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, subjectname]

• genById(id) generates a problem, solution set with generator id id 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	Kwargs
11	Basic Algebra	7x + 9 = 9	0	basic_algebra	maxVariable=10
12	Logarithm	log2(32)	5	log	maxBase=3 maxVal=8
17	Integer Multiplication with 2x2 Matrix	1 * 9, 0], [1, 4 =	9,0],[1,4	multiply_int_to_22_matrix	maxMatrixVal=10 maxRes=100
20	Midpoint of the two point	(0,9),(10,-1)=	(5.0,4.0)	midpoint_of_two_points	maxValue=20
21	Factoring Quadratic	x^2+x-20	(x-4)(x+5)	factoring	range_x1=10 range_x2=10
23	Solve a System of Equations in R^2	-x + 9y = -80, -10x - 7y = -24	x = 8, y = -8	system_of_equations	range_x=10 range_y=10 coeff_mult_range=10
24	Distance between 2 points	Find the distance between (-2, 1) and (-1, 1)	sqrt(1)	distance_two_points	maxValXY=20 minValXY=-20
26	Linear Equations	6x + 15y = 300, 1x + 15y = 275	x = 5, y = 18	linear_equations	n=2 varRange=20 coeffRange=20
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = -6/6x + 1 and y = 7/4x - 4	(20/11, -9/11)	intersection_of_two_lines	minM=-10 maxM=10 minB=-10 maxB=10 minDenominator=1 maxDenominator=6
43	Cross Product of 2 Vectors	[-7, 3, -16] X [9, -4, 5] =	[-49, -109, 1]	vector_cross	minVal=-20 maxVal=20
45	Simple Interest	Simple interest for a principle amount of 4672 dollars, 4% rate of interest and for a time period of 1 years is =	186.88	simple_interest	maxPrinciple=10000 maxRate=10 maxTime=10
46	Multiplication of two matrices	Multiply 6 1 4 0 -4 -5 -5 -9 and -5 1 -10 -7 -1 0 8 -4 0 -8 -7 -5 3 -6 10 1	-31 -26 -80 -66 -2 90 -55 64	matrix_multiplication	maxVal=100 max_dim=10
50	Quadratic Equation	Zeros of the Quadratic Equation 16x^2+181x+77=0	[-0.44, -10.87]	quadratic_equation	maxVal=100
65	Multiplication of 2 complex numbers	(-5-14j) * (-13-7j) =	(-33+217j)	multiply_complex_numbers	minRealImaginaryNum=-20 maxRealImaginaryNum=20
72	Dot Product of 2 Vectors	[10, 14, 7] . [-3, -10, 14] =	-72	vector_dot	minVal=-20 maxVal=20
74	Inverse of a Matrix	Inverse of Matrix Matrix(49, 4, 29], [43, 15, 10], [11, 77, 74) is:	Matrix(170/47803, 1937/95606, -395/95606], [-1536/47803, 3307/95606, 757/95606], [1573/47803, -3729/95606, 563/95606)	invert_matrix	SquareMatrixDimension=3 MaxMatrixElement=99 OnlyIntegerElementsInInvertedMatrix=False
77	Determinant to 2x2 Matrix	Det(67, 21], [69, 23) =	92	int_matrix_22_determinant	maxMatrixVal=100
78	Compound Interest	Compound interest for a principle amount of 8340 dollars, 8% rate of interest and for a time period of 9 year is =	16671.7	compound_interest	maxPrinciple=10000 maxRate=10 maxTime=10
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 3x^2 + 9x + 3 = 0	simplified solution : ((-0.382, -2.618)), generalized solution : ((-9 + sqrt(45))/23, (-9 - sqrt(45))/23)	complex_quadratic	prob_type=0 max_range=10
105	Combine Like terms	2x^1 + 3x^2 + 1x^1	3x^1 + 3x^2	combine_like_terms	maxCoef=10 maxExp=20 maxTerms=10
111	Expanding Factored Binomial	(-5x-6)(-5x-3)	25x^2+45x+18	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	47+14=	61	addition	maxSum=99 maxAddend=50
1	Subtraction	57-36=	21	subtraction	maxMinuend=99 maxDiff=99
2	Multiplication	1*7=	7	multiplication	maxMulti=12
3	Division	45/15=	3	division	maxA=25 maxB=25
6	Square Root	sqrt(25)=	5	square_root	minNo=1 maxNo=12
8	Square	7^2=	49	square	maxSquareNum=20
13	Complex Division	67/23=	2.91	complex_division	maxRes=99 maxDivid=99
16	Fraction Division	(7/4)/(7/6)	3/2	divide_fractions	maxVal=10
28	Fraction Multiplication	(6/10)*(7/5)	21/25	fraction_multiplication	maxVal=10
31	Factorial	3! =	6	factorial	maxInput=6
44	Compare Fractions	Which symbol represents the comparison between 3/7 and 6/5?	<	compare_fractions	maxVal=10
47	Cube Root	What is the cube root of 466 up to 2 decimal places?	7.75	cube_root	minNo=1 maxNo=1000
53	Exponentiation	8^4 =	4096	exponentiation	maxBase=20 maxExpo=10
71	Absolute difference between two numbers		33--24	=	57
80	Percentage of a number	What is 95% of 67?	63.65	percentage	maxValue=99 maxpercentage=99
90	isprime	Is 78 prime?	No	is_prime	max_num=100
97	Power of Powers	Simplify 49^1^1=	49^1	power_of_powers	maxBase=50 maxPower=10

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	4x^9 + 8x^10 + 1x^7	36x^8 + 80x^9 + 7x^6	power_rule_differentiation	maxCoef=10 maxExp=10 maxTerms=5
48	Power Rule Integration	7x^3 + 3x^1 + 7x^3 + 3x^3	(7/3)x^4 + (3/1)x^2 + (7/3)x^4 + (3/3)x^4 + c	power_rule_integration	maxCoef=10 maxExp=10 maxTerms=5
88	Differentiation	differentiate w.r.t x : d(sin(x)+6*x^4)/dx	24*x^3 + cos(x)	differentiation	diff_lvl=2
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 5x^2 + 6x + 46 is =	50.6667	definite_integral	max_coeff=100
110	Stationary Points	f(x)=3x^3 + 8x^2 + 7*x + 4	(-1,2),(-7/9,482/243)	stationary_points	maxExp=3 maxCoef=10

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	1100=	0011	binary_complement_1s	maxDigits=10
5	Modulo Division	84%82=	2	modulo_division	maxRes=99 maxModulo=99
14	Decimal to Binary	Binary of 20=	10100	decimal_to_binary	max_dec=99
15	Binary to Decimal	1100111	103	binary_to_decimal	max_dig=10
56	Fibonacci Series	The Fibonacci Series of the first 12 numbers is ?	[0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89]	fibonacci_series	minNo=1
62	nth Fibonacci number	What is the 12th Fibonacci number?	144	nth_fibonacci_number	maxN=100
64	Binary to Hexidecimal	00111	0x7	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 864=	0x360	decimal_to_hexadeci	max_dec=1000
84	Converts decimal to octal	The decimal number 1800 in Octal is:	0o3410	decimal_to_octal	maxDecimal=4096
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 1 is =	5432	bcd_to_decimal	maxNumber=10000
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 4344 is =	10158	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 19 7 =	(4.024600061217022e-15+65.72670690061993j)	area_of_triangle	maxA=20 maxB=20 maxC=20
19	Triangle exists check	Does triangle with sides 31, 29 and 48 exist?	Yes	valid_triangle	maxSideLength=50
22	Third Angle of Triangle	Third angle of triangle with angles 41 and 10 =	129	third_angle_of_triangle	maxAngle=89
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 18 and 16 =	24.08	pythagorean_theorem	maxLength=20
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 8 sides	135.0	angle_regular_polygon	minVal=3 maxVal=20
32	Surface Area of Cube	Surface area of cube with side = 18m is	1944 m^2	surface_area_cube	maxSide=20 unit='m'
33	Surface Area of Cuboid	Surface area of cuboid with sides = 2m, 1m, 6m is	40 m^2	surface_area_cuboid	maxSide=20 unit='m'
34	Surface Area of Cylinder	Surface area of cylinder with height = 28m and radius = 4m is	804 m^2	surface_area_cylinder	maxRadius=20 maxHeight=50 unit='m'
35	Volum of Cube	Volume of cube with side = 16m is	4096 m^3	volume_cube	maxSide=20 unit='m'
36	Volume of Cuboid	Volume of cuboid with sides = 16m, 5m, 3m is	240 m^3	volume_cuboid	maxSide=20 unit='m'
37	Volume of cylinder	Volume of cylinder with height = 18m and radius = 19m is	20414 m^3	volume_cylinder	maxRadius=20 maxHeight=50 unit='m'
38	Surface Area of cone	Surface area of cone with height = 5m and radius = 17m is	1854 m^2	surface_area_cone	maxRadius=20 maxHeight=50 unit='m'
39	Volume of cone	Volume of cone with height = 36m and radius = 19m is	13609 m^3	volume_cone	maxRadius=20 maxHeight=50 unit='m'
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 165 , 14, 158 =	23	fourth_angle_of_quadrilateral	maxAngle=180
57	Trigonometric Values	What is tan(0)?	0	basic_trigonometry	angles=[0, 30, 45, 60, 90] functions=['sin', 'cos', 'tan']
58	Sum of Angles of Polygon	Sum of angles of polygon with 11 sides =	1620	sum_of_polygon_angles	maxSides=12
60	Surface Area of Sphere	Surface area of Sphere with radius = 11m is	1520.5308443374597 m^2	surface_area_sphere	maxSide=20 unit='m'
61	Volume of Sphere	Volume of sphere with radius 77 m =	1912320.9585617452 m^3	volume_sphere	maxRadius=100
70	Angle between 2 vectors	angle between the vectors [930.31, 981.85, 804.37, 752.12, 365.53, 999.04, 145.81, 535.45, 830.04, 892.98] and [343.3, 858.49, 633.38, 397.4, 225.25, 612.5, 410.13, 294.0, 129.72, 344.08] is:	0.44 radians	angle_btw_vectors	maxEltAmt=20
75	Area of a Sector	Given radius, 31 and angle, 181. Find the area of the sector.	Area of sector = 1517.92158	sector_area	maxRadius=49 maxAngle=359
86	Degrees to Radians	Angle 106 in radians is =	1.85	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, 34 and height, 95?	CSA of cylinder = 20294.69	curved_surface_area_cylinder	maxRadius=49 maxHeight=99
96	Perimeter of Polygons	The perimeter of a 5 sided polygon with lengths of [86, 48, 39, 31, 82]cm is:	286	perimeter_of_polygons	maxSides=12 maxLength=120
104	Circumference	Circumference of circle with radius 69	433.53978619539146	circumference	maxRadius=100
108	Arc length of Angle	Given radius, 10 and angle, 237. Find the arc length of the angle.	Arc length of the angle = 41.36430	arc_length	maxRadius=49 maxAngle=359
112	Area of Circle	Area of circle with radius 100	31428.571428571428	area_of_circle	maxRadius=100

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 5 and 18 =	90	lcm	maxVal=20
10	GCD (Greatest Common Denominator)	GCD of 6 and 16 =	2	gcd	maxVal=20
27	Prime Factorisation	Find prime factors of 108	[2, 2, 3, 3, 3]	prime_factors	minVal=1 maxVal=200
40	Common Factors	Common Factors of 94 and 48 =	[1, 2]	common_factors	maxVal=100
51	HCF (Highest Common Factor)	HCF of 18 and 4 =	2	hcf	maxVal=20
55	Comparing surds	Fill in the blanks 37^(1/8) _ 14^(1/2)	<	surds_comparison	maxValue=100 maxRoot=10
63	Profit or Loss Percent	Loss percent when CP = 683 and SP = 14 is:	97.9502196193265	profit_loss_percent	maxCP=1000 maxSP=1000
66	Geometric Progression	For the given GP [6, 18, 54, 162, 486, 1458] ,Find the value of a,common ratio,7th term value, sum upto 6th term	The value of a is 6, common ratio is 3 , 7th term is 4374 , sum upto 6th term is 2184.0	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 41 and 75 =	(41*75)^(1/2) = 55.452682532047085	geometric_mean	maxValue=100 maxNum=4
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 60 , 5 and 46 =	3/((1/60) + (1/5) + (1/46)) = 12.583586626139818	harmonic_mean	maxValue=100 maxNum=4
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[787.3844948140925, 238.00418481556463, 957.8185591527733] is:	1262.5516729705996	euclidian_norm	maxEltAmt=20
81	Celsius To Fahrenheit	Convert 70 degrees Celsius to degrees Fahrenheit =	158.0	celsius_to_fahrenheit	maxTemp=100
82	AP Term Calculation	Find the term number 47 of the AP series: 31, 69, 107 ...	1779	arithmetic_progression_term	maxd=100 maxa=100 maxn=100
83	AP Sum Calculation	Find the sum of first 78 terms of the AP series: -75, -163, -251 ...	-270114.0	arithmetic_progression_sum	maxd=100 maxa=100 maxn=100
85	Converts decimal to Roman Numerals	The number 2239 in Roman Numerals is:	MMCCXXXIX	decimal_to_roman_numerals	maxDecimal=4000
92	Complex To Polar Form	rexp(itheta) =	11.4exp(i1.84)	complex_to_polar	minRealImaginaryNum=-20, maxRealImaginaryNum=20
93	Union,Intersection,Difference of Two Sets	Given the two sets a={1, 3, 5, 7, 8} ,b={2, 4, 5, 6, 10}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 3, 4, 5, 6, 7, 8, 10},Intersection is {5}, a-b is {8, 1, 3, 7},b-a is {2, 10, 4, 6}, Symmetric difference is {1, 2, 3, 4, 6, 7, 8, 10}	set_operation	minval=3 maxval=7 n_a=4 n_b=5
94	Base Conversion	Convert 1A504 from base 12 to base 16.	9754	base_conversion	maxNum=60000 maxBase=16
98	Quotient of Powers with Same Base	The Quotient of 16^3 and 16^5 = 16^(3-5) = 16^-2	0.00390625	quotient_of_power_same_base	maxBase=50 maxPower=10
99	Quotient of Powers with Same Power	The Quotient of 25^9 and 10^9 = (25/10)^9 = 2.5^9	3814.697265625	quotient_of_power_same_power	maxBase=50 maxPower=10
101	Leap Year or Not	Year 1959	is not a leap year	is_leap_year	minNumber=1900 maxNumber=2099
102	Minute to Hour conversion	Convert 251 minutes to Hours & Minutes	4 hours and 11 minutes	minutes_to_hours	maxMinutes=999
106	signum function	signum of 362 is =	1	signum_function	min=-999 max=999
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 32.59% 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 4 rejected pistons?	42.82	binomial_distribution	``

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 12 objects picked 8 at a time	495	combinations	maxlength=20
42	Permutations	Number of Permutations from 14 objects picked 5 at a time =	240240	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 9 =	4/36	dice_sum_probability	maxDice=3
54	Confidence interval For sample S	The confidence interval for sample [293, 222, 205, 214, 255, 298, 209, 296, 287, 219, 211, 277, 269, 284, 270, 206, 273, 248, 223, 227, 282, 260, 275, 291, 246, 242, 251, 249, 263, 250, 207] with 90% confidence is	(260.5165684278054, 242.83827028187204)	confidence_interval	``
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[40, 6, 7, 46, 50, 30, 18, 29, 27, 38, 12, 15, 22, 44, 21]	The Mean is 27.0 , Standard Deviation is 188.93333333333334, Variance is 13.745302227791623	data_summary	number_values=15 minval=5 maxval=50
76	Mean and Median	Given the series of numbers [5, 98, 52, 58, 6, 50, 38, 55, 48, 16]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 42.6 and Arithmetic median of this series is 49.0	mean_median	maxlen=10
107	Conditional Probability	Someone tested positive for a nasty disease which only 1.66% of population have. Test sensitivity (true positive) is equal to SN= 91.53% whereas test specificity (true negative) SP= 98.48%. What is the probability that this guy really has that disease?	50.41%	conditional_probability	``