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
• 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	4x + 7 = 7	0	basic_algebra
12	Logarithm	log3(6561)	8	log
17	Integer Multiplication with 2x2 Matrix	10 * 3, 9], [5, 7 =	30,90],[50,70	multiply_int_to_22_matrix
20	Midpoint of the two point	(-12,-6),(19,-10)=	(3.5,-8.0)	midpoint_of_two_points
21	Factoring Quadratic	x^2+18x+80	(x+8)(x+10)	factoring
23	Solve a System of Equations in R^2	8x + 6y = 72, -3x + 3y = -6	x = 6, y = 4	system_of_equations
24	Distance between 2 points	Find the distance between (17, -8) and (-9, -14)	sqrt(712)	distance_two_points
26	Linear Equations	-1x + 1y = -27, 11x + -17y = 405	x = 9, y = -18	linear_equations
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -9/4x + 2 and y = -9x - 1	(-4/9, 3)	intersection_of_two_lines
43	Cross Product of 2 Vectors	[-19, 19, 20] X [-12, 20, -4] =	[-476, -316, -152]	vector_cross
45	Simple Interest	Simple interest for a principle amount of 7547 dollars, 10% rate of interest and for a time period of 8 years is =	6037.6	simple_interest
46	Multiplication of two matrices	Multiply -7 -4 -4 -9 -3 7 and 10 -2 4 -6 -5 2	-46 34 -36 14 53 -34 -72 -29 2	matrix_multiplication
50	Quadratic Equation	Zeros of the Quadratic Equation 66x^2+187x+25=0	[-0.14, -2.69]	quadratic_equation
65	Multiplication of 2 complex numbers	(-1+5j) * (-18+20j) =	(-82-110j)	multiply_complex_numbers
72	Dot Product of 2 Vectors	[1, -1, -14] . [17, 6, 20] =	-269	vector_dot
74	Inverse of a Matrix	Inverse of Matrix Matrix(37, 76, 39], [67, 82, 13], [61, 73, 79) is:	Matrix(-1843/47252, 3157/141756, 1105/70878], [375/11813, -136/35439, -533/35439], [37/47252, -645/47252, 343/23626)	invert_matrix
77	Determinant to 2x2 Matrix	Det(91, 18], [68, 24) =	960	int_matrix_22_determinant
78	Compound Interest	Compound interest for a principle amount of 2610 dollars, 5% rate of interest and for a time period of 1 year is =	2740.5	compound_interest
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 4x^2 + 4x + 1 = 0	simplified solution : ((-0.5, -0.5)), generalized solution : ((-4 + 0)/24, (-4 - 0)/24)	complex_quadratic
105	Combine Like terms	1x^2 + 7x^2 + 6x^4 + 5x^4 + 5x^2	13x^2 + 11x^4	combine_like_terms
111	Expanding Factored Binomial	(-5x-10)(+5x+9)	-25x^2-95x-90	expanding

basic_math

Id	Skill	Example problem	Example Solution	Function Name
0	Addition	49+48=	97	addition
1	Subtraction	61-29=	32	subtraction
2	Multiplication	14*1=	14	multiplication
3	Division	57/19=	3	division
6	Square Root	sqrt(1)=	1	square_root
8	Square	6^2=	36	square
13	Complex Division	25/4=	6.25	complex_division
16	Fraction Division	(3/2)/(1/4)	6	divide_fractions
28	Fraction Multiplication	(8/3)*(1/4)	2/3	fraction_multiplication
31	Factorial	5! =	120	factorial
44	Compare Fractions	Which symbol represents the comparison between 9/8 and 5/4?	<	compare_fractions
47	Cube Root	cuberoot of 658 upto 2 decimal places is:	8.7	cube_root
53	Exponentiation	15^10 =	576650390625	exponentiation
71	Absolute difference between two numbers	Absolute difference between numbers -6 and -50 =	44	absolute_difference
80	Percentage of a number	What is 55% of 14?	Required percentage = 7.70%	percentage
90	isprime	71	True	is_prime
97	Power of Powers	The 12^6^4 = 12^(6*4) = 12^24	79496847203390844133441536	power_of_powers

calculus

Id	Skill	Example problem	Example Solution	Function Name
7	Power Rule Differentiation	9x^10 + 6x^10 + 1x^6 + 10x^3	90x^9 + 60x^9 + 6x^5 + 30x^2	power_rule_differentiation
48	Power Rule Integration	3x^10 + 5x^6 + 10x^6	(3/10)x^11 + (5/6)x^7 + (10/6)x^7 + c	power_rule_integration
88	Differentiation	differentiate w.r.t x : d(ln(x)+5*x^2)/dx	10*x + 1/x	differentiation
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 80x^2 + 100x + 5 is =	81.6667	definite_integral
110	Stationary Points	f(x)=10x^3 + 9x^2 + 3	(-3/5,102/25),(0,3)	stationary_points

computer_science

Id	Skill	Example problem	Example Solution	Function Name
4	Binary Complement 1s	010000=	101111	binary_complement_1s
5	Modulo Division	87%99=	87	modulo_division
14	Decimal to Binary	Binary of 3=	11	decimal_to_binary
15	Binary to Decimal	0010110100	180	binary_to_decimal
56	Fibonacci Series	The Fibonacci Series of the first 7 numbers is ?	[0, 1, 1, 2, 3, 5, 8]	fibonacci_series
62	nth Fibonacci number	What is the 47th Fibonacci number?	2971215073	nth_fibonacci_number
64	Binary to Hexidecimal	000011010	0x1a	binary_to_hex
73	Binary 2's Complement	2's complement of 10011 =	1101	binary_2s_complement
79	Decimal to Hexadecimal	Binary of 978=	0x3d2	decimal_to_hexadeci
84	Converts decimal to octal	The decimal number 2183 in Octal is:	0o4207	decimal_to_octal
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 6 is =	26179	bcd_to_decimal
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 8980 is =	2314	decimal_to_bcd

geometry

Id	Skill	Example problem	Example Solution	Function Name
18	Area of Triangle	Area of triangle with side lengths: 10 8 8 =	31.22498999199199	area_of_triangle
19	Triangle exists check	Does triangle with sides 3, 49 and 40 exist?	No	valid_triangle
22	Third Angle of Triangle	Third angle of triangle with angles 40 and 55 =	85	third_angle_of_triangle
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 10 and 8 =	12.81	pythagorean_theorem
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 13 sides	152.31	angle_regular_polygon
32	Surface Area of Cube	Surface area of cube with side = 11m is	726 m^2	surface_area_cube
33	Surface Area of Cuboid	Surface area of cuboid with sides = 2m, 9m, 3m is	102 m^2	surface_area_cuboid
34	Surface Area of Cylinder	Surface area of cylinder with height = 10m and radius = 5m is	471 m^2	surface_area_cylinder
35	Volum of Cube	Volume of cube with side = 14m is	2744 m^3	volume_cube
36	Volume of Cuboid	Volume of cuboid with sides = 19m, 4m, 20m is	1520 m^3	volume_cuboid
37	Volume of cylinder	Volume of cylinder with height = 42m and radius = 17m is	38132 m^3	volume_cylinder
38	Surface Area of cone	Surface area of cone with height = 45m and radius = 1m is	144 m^2	surface_area_cone
39	Volume of cone	Volume of cone with height = 4m and radius = 11m is	506 m^3	volume_cone
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 81 , 55, 163 =	61	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 9 sides =	1260	sum_of_polygon_angles
60	Surface Area of Sphere	Surface area of Sphere with radius = 6m is	452.3893421169302 m^2	surface_area_sphere
61	Volume of Sphere	Volume of sphere with radius 80 m =	2144660.584850632 m^3	volume_sphere
70	Angle between 2 vectors	angle between the vectors [956.55, 864.51, 874.49, 333.53, 113.01, 10.44, 653.97, 374.14, 904.82, 608.05, 99.98, 572.65, 354.05, 655.03, 327.04, 853.25, 319.43, 678.41] and [15.79, 792.32, 392.52, 370.7, 283.13, 531.51, 389.19, 480.01, 188.33, 278.59, 964.88, 541.74, 303.95, 941.8, 96.12, 76.43, 864.81, 112.41] is:	0.88 radians	angle_btw_vectors
75	Area of a Sector	Given radius, 35 and angle, 335. Find the area of the sector.	Area of sector = 3581.19746	sector_area
86	Degrees to Radians	Angle 147 in radians is =	2.57	degree_to_rad
87	Radians to Degrees	Angle 1 in degrees is =	57.3	radian_to_deg
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 48 and height, 55?	CSA of cylinder = 16587.61	curved_surface_area_cylinder
96	Perimeter of Polygons	The perimeter of a 10 sided polygon with lengths of [104, 52, 101, 64, 71, 4, 34, 86, 81, 30]cm is:	627	perimeter_of_polygons
104	Circumference	Circumference of circle with radius 12	75.39822368615503	circumference
108	Arc length of Angle	Given radius, 42 and angle, 156. Find the arc length of the angle.	Arc length of the angle = 114.35397	arc_length
112	Area of Circle	Area of circle with radius 39	4780.285714285714	area_of_circle

misc

Id	Skill	Example problem	Example Solution	Function Name
9	LCM (Least Common Multiple)	LCM of 6 and 20 =	60	lcm
10	GCD (Greatest Common Denominator)	GCD of 2 and 2 =	2	gcd
27	Prime Factorisation	Find prime factors of 100	[2, 2, 5, 5]	prime_factors
40	Common Factors	Common Factors of 84 and 41 =	[1]	common_factors
51	HCF (Highest Common Factor)	HCF of 3 and 20 =	1	hcf
55	Comparing surds	Fill in the blanks 20^(1/4) _ 26^(1/6)	>	surds_comparison
63	Profit or Loss Percent	Profit percent when CP = 235 and SP = 844 is:	259.1489361702128	profit_loss_percent
66	Geometric Progression	For the given GP [7, 42, 252, 1512, 9072, 54432] ,Find the value of a,common ratio,9th term value, sum upto 8th term	The value of a is 7, common ratio is 6 , 9th term is 11757312 , sum upto 8th term is 2351461.0	geometric_progression
67	Geometric Mean of N Numbers	Geometric mean of 2 numbers 74 and 4 =	(74*4)^(1/2) = 17.204650534085253	geometric_mean
68	Harmonic Mean of N Numbers	Harmonic mean of 4 numbers 41 , 30 , 67 , 10 =	4/((1/41) + (1/30) + (1/67) + (1/10)) = 23.168400337362947	harmonic_mean
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[88.31792181152476, 63.99729325678627, 241.6129026822925, 248.43562116710117, 359.69249783374147, 165.59992609948227, 105.69265168153541] is:	547.6912694265379	euclidian_norm
81	Celsius To Fahrenheit	Convert 47 degrees Celsius to degrees Fahrenheit =	116.60000000000001	celsius_to_fahrenheit
82	AP Term Calculation	Find the term number 72 of the AP series: 50, 91, 132 ...	2961	arithmetic_progression_term
83	AP Sum Calculation	Find the sum of first 96 terms of the AP series: -11, 58, 127 ...	313584.0	arithmetic_progression_sum
85	Converts decimal to Roman Numerals	The number 3140 in Roman Numerals is:	MMMCXL	decimal_to_roman_numerals
92	Complex To Polar Form	rexp(itheta) =	17.12exp(i1.69)	complex_to_polar
93	Union,Intersection,Difference of Two Sets	Given the two sets a={8, 4, 7} ,b={1, 2, 5, 7}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 4, 5, 7, 8},Intersection is {7}, a-b is {8, 4},b-a is {1, 2, 5}, Symmetric difference is {1, 2, 4, 5, 8}	set_operation
94	Base Conversion	Convert B76F from base 16 to base 10.	46959	base_conversion
98	Quotient of Powers with Same Base	The Quotient of 2^10 and 2^5 = 2^(10-5) = 2^5	32	quotient_of_power_same_base
99	Quotient of Powers with Same Power	The Quotient of 20^3 and 13^3 = (20/13)^3 = 1.5384615384615385^3	3.641329085116068	quotient_of_power_same_power
101	Leap Year or Not	Year 1988	is a leap year	is_leap_year
102	Minute to Hour conversion	Convert 860 minutes to Hours & Minutes	14 hours and 20 minutes	minutes_to_hours
106	signum function	signum of -220 is =	-1	signum_function
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 35.73% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 14 pistons will contain no more than 2 rejected pistons?	7.57	binomial_distribution

statistics

Id	Skill	Example problem	Example Solution	Function Name
30	Combinations of Objects	Number of combinations from 13 objects picked 7 at a time	1716	combinations
42	Permutations	Number of Permutations from 20 objects picked 5 at a time =	1860480	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 16 =	6/216	dice_sum_probability
54	Confidence interval For sample S	The confidence interval for sample [248, 294, 218, 252, 232, 271, 263, 213, 282, 244, 202, 270, 268, 257, 215, 262, 250, 239, 223, 253] with 80% confidence is	(254.68566484458836, 240.91433515541166)	confidence_interval
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[45, 33, 42, 7, 43, 38, 28, 26, 20, 48, 44, 46, 12, 39, 25]	The Mean is 33.06666666666667 , Standard Deviation is 154.9955555555556, Variance is 12.449721103524993	data_summary
76	Mean and Median	Given the series of numbers [12, 81, 93, 55, 5, 46, 35, 6, 91, 50]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 47.4 and Arithmetic median of this series is 48.0	mean_median
107	Conditional Probability	Someone tested positive for a nasty disease which only 0.52% of population have. Test sensitivity (true positive) is equal to SN= 98.31% whereas test specificity (true negative) SP= 96.83%. What is the probability that this guy really has that disease?	13.95%	conditional_probability