mathgenerator/README.md

mathgenerator

A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.

To try out generators, go to https://lukew3.github.io/mathgenerator

See CONTRIBUTING.md for information about how to contribute.

Table of Contents

• Installation
• Usage
• List of Generators
  • algebra
  • basic_math
  • calculus
  • computer_science
  • geometry
  • misc
  • statistics

Installation

The project can be install via pip

pip install mathgenerator

Usage

Here is an example of how you would generate an addition problem:

import mathgenerator

#generate an addition problem
problem, solution = mathgenerator.addition()

#another way to generate an addition problem using genById()
problem, solution = mathgenerator.genById(0)

You may prefer to use import mathgenerator as mg and run functions like mg.addition() so that you don't have to type as much.

Problem/solution pairs are generated with either:

• mathgenerator.<generator_name>() - generates a problem, solution set from the given generator name.
• mathgenerator.genById(id) - generates a problem, solution set with generator id provided by the id parameter

You can also use getGenList() to return a list of all generators included in the library in the format:

[id, title, self, funcname, subjectname]

List of Generators

algebra

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
11	Basic Algebra	9x + 5 = 9	4/9	basic_algebra	maxVariable=10
12	Logarithm	log2(32)	5	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	0 * 8, 10], [1, 10 =	0,0],[0,0	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	(8,-9),(20,-14)=	(14.0,-11.5)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2+x-30	(x-5)(x+6)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	10x - 10y = -10, 6x + 7y = 98	x = 7, y = 8	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (-10, 11) and (-2, 19)	sqrt(128)	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	5x + -11y = -44, 14x + 12y = -166	x = -11, y = -1	linear_equations	n=2 varRange=20 coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -9x - 9 and y = -6/3x + 2	(-11/7, 36/7)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[6, -20, 10] X [-13, 12, -19] =	[260, -16, -188]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 3854 dollars, 2% rate of interest and for a time period of 3 years is =	231.24	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply 8 -9 -8 2 8 5 -6 -6 7 and -8 3 5 -10 -4 -1 -10 10 -6	106 -20 97 -146 24 -28 38 76 -66	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 78x^2+156x+38=0	[-0.28, -1.72]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(-2-13j) * (-15-11j) =	(-113+217j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[-4, 7, -3] . [-10, 9, -16] =	151	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix(5, 89, 34], [43, 21, 47], [3, 86, 7) is:	Matrix(-779/17975, 2301/89875, 3469/89875], [-32/17975, -67/89875, 1227/89875], [727/17975, -163/89875, -3722/89875)	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det(77, 20], [68, 89) =	5493	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 8503 dollars, 10% rate of interest and for a time period of 10 year is =	22054.59	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 5x^2 + 8x + 2 = 0	simplified solution : ((-0.31, -1.29)), generalized solution : ((-8 + sqrt(24))/25, (-8 - sqrt(24))/25)	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	1x^5 + 10x^1 + 2x^1 + 3x^2 + 5x^1 + 4x^2 + 2x^3	17x^1 + 7x^2 + 2x^3 + 1x^5	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(7x-2)(+6x-3)	42x^2-33x+6	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	14+15=	29	addition	maxSum=99 maxAddend=50
1	Subtraction	55-55=	0	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	2*11=	22	multiplication	maxMulti=12
3	Division	156/12=	13	division	maxA=25 maxB=25
6	Square Root	sqrt(9)=	3	square_root	minNo=1 maxNo=12
8	Square	8^2=	64	square	maxSquareNum=20
13	Fraction to Decimal	32/35=	0.91	fraction_to_decimal	maxRes=99 maxDivid=99
16	Fraction Division	(9/10)/(10/4)	9/25	divide_fractions	maxVal=10
28	Fraction Multiplication	(10/4)*(1/2)	5/4	fraction_multiplication	maxVal=10
31	Factorial	5! =	120	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 7/6 and 1/5?	>	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 648 up to 2 decimal places?	8.65	cube_root	minNo=1 maxNo=1000
53	Exponentiation	7^9 =	40353607	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers		-96--27	=	69
80	Percentage of a number	What is 61% of 38?	23.18	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 40 prime?	No	is_prime	max_num=100
97	Power of Powers	Simplify 2^9^4=	2^36	power_of_powers	maxBase=50 maxPower=10
118	Percentage difference	What is the percentage difference between 160 and 190?	17.14%	percentage_difference	maxValue=200 minValue=0
119	Percentage error	Find the percentage error when observed value equals 27 and exact value equals 82.	67.07%	percentage_error	maxValue=100 minValue=-100
120	Greatest Common Divisor of N Numbers	GCD(850468745,474001818)=	1	greatest_common_divisor	numbersCount=2 maximalNumberLimit=10**9
124	Is Composite	Is 231 composite?	Yes	is_composite	maxNum=250

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	8x^4 + 7x^8	32x^3 + 56x^7	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	5x^5 + 3x^7 + 7x^8 + 8x^6	(5/5)x^6 + (3/7)x^8 + (7/8)x^9 + (8/6)x^7 + c	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Differentiation	differentiate w.r.t x : d(sec(x)+7*x^2)/dx	14*x + tan(x)*sec(x)	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 10x^2 + 70x + 10 is =	48.3333	definite_integral	max_coeff=100
110	Stationary Points	f(x)=7x^3 + 2x		stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	1000=	0111	binary_complement_1s	maxDigits=10
5	Modulo Division	25%15=	10	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 72=	1001000	decimal_to_binary	max_dec=99
15	Binary to Decimal	1	1	binary_to_decimal	max_dig=10
56	Fibonacci Series	The Fibonacci Series of the first 11 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55]	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 85th Fibonacci number?	259695496911123328	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	001	0x1	binary_to_hex	max_dig=10
73	Binary 2's Complement	2's complement of 1011011001 =	100100111	binary_2s_complement	maxDigits=10
79	Decimal to Hexadecimal	Binary of 545=	0x221	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 470 in Octal is:	0o726	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 6 is =	25205	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 4491 is =	11811	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: 6 20 22 =	58.79	area_of_triangle	maxA=20 maxB=20
19	Triangle exists check	Does triangle with sides 38, 28 and 27 exist?	Yes	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 14 and 63 =	103	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 9 and 4 =	9.85	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 11 sides	147.27	angle_regular_polygon	minVal=3 maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 8m is	384 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 1m, 15m, 11m is	382 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 3m and radius = 17m is	2136 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volume of Cube	Volume of cube with side = 9m is	729 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 10m, 12m, 9m is	1080 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 4m and radius = 15m is	2827 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 26m and radius = 15m is	2121 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 31m and radius = 7m is	1590 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 39 , 151, 137 =	33	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is tan(45)?	1	basic_trigonometry	angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan']
58	Sum of Angles of Polygon	Sum of angles of polygon with 5 sides =	540	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 19m is	4536.459791783661 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 92 m =	3261760.666984705 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [497.44, 781.23, 668.33, 665.31, 359.43, 287.08, 844.18, 596.49, 367.01, 674.44, 524.18, 217.7, 698.12] and [909.53, 70.04, 869.99, 53.15, 508.12, 404.16, 470.25, 955.48, 868.15, 987.99, 480.44, 354.16, 742.91] is:	0.58 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 28 and angle, 255. Find the area of the sector.	Area of sector = 1744.63112	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 47 in radians is =	0.82	degree_to_rad	max_deg=360
87	Radians to Degrees	Angle 0 in degrees is =	0.0	radian_to_deg	max_rad=3
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 23 and height, 27?	CSA of cylinder = 3901.86	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 10 sided polygon with lengths of [58, 17, 71, 60, 116, 104, 35, 71, 105, 116]cm is:	753	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 15	94.24777960769379	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 37 and angle, 201. Find the arc length of the angle.	Arc length of the angle = 129.80014	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 91	26026.0	area_of_circle	maxRadius=100
113	Volume of frustum	Volume of frustum with height = 40m and r1 = 6m is and r2 = 6m is	21404.0 m^3	volume_frustum	maxR1=20 maxR2=20 maxHeight=50 unit='m'
114	Equation of line from two points	What is the equation of the line between points (10,4) and (14,15) in slope-intercept form?	4y = 11x -94	equation_of_line_from_two_points	maxCoordinate=20 minCoordinate=-20
115	Area of Circle given center and a point on circle	Area of circle with center (10,7) and passing through (14.86, 14.57) is	254.47	area_of_circle_given_center_and_point	maxCoordinate = 10 maxRadius=10
117	Volume of Hemisphere	Volume of hemisphere with radius 39 m =	124237.423 m^3	volume_hemisphere	maxRadius=100
122	Volume of pyramid	Volume of pyramid with base length = 15 m, base width = 13 m and height = 37 m is	2405.0 m^3	volume_pyramid	maxLength=20 maxWidth=20 maxHeight=50 unit='m'
123	Surface area of pyramid	Surface area of pyramid with base length = 40m, base width = 40m, and height = 16m	2560 m^2	surface_area_pyramid	unit='m'
125	Complementary and Supplementary Angle	The supplementary angle of 60 =	120	complementary_and_supplementary_angle	maxSupp=180 maxComp=90

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 8 and 17 =	136	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 12 and 6 =	6	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 151	[151]	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 8 and 95 =	[1]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 16 and 3 =	1	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 84^(1/6) _ 97^(1/1)	<	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Profit percent when CP = 258 and SP = 601 is:	132.9457364341085	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [7, 14, 28, 56, 112, 224] ,Find the value of a,common ratio,7th term value, sum upto 11th term	The value of a is 7, common ratio is 2 , 7th term is 448 , sum upto 11th term is 14329.0	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 2 numbers 58 and 61 =	(58*61)^(1/2) = 59.481089431852205	geometric_mean	maxValue=100 maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 65 , 98 and 30 =	3/((1/65) + (1/98) + (1/30)) = 50.91474245115453	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[666.3121024557763, 339.3827343783811, 598.1073078463166, 514.5857680685369, 604.2767600509419, 642.5534920836018, 452.63625705604005, 833.1252882301409] is:	1690.7649282758944	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert 76 degrees Celsius to degrees Fahrenheit =	168.8	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 37 of the AP series: -100, -61, -22 ...	1304	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 28 terms of the AP series: 81, 64, 47 ...	-4158.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 0 in Roman Numerals is:	XIII	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	18.6(11.0theta + i15.0theta)	0.94	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={9, 2, 3, 1} ,b={8, 6}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 3, 6, 8, 9},Intersection is set(), a-b is {9, 2, 3, 1},b-a is {8, 6}, Symmetric difference is {1, 2, 3, 6, 8, 9}	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert D6E8 from base 16 to base 10.	55016	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 46^9 and 46^1 = 46^(9-1) = 46^8	20047612231936	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 1^8 and 21^8 = (1/21)^8 = 0.047619047619047616^8	2.643903757924558e-11	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Year 1942	is not a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 20 minutes to Hours & Minutes	0 hours and 20 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of -217 is =	-1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 34.16% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 11 pistons will contain no more than 9 rejected pistons?	99.98	binomial_distribution	``
116	Factors of a number	Factors of 513 =	[1, 3, 9, 19, 27, 57, 171, 513]	factors	maxVal=1000
121	Product of scientific notations	Product of scientific notations 2.39x10^78 and 9.75x10^44 =	2.33x10^123	product_of_scientific_notations	minExpVal=-100 maxExpVal=100

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 13 objects picked 9 at a time	715	combinations	maxlength=20
42	Permutations	Number of Permutations from 11 objects picked 3 at a time =	990	permutation	maxlength=20
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 4 =	3/36	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [254, 295, 271, 281, 218, 270, 242, 274, 247, 202, 253, 226, 237, 296, 286, 214, 215, 240, 248, 283, 290, 205, 230, 251, 224, 227] with 90% confidence is	(258.3421056762939, 240.04250970832146)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[21, 49, 37, 16, 24, 23, 18, 38, 50, 40, 13, 7, 29, 46, 41]	The Mean is 30.133333333333333 , Standard Deviation is 178.38222222222223, Variance is 13.35598076601723	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [4, 5, 20, 30, 32, 42, 52, 56, 71, 86]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 39.8 and Arithmetic median of this series is 37.0	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.84% of population have. Test sensitivity (true positive) is equal to SN= 95.07% whereas test specificity (true negative) SP= 95.68%. What is the probability that this guy really has that disease?	29.2%	conditional_probability	``