[13, 42, 48, 42, 44, 10, 37, 26, 33, 20, 50, 9, 43, 24, 41]	The Mean is 32.13333333333333 , Standard Deviation is 184.64888888888893, Variance is 13.588557277683638	data_summary
76	Mean and Median	Given the series of numbers [26, 66, 31, 85, 23, 25, 42, 19, 46, 92]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 45.5 and Arithmetic median of this series is 36.5	mean_median
107	Conditional Probability	Someone tested positive for a nasty disease which only 0.05% of population have. Test sensitivity (true positive) is equal to SN= 95.33% whereas test specificity (true negative) SP= 95.03%. What is the probability that this guy really has that disease?	0.95%	conditional_probability