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	10x + 2 = 4	1/5	basic_algebra	['maxVariable=10']
12	Logarithm	log3(27)	3	log	['maxBase=3', 'maxVal=8']
17	Integer Multiplication with 2x2 Matrix	0 * 0, 7], [10, 2 =	0,0],[0,0	multiply_int_to_22_matrix	['maxMatrixVal=10', 'maxRes=100']
20	Midpoint of the two point	(-10,-18),(18,3)=	(4.0,-7.5)	midpoint_of_two_points	['maxValue=20']
21	Factoring Quadratic	x^2-16x+64	(x-8)(x-8)	factoring	['range_x1=10', 'range_x2=10']
23	Solve a System of Equations in R^2	9x - 3y = 0, -x + 7y = -40	x = -2, y = -6	system_of_equations	['range_x=10', 'range_y=10', 'coeff_mult_range=10']
24	Distance between 2 points	Find the distance between (-13, -17) and (-18, -20)	sqrt(34)	distance_two_points	['maxValXY=20', 'minValXY=-20']
26	Linear Equations	-18x + 1y = -319, 6x + -9y = 219	x = 17, y = -13	linear_equations	['n=2', 'varRange=20', 'coeffRange=20']
41	Intersection of Two Lines	Find the point of intersection of the two lines: y = 0/3x and y = 7/3x + 10	(-30/7, 0)	intersection_of_two_lines	['minM=-10', 'maxM=10', 'minB=-10', 'maxB=10', 'minDenominator=1', 'maxDenominator=6']
43	Cross Product of 2 Vectors	[-2, -8, 6] X [12, 9, 11] =	[-142, 94, 78]	vector_cross	['minVal=-20', 'maxVal=20']
45	Simple Interest	Simple interest for a principle amount of 4555 dollars, 7% rate of interest and for a time period of 7 years is =	2231.95	simple_interest	['maxPrinciple=10000', 'maxRate=10', 'maxTime=10']
46	Multiplication of two matrices	Multiply 1 10 -4 8 6 10 -4 4 and 6 7 -1 0 6 -9 -10 6 -9 8 -5 7 -7 6 -6 8	46 -67 -129 96 104 -56 -110 64	matrix_multiplication	['maxVal=100', 'max_dim=10']
50	Quadratic Equation	Zeros of the Quadratic Equation 44x^2+159x+52=0	[-0.36, -3.25]	quadratic_equation	['maxVal=100']
65	Multiplication of 2 complex numbers	(8-1j) * (8-4j) =	(60-40j)	multiply_complex_numbers	['minRealImaginaryNum=-20', 'maxRealImaginaryNum=20']
72	Dot Product of 2 Vectors	[3, 11, 6] . [19, -1, 2] =	58	vector_dot	['minVal=-20', 'maxVal=20']
74	Inverse of a Matrix	Inverse of Matrix Matrix(7, 31, 15], [30, 43, 68], [13, 41, 61) is:	Matrix(15/1856, 1/16, -133/1856], [43/928, -1/88, 13/10208], [-61/1856, -1/176, 629/20416)	invert_matrix	['SquareMatrixDimension=3', 'MaxMatrixElement=99', 'OnlyIntegerElementsInInvertedMatrix=False']
77	Determinant to 2x2 Matrix	Det(93, 61], [9, 66) =	5589	int_matrix_22_determinant	['maxMatrixVal=100']
78	Compound Interest	Compound interest for a principle amount of 3225 dollars, 9% rate of interest and for a time period of 9 year is =	7004.36	compound_interest	['maxPrinciple=10000', 'maxRate=10', 'maxTime=10']
100	complex Quadratic Equation	Find the roots of given Quadratic Equation 4x^2 + 8x + 3 = 0	simplified solution : ((-0.5, -1.5)), generalized solution : ((-8 + 4)/24, (-8 - 4)/24)	complex_quadratic	['prob_type=0', 'max_range=10']
105	Combine Like terms	4x^3 + 3x^6 + 5x^1 + 7x^6 + 6x^4 + 1x^4 + 3x^5 + 6x^5 + 2x^6 + 4x^3	5x^1 + 8x^3 + 7x^4 + 9x^5 + 12x^6	combine_like_terms	['maxCoef=10', 'maxExp=20', 'maxTerms=10']
111	Expanding Factored Binomial	(7x-8)(-9x+9)	-63x^2+135x-72	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	31+34=	65	addition	['maxSum=99', 'maxAddend=50']
1	Subtraction	27-19=	8	subtraction	['maxMinuend=99', 'maxDiff=99']
2	Multiplication	9*9=	81	multiplication	['maxMulti=12']
3	Division	12/4=	3	division	['maxA=25', 'maxB=25']
6	Square Root	sqrt(16)=	4	square_root	['minNo=1', 'maxNo=12']
8	Square	3^2=	9	square	['maxSquareNum=20']
13	Complex Division	61/61=	1.0	complex_division	['maxRes=99', 'maxDivid=99']
16	Fraction Division	(7/1)/(1/5)	35	divide_fractions	['maxVal=10']
28	Fraction Multiplication	(9/4)*(2/7)	9/14	fraction_multiplication	['maxVal=10']
31	Factorial	3! =	6	factorial	['maxInput=6']
44	Compare Fractions	Which symbol represents the comparison between 9/4 and 8/2?	<	compare_fractions	['maxVal=10']
47	Cube Root	What is the cube root of 921 up to 2 decimal places?	9.73	cube_root	['minNo=1', 'maxNo=1000']
53	Exponentiation	16^10 =	1099511627776	exponentiation	['maxBase=20', 'maxExpo=10']
71	Absolute difference between two numbers		0--22	=	22
80	Percentage of a number	What is 72% of 15?	10.80	percentage	['maxValue=99', 'maxpercentage=99']
90	isprime	Is 19 prime?	Yes	is_prime	['max_num=100']
97	Power of Powers	Simplify 1^10^7=	1^70	power_of_powers	['maxBase=50', 'maxPower=10']

calculus

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
7	Power Rule Differentiation	10x^9 + 3x^5	90x^8 + 15x^4	power_rule_differentiation	['maxCoef=10', 'maxExp=10', 'maxTerms=5']
48	Power Rule Integration	9x^5 + 1x^2 + 8x^2 + 8x^4	(9/5)x^6 + (1/2)x^3 + (8/2)x^3 + (8/4)x^5 + c	power_rule_integration	['maxCoef=10', 'maxExp=10', 'maxTerms=5']
88	Differentiation	differentiate w.r.t x : d(sec(x)+2*x^(-3))/dx	tan(x)*sec(x) - 6/x^4	differentiation	['diff_lvl=2']
89	Definite Integral of Quadratic Equation	The definite integral within limits 0 to 1 of the equation 86x^2 + 2x + 59 is =	88.6667	definite_integral	['max_coeff=100']
110	Stationary Points	f(x)=5x^3 + 10x^2 + 6*x + 2	(-2/3 - sqrt(10)/15,5*(-2/3 - sqrt(10)/15)**3 - 2 - 2sqrt(10)/5 + 10(-2/3 - sqrt(10)/15)*2),(-2/3 + sqrt(10)/15,-2 + 5(-2/3 + sqrt(10)/15)**3 + 2sqrt(10)/5 + 10(-2/3 + sqrt(10)/15)**2)	stationary_points	['maxExp=3', 'maxCoef=10']

computer_science

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
4	Binary Complement 1s	0011100=	1100011	binary_complement_1s	['maxDigits=10']
5	Modulo Division	68%37=	31	modulo_division	['maxRes=99', 'maxModulo=99']
14	Decimal to Binary	Binary of 77=	1001101	decimal_to_binary	['max_dec=99']
15	Binary to Decimal	001101110	110	binary_to_decimal	['max_dig=10']
56	Fibonacci Series	The Fibonacci Series of the first 1 numbers is ?	[0]	fibonacci_series	['minNo=1']
62	nth Fibonacci number	What is the 42th Fibonacci number?	267914296	nth_fibonacci_number	['maxN=100']
64	Binary to Hexidecimal	000000000	0x0	binary_to_hex	['max_dig=10']
73	Binary 2's Complement	2's complement of 110110 =	1010	binary_2s_complement	['maxDigits=10']
79	Decimal to Hexadecimal	Binary of 927=	0x39f	decimal_to_hexadeci	['max_dec=1000']
84	Converts decimal to octal	The decimal number 2925 in Octal is:	0o5555	decimal_to_octal	['maxDecimal=4096']
91	Binary Coded Decimal to Integer	Integer of Binary Coded Decimal 7 is =	28981	bcd_to_decimal	['maxNumber=10000']
103	Decimal to Binary Coded Decimal	BCD of Decimal Number 9755 is =	26111	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: 3 1 5 =	(2.1045137462542978e-16+3.43693177121688j)	area_of_triangle	['maxA=20', 'maxB=20', 'maxC=20']
19	Triangle exists check	Does triangle with sides 20, 16 and 9 exist?	Yes	valid_triangle	['maxSideLength=50']
22	Third Angle of Triangle	Third angle of triangle with angles 36 and 25 =	119	third_angle_of_triangle	['maxAngle=89']
25	Pythagorean Theorem	The hypotenuse of a right triangle given the other two lengths 15 and 1 =	15.03	pythagorean_theorem	['maxLength=20']
29	Angle of a Regular Polygon	Find the angle of a regular polygon with 10 sides	144.0	angle_regular_polygon	['minVal=3', 'maxVal=20']
32	Surface Area of Cube	Surface area of cube with side = 19m is	2166 m^2	surface_area_cube	['maxSide=20', "unit='m'"]
33	Surface Area of Cuboid	Surface area of cuboid with sides = 11m, 16m, 16m is	1216 m^2	surface_area_cuboid	['maxSide=20', "unit='m'"]
34	Surface Area of Cylinder	Surface area of cylinder with height = 42m and radius = 7m is	2155 m^2	surface_area_cylinder	['maxRadius=20', 'maxHeight=50', "unit='m'"]
35	Volum of Cube	Volume of cube with side = 11m is	1331 m^3	volume_cube	['maxSide=20', "unit='m'"]
36	Volume of Cuboid	Volume of cuboid with sides = 2m, 9m, 8m is	144 m^3	volume_cuboid	['maxSide=20', "unit='m'"]
37	Volume of cylinder	Volume of cylinder with height = 11m and radius = 7m is	1693 m^3	volume_cylinder	['maxRadius=20', 'maxHeight=50', "unit='m'"]
38	Surface Area of cone	Surface area of cone with height = 28m and radius = 1m is	91 m^2	surface_area_cone	['maxRadius=20', 'maxHeight=50', "unit='m'"]
39	Volume of cone	Volume of cone with height = 27m and radius = 17m is	8171 m^3	volume_cone	['maxRadius=20', 'maxHeight=50', "unit='m'"]
49	Fourth Angle of Quadrilateral	Fourth angle of quadrilateral with angles 34 , 198, 6 =	122	fourth_angle_of_quadrilateral	['maxAngle=180']
57	Trigonometric Values	What is cos(0)?	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 12 sides =	1800	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 98 m =	3942455.8304233127 m^3	volume_sphere	['maxRadius=100']
70	Angle between 2 vectors	angle between the vectors [253.9, 948.86, 389.18, 418.88, 219.41, 261.47, 394.28, 869.28, 456.84, 814.01] and [134.25, 733.56, 393.07, 547.66, 634.17, 151.21, 830.97, 448.18, 494.12, 616.65] is:	0.47 radians	angle_btw_vectors	['maxEltAmt=20']
75	Area of a Sector	Given radius, 7 and angle, 13. Find the area of the sector.	Area of sector = 5.55887	sector_area	['maxRadius=49', 'maxAngle=359']
86	Degrees to Radians	Angle 337 in radians is =	5.88	degree_to_rad	['max_deg=360']
87	Radians to Degrees	Angle 3 in degrees is =	171.89	radian_to_deg	['max_rad=3']
95	Curved surface area of a cylinder	What is the curved surface area of a cylinder of radius, 9 and height, 32?	CSA of cylinder = 1809.56	curved_surface_area_cylinder	['maxRadius=49', 'maxHeight=99']
96	Perimeter of Polygons	The perimeter of a 3 sided polygon with lengths of [79, 113, 2]cm is:	194	perimeter_of_polygons	['maxSides=12', 'maxLength=120']
104	Circumference	Circumference of circle with radius 41	257.610597594363	circumference	['maxRadius=100']
108	Arc length of Angle	Given radius, 12 and angle, 42. Find the arc length of the angle.	Arc length of the angle = 8.79646	arc_length	['maxRadius=49', 'maxAngle=359']
112	Area of Circle	Area of circle with radius 92	26601.142857142855	area_of_circle	['maxRadius=100']

misc

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
9	LCM (Least Common Multiple)	LCM of 4 and 8 =	8	lcm	['maxVal=20']
10	GCD (Greatest Common Denominator)	GCD of 16 and 2 =	2	gcd	['maxVal=20']
27	Prime Factorisation	Find prime factors of 195	[3, 5, 13]	prime_factors	['minVal=1', 'maxVal=200']
40	Common Factors	Common Factors of 100 and 86 =	[1, 2]	common_factors	['maxVal=100']
51	HCF (Highest Common Factor)	HCF of 10 and 20 =	10	hcf	['maxVal=20']
55	Comparing surds	Fill in the blanks 43^(1/7) _ 63^(1/1)	<	surds_comparison	['maxValue=100', 'maxRoot=10']
63	Profit or Loss Percent	Profit percent when CP = 78 and SP = 953 is:	1121.7948717948718	profit_loss_percent	['maxCP=1000', 'maxSP=1000']
66	Geometric Progression	For the given GP [5, 45, 405, 3645, 32805, 295245] ,Find the value of a,common ratio,9th term value, sum upto 10th term	The value of a is 5, common ratio is 9 , 9th term is 215233605 , sum upto 10th term is 2179240250.0	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 4 numbers 62 , 92 , 44 , 41 =	(629244*41)^(1/4) = 56.637491826411804	geometric_mean	['maxValue=100', 'maxNum=4']
68	Harmonic Mean of N Numbers	Harmonic mean of 3 numbers 10 , 6 and 11 =	3/((1/10) + (1/6) + (1/11)) = 8.389830508474576	harmonic_mean	['maxValue=100', 'maxNum=4']
69	Euclidian norm or L2 norm of a vector	Euclidian norm or L2 norm of the vector[314.0249431219423, 38.65678352467894, 71.60664616684642, 523.0882779296917, 608.4289997907042, 834.5672633353779, 650.2465891686563, 440.8107041244245, 266.74878772920385, 923.0576586175151, 799.0635785268884, 154.79227349145074] is:	1910.0606131376528	euclidian_norm	['maxEltAmt=20']
81	Celsius To Fahrenheit	Convert 94 degrees Celsius to degrees Fahrenheit =	201.20000000000002	celsius_to_fahrenheit	['maxTemp=100']
82	AP Term Calculation	Find the term number 94 of the AP series: 59, -26, -111 ...	-7846	arithmetic_progression_term	['maxd=100', 'maxa=100', 'maxn=100']
83	AP Sum Calculation	Find the sum of first 24 terms of the AP series: 48, 61, 74 ...	4740.0	arithmetic_progression_sum	['maxd=100', 'maxa=100', 'maxn=100']
85	Converts decimal to Roman Numerals	The number 2298 in Roman Numerals is:	MMCCXCVIII	decimal_to_roman_numerals	['maxDecimal=4000']
92	Complex To Polar Form	rexp(itheta) =	11.4exp(i-1.84)	complex_to_polar	['minRealImaginaryNum=-20, maxRealImaginaryNum=20']
93	Union,Intersection,Difference of Two Sets	Given the two sets a={9, 10, 5, 6} ,b={1, 2, 3, 7, 9}.Find the Union,intersection,a-b,b-a and symmetric difference	Union is {1, 2, 3, 5, 6, 7, 9, 10},Intersection is {9}, a-b is {10, 5, 6},b-a is {1, 2, 3, 7}, Symmetric difference is {1, 2, 3, 5, 6, 7, 10}	set_operation	['minval=3', 'maxval=7', 'n_a=4', 'n_b=5']
94	Base Conversion	Convert 48E4 from base 16 to base 2.	100100011100100	base_conversion	['maxNum=60000', 'maxBase=16']
98	Quotient of Powers with Same Base	The Quotient of 13^7 and 13^1 = 13^(7-1) = 13^6	4826809	quotient_of_power_same_base	['maxBase=50', 'maxPower=10']
99	Quotient of Powers with Same Power	The Quotient of 36^9 and 17^9 = (36/17)^9 = 2.1176470588235294^9	856.4109558955231	quotient_of_power_same_power	['maxBase=50', 'maxPower=10']
101	Leap Year or Not	Year 2083	is not a leap year	is_leap_year	['minNumber=1900', 'maxNumber=2099']
102	Minute to Hour conversion	Convert 303 minutes to Hours & Minutes	5 hours and 3 minutes	minutes_to_hours	['maxMinutes=999']
106	signum function	signum of -415 is =	-1	signum_function	['min=-999', 'max=999']
109	Binomial distribution	A manufacturer of metal pistons finds that, on average, 39.54% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 20 pistons will contain no more than 7 rejected pistons?	43.25	binomial_distribution	['']

statistics

Id	Skill	Example problem	Example Solution	Function Name	Kwargs
30	Combinations of Objects	Number of combinations from 10 objects picked 1 at a time	10	combinations	['maxlength=20']
42	Permutations	Number of Permutations from 12 objects picked 0 at a time =	1	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 [235, 268, 270, 280, 260, 288, 212, 244, 223, 240, 219, 263, 229, 287, 226, 299, 281, 255, 278, 265, 207, 201] with 80% confidence is	(259.14322898071816, 243.58404374655458)	confidence_interval	['']
59	Mean,Standard Deviation,Variance	Find the mean,standard deviation and variance for the data[48, 45, 15, 16, 28, 10, 29, 22, 43, 33, 32, 33, 8, 10, 45]	The Mean is 27.8 , Standard Deviation is 177.76000000000005, Variance is 13.332666649999169	data_summary	['number_values=15', 'minval=5', 'maxval=50']
76	Mean and Median	Given the series of numbers [57, 25, 62, 16, 24, 77, 32, 14, 61, 28]. find the arithmatic mean and mdian of the series	Arithmetic mean of the series is 39.6 and Arithmetic median of this series is 30.0	mean_median	['maxlen=10']
107	Conditional Probability	Someone tested positive for a nasty disease which only 0.06% of population have. Test sensitivity (true positive) is equal to SN= 95.20% whereas test specificity (true negative) SP= 95.25%. What is the probability that this guy really has that disease?	1.19%	conditional_probability	['']