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://lukew3.github.io/mathgenerator

See CONTRIBUTING.md for information about how to contribute.

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)

Documentation

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

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

• Pass the kwarg format=latex to return problem and solution set as latex. If latex is not available for that generator, the problem will return the string "Latex unavailable"

• Pass the kwarg format=raw to return just the raw data for each generator. An array of each variable necessary to the generator is returned.

List of Generators

algebra

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
11	Basic Algebra	9x + 5 = 8	1/3	basic_algebra	maxVariable=10
12	Logarithm	log2(256)	8	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	9 * 7, 8], [6, 8 =	63,72],[54,72	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	(-12,5),(-20,6)=	(-16.0,5.5)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2-8x+15	(x-3)(x-5)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	5x + 3y = -1, -9x - 3y = -15	x = 4, y = -7	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (-19, -9) and (16, 14)	sqrt(1754)	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	7x + -13y = 198, -4x + 19y = -171	x = 19, y = -5	linear_equations	n=2 varRange=20 coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -10/6x + 7 and y = -1/3x + 9	(-3/2, 19/2)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[12, 14, -20] X [11, 13, 3] =	[302, -256, 2]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 2634 dollars, 1% rate of interest and for a time period of 10 years is =	263.4	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply 7 4 -1 -4 5 8 -9 7 -6 0 -3 -10 and 1 -5 -9 2 -10 10 -9 6 -8 -7 4 10	52 -97 -55 53 -131 177 91 -28 -22	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 4x^2+176x+52=0	[-0.3, -43.7]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(2+14j) * (-7-11j) =	(140-120j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[-18, 1, -5] . [10, 6, 19] =	-269	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix(23, 69, 7], [40, 91, 89], [11, 1, 47) is:	Matrix(1047/6857, -809/6857, 1376/6857], [-901/27428, 251/6857, -1767/27428], [-961/27428, 184/6857, -667/27428)	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det(87, 46], [20, 61) =	4387	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 1502 dollars, 8% rate of interest and for a time period of 8 year is =	2780.1	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 4x^2 + 9x + 2 = 0	simplified solution : ((-0.25, -2.0)), generalized solution : ((-9 + 7)/24, (-9 - 7)/24)	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	4x^6 + 9x^6 + 1x^4 + 2x^4 + 4x^1 + 3x^2 + 8x^5	4x^1 + 3x^2 + 3x^4 + 8x^5 + 13x^6	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(x-4)(-1x+9)	-1x^2+13x-36	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	(33+2)	35	addition	maxSum=99 maxAddend=50
1	Subtraction	11-9=	2	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	10*9=	90	multiplication	maxMulti=12
3	Division	208/16=	13	division	maxA=25 maxB=25
6	Square Root	sqrt(144)=	12	square_root	minNo=1 maxNo=12
8	Square	15^2=	225	square	maxSquareNum=20
13	Complex Division	62/71=	0.87	complex_division	maxRes=99 maxDivid=99
16	Fraction Division	(1/8)/(4/6)	3/16	divide_fractions	maxVal=10
28	Fraction Multiplication	(4/7)*(8/5)	32/35	fraction_multiplication	maxVal=10
31	Factorial	6! =	720	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 8/7 and 9/4?	<	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 419 up to 2 decimal places?	7.48	cube_root	minNo=1 maxNo=1000
53	Exponentiation	19^4 =	130321	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers		86--54	=	140
80	Percentage of a number	What is 87% of 15?	13.05	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 59 prime?	Yes	is_prime	max_num=100
97	Power of Powers	Simplify 23^9^4=	23^36	power_of_powers	maxBase=50 maxPower=10
118	Percentage difference	What is the percentage difference between 151 and 58?	89.0%	percentage_difference	maxValue=200 minValue=0
119	Percentage error	Find the percentage error when observed value equals -81 and exact value equals -71.	14.08%	percentage_error	maxValue=100 minValue=-100
120	Greatest Common Divisor of N Numbers	GCD(216648151,624159450)=	1	greatest_common_divisor	numbersCount=2 maximalNumberLimit=10**9

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	2x^1	2x^0	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	8x^3 + 6x^2 + 2x^6	(8/3)x^4 + (6/2)x^3 + (2/6)x^7 + c	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Differentiation	differentiate w.r.t x : d(exp(x)+9*x^(-2))/dx	exp(x) - 18/x^3	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 76x^2 + 77x + 65 is =	128.8333	definite_integral	max_coeff=100
110	Stationary Points	f(x)=x^3 + x^2 + x + 10		stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	00=	11	binary_complement_1s	maxDigits=10
5	Modulo Division	7%69=	7	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 87=	1010111	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 8 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13]	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 13th Fibonacci number?	233	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	00100	0x4	binary_to_hex	max_dig=10
73	Binary 2's Complement	2's complement of 1010 =	110	binary_2s_complement	maxDigits=10
79	Decimal to Hexadecimal	Binary of 461=	0x1cd	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 1681 in Octal is:	0o3221	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 8 is =	33878	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 6236 is =	18512	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: 8 4 6 =	11.62	area_of_triangle	maxA=20 maxB=20
19	Triangle exists check	Does triangle with sides 3, 48 and 23 exist?	No	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 37 and 79 =	64	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 7 and 3 =	7.62	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 18 sides	160.0	angle_regular_polygon	minVal=3 maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 16m is	1536 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 14m, 3m, 18m is	696 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 2m and radius = 2m is	50 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volume of Cube	Volume of cube with side = 12m is	1728 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 12m, 11m, 10m is	1320 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 25m and radius = 18m is	25446 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 2m and radius = 12m is	911 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 25m and radius = 11m is	3167 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 98 , 38, 15 =	209	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is tan(60)?	√3	basic_trigonometry	angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan']
58	Sum of Angles of Polygon	Sum of angles of polygon with 4 sides =	360	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 15m is	2827.4333882308138 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 74 m =	1697398.3219443604 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [415.62, 687.72, 239.91, 870.78, 127.29, 911.51, 534.49, 646.85, 347.39] and [705.5, 491.92, 634.77, 338.27, 249.11, 600.92, 272.22, 675.23, 798.99] is:	0.57 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 46 and angle, 245. Find the area of the sector.	Area of sector = 4524.06795	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 168 in radians is =	2.93	degree_to_rad	max_deg=360
87	Radians to Degrees	Angle 1 in degrees is =	57.3	radian_to_deg	max_rad=3
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 29 and height, 69?	CSA of cylinder = 12572.65	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 9 sided polygon with lengths of [3, 100, 108, 49, 101, 99, 30, 88, 108]cm is:	686	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 98	615.7521601035994	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 33 and angle, 353. Find the arc length of the angle.	Arc length of the angle = 203.31340	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 47	6942.571428571429	area_of_circle	maxRadius=100
113	Volume of frustum	Volume of frustum with height = 3m and r1 = 7m is and r2 = 7m is	461.0 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 (-17,-4) and (-8,19) in slope-intercept form?	9y = 23x + 355	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,-6) and passing through (2.0, -6.0) is	201.06	area_of_circle_given_center_and_point	maxCoordinate = 10 maxRadius=10
117	Volume of Hemisphere	Volume of hemisphere with radius 7 m =	718.378 m^3	volume_hemisphere	maxRadius=100
122	Volume of pyramid	Volume of pyramid with base length = 4 m, base width = 8 m and height = 24 m is	256.0 m^3	volume_pyramid	maxLength=20 maxWidth=20 maxHeight=50 unit='m'
123	Surface area of pyramid	Surface area of pyramid with base length = 10m, base width = 24m, and height = 13m	480 m^2	surface_area_pyramid	unit='m'

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 7 and 20 =	140	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 16 and 2 =	2	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 13	[13]	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 58 and 85 =	[1]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 15 and 13 =	1	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 52^(1/6) _ 49^(1/9)	>	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Loss percent when CP = 899 and SP = 190 is:	78.86540600667408	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [7, 35, 175, 875, 4375, 21875] ,Find the value of a,common ratio,6th term value, sum upto 9th term	The value of a is 7, common ratio is 5 , 6th term is 21875 , sum upto 9th term is 3417967.0	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 85 and 45 =	(85*45)^(1/2) = 61.84658438426491	geometric_mean	maxValue=100 maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 12 , 39 and 76 =	3/((1/12) + (1/39) + (1/76)) = 24.56353591160221	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[994.7263200922915, 971.6812595950137, 51.85289296192064, 526.1757082313851, 51.16775130159046, 488.76324739869983, 896.5928964376717] is:	1805.1540081935675	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert 91 degrees Celsius to degrees Fahrenheit =	195.8	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 7 of the AP series: 3, -28, -59 ...	-183	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 70 terms of the AP series: 53, 70, 87 ...	44765.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 0 in Roman Numerals is:	MCCLXXVII	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	18.44(-12.0theta + i-14.0theta)	-2.28	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={2, 10, 5} ,b={1, 5, 6, 8, 9}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 5, 6, 8, 9, 10},Intersection is {5}, a-b is {2, 10},b-a is {8, 1, 6, 9}, Symmetric difference is {1, 2, 6, 8, 9, 10}	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert 1A1A9 from base 12 to base 2.	1001010110010001	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 10^6 and 10^9 = 10^(6-9) = 10^-3	0.001	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 16^5 and 18^5 = (16/18)^5 = 0.8888888888888888^5	0.5549289573066435	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Year 1910	is not a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 614 minutes to Hours & Minutes	10 hours and 14 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of -726 is =	-1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 32.46% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 19 pistons will contain no more than 6 rejected pistons?	57.56	binomial_distribution	``
116	Factors of a number	Factors of 900 =	[1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900]	Factors	maxVal=1000
121	Product of scientific notaions	Product of scientific notations 7.84x10^60 and 5.05x10^5 =	3.96x10^66	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 15 objects picked 3 at a time	455	combinations	maxlength=20
42	Permutations	Number of Permutations from 18 objects picked 6 at a time =	13366080	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 2 =	1/36	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [257, 235, 281, 246, 292, 284, 214, 244, 229, 220, 279, 275, 239, 282, 211, 256, 269, 204, 212, 271, 249, 264, 267, 200, 251, 258, 298, 252, 210] with 90% confidence is	(258.442496139615, 241.4885383431436)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[26, 28, 15, 9, 21, 23, 5, 41, 7, 50, 33, 42, 24, 39, 11]	The Mean is 24.933333333333334 , Standard Deviation is 182.46222222222224, Variance is 13.50785779545455	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [1, 7, 9, 17, 23, 30, 64, 74, 79, 85]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 38.9 and Arithmetic median of this series is 26.5	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.13% of population have. Test sensitivity (true positive) is equal to SN= 92.22% whereas test specificity (true negative) SP= 91.47%. What is the probability that this guy really has that disease?	11.0%	conditional_probability	``