# 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](https://github.com/lukew3/mathgenerator/blob/main/CONTRIBUTING.md) for information about how to contribute.

## Table of Contents
* [Installation](#installation)
* [Basic Usage](#basic-usage)
  * [More Complicated Usage](#more-complicated-usage)
* [Documentation](#documentation)
* [List of Generators](#list-of-generators)
  * [algebra](#algebra)
  * [basic_math](#basic_math)
  * [calculus](#calculus)
  * [computer_science](#computer_science)
  * [geometry](#geometry)
  * [misc](#misc)
  * [statistics](#statistics)

## Installation

The project can be install via pip

```bash
pip install mathgenerator
```

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

```python
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)
```
<!--
### Creating a worksheet
If you wish to create a worksheet, you can use the [worksheetgen](https://github.com/lukew3/worksheetgen) package. Install this with `pip install worksheetgen`. Here is an example of how a worksheet would be generated.
```
from mathgenerator import mathgen
from worksheetgen.wg import Worksheet

ws = Worksheet("Worksheet title")
with ws.section('Section 1', description='These are instructions')
	# Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.
	for _ in range(10):
		ws.add_problem(mathgen.genById(1)[0])
ws.write_pdf()
```
This creates the pdf `ws.pdf` in your current directory
-->

## 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/basic_algebra.py) | 9x + 5 = 8 | 1/3 | basic_algebra | `maxVariable=10`  |
| 12 | [Logarithm](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/log.py) | log2(256) | 8 | log | `maxBase=3` `maxVal=8`  |
| 17 | [Integer Multiplication with 2x2 Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_int_to_22_matrix.py) | 9 * [[7, 8], [6, 8]] =  | [[63,72],[54,72]] | multiply_int_to_22_matrix | `maxMatrixVal=10` `maxRes=100`  |
| 20 | [Midpoint of the two point](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/midpoint_of_two_points.py) | (-12,5),(-20,6)= | (-16.0,5.5) | midpoint_of_two_points | `maxValue=20`  |
| 21 | [Factoring Quadratic](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/factoring.py) | x^2-8x+15 | (x-3)(x-5) | factoring | `range_x1=10` `range_x2=10`  |
| 23 | [Solve a System of Equations in R^2](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/system_of_equations.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/distance_two_points.py) | Find the distance between (-19, -9) and (16, 14) | sqrt(1754) | distance_two_points | `maxValXY=20` `minValXY=-20`  |
| 26 | [Linear Equations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/linear_equations.py) | 7x + -13y = 198, -4x + 19y = -171 | x = 19, y = -5 | linear_equations | `n=2` `varRange=20` `coeffRange=20`  |
| 41 | [Intersection of Two Lines](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/intersection_of_two_lines.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/vector_cross.py) | [12, 14, -20] X [11, 13, 3] =  | [302, -256, 2] | vector_cross | `minVal=-20` `maxVal=20`  |
| 45 | [Simple Interest](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/simple_interest.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/matrix_multiplication.py) | Multiply<table><tr><td>7</td><td>4</td><td>-1</td><td>-4</td></tr><tr><td>5</td><td>8</td><td>-9</td><td>7</td></tr><tr><td>-6</td><td>0</td><td>-3</td><td>-10</td></tr></table>and<table><tr><td>1</td><td>-5</td><td>-9</td></tr><tr><td>2</td><td>-10</td><td>10</td></tr><tr><td>-9</td><td>6</td><td>-8</td></tr><tr><td>-7</td><td>4</td><td>10</td></tr></table> | <table><tr><td>52</td><td>-97</td><td>-55</td></tr><tr><td>53</td><td>-131</td><td>177</td></tr><tr><td>91</td><td>-28</td><td>-22</td></tr></table> | matrix_multiplication | `maxVal=100` `max_dim=10`  |
| 50 | [Quadratic Equation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/quadratic_equation.py) | Zeros of the Quadratic Equation 4x^2+176x+52=0 | [-0.3, -43.7] | quadratic_equation | `maxVal=100`  |
| 65 | [Multiplication of 2 complex numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_complex_numbers.py) | (2+14j) * (-7-11j) =  | (140-120j) | multiply_complex_numbers | `minRealImaginaryNum=-20` `maxRealImaginaryNum=20`  |
| 72 | [Dot Product of 2 Vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/vector_dot.py) | [-18, 1, -5] . [10, 6, 19] =  | -269 | vector_dot | `minVal=-20` `maxVal=20`  |
| 74 | [Inverse of a Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/invert_matrix.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/int_matrix_22_determinant.py) | Det([[87, 46], [20, 61]]) =  |  4387 | int_matrix_22_determinant | `maxMatrixVal=100`  |
| 78 | [Compound Interest](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/compound_interest.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/complex_quadratic.py) | Find the roots of given Quadratic Equation 4x^2 + 9x + 2 = 0 | simplified solution : ((-0.25, -2.0)), generalized solution : ((-9 + 7)/2*4, (-9 - 7)/2*4) | complex_quadratic | `prob_type=0` `max_range=10`  |
| 105 | [Combine Like terms](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/combine_like_terms.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/expanding.py) | (x-4)(-1x+9) | -1*x^2+13*x-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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/addition.py) | \(33+2\) | 35 | addition | `maxSum=99` `maxAddend=50`  |
| 1 | [Subtraction](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/subtraction.py) | 11-9= | 2 | subtraction | `maxMinuend=99` `maxDiff=99`  |
| 2 | [Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/multiplication.py) | 10*9= | 90 | multiplication | `maxMulti=12`  |
| 3 | [Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/division.py) | 208/16= | 13 | division | `maxA=25` `maxB=25`  |
| 6 | [Square Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square_root.py) | sqrt(144)= | 12 | square_root | `minNo=1` `maxNo=12`  |
| 8 | [Square](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square.py) | 15^2= | 225 | square | `maxSquareNum=20`  |
| 13 | [Complex Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/complex_division.py) | 62/71= | 0.87 | complex_division | `maxRes=99` `maxDivid=99`  |
| 16 | [Fraction Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/divide_fractions.py) | (1/8)/(4/6) | 3/16 | divide_fractions | `maxVal=10`  |
| 28 | [Fraction Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/fraction_multiplication.py) | (4/7)*(8/5) | 32/35 | fraction_multiplication | `maxVal=10`  |
| 31 | [Factorial](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/factorial.py) | 6! =  | 720 | factorial | `maxInput=6`  |
| 44 | [Compare Fractions](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/compare_fractions.py) | Which symbol represents the comparison between 8/7 and 9/4? | < | compare_fractions | `maxVal=10`  |
| 47 | [Cube Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/cube_root.py) | What is the cube root of 419 up to 2 decimal places? | 7.48 | cube_root | `minNo=1` `maxNo=1000`  |
| 53 | [Exponentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/exponentiation.py) | 19^4 = | 130321 | exponentiation | `maxBase=20` `maxExpo=10`  |
| 71 | [Absolute difference between two numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/absolute_difference.py) | |86--54|= | 140 | absolute_difference | `maxA=100` `maxB=100`  |
| 80 | [Percentage of a number](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage.py) | What is 87% of 15? | 13.05 | percentage | `maxValue=99` `maxpercentage=99`  |
| 90 | [isprime](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/is_prime.py) | Is 59 prime? | Yes | is_prime | `max_num=100`  |
| 97 | [Power of Powers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/power_of_powers.py) | Simplify 23^9^4= | 23^36 | power_of_powers | `maxBase=50` `maxPower=10`  |
| 118 | [Percentage difference](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage_difference.py) | What is the percentage difference between 151 and 58? | 89.0% | percentage_difference | `maxValue=200` `minValue=0`  |
| 119 | [Percentage error](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage_error.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/greatest_common_divisor.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/power_rule_differentiation.py) | 2x^1 | 2x^0 | power_rule_differentiation | `maxCoef=10` `maxExp=10` `maxTerms=5`  |
| 48 | [Power Rule Integration](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/power_rule_integration.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/differentiation.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/definite_integral.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/stationary_points.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_complement_1s.py) | 00= | 11 | binary_complement_1s | `maxDigits=10`  |
| 5 | [Modulo Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/modulo_division.py) | 7%69= | 7 | modulo_division | `maxRes=99` `maxModulo=99`  |
| 14 | [Decimal to Binary](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_binary.py) | Binary of 87= | 1010111 | decimal_to_binary | `max_dec=99`  |
| 15 | [Binary to Decimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_decimal.py) | 1 | 1 | binary_to_decimal | `max_dig=10`  |
| 56 | [Fibonacci Series](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/fibonacci_series.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/nth_fibonacci_number.py) | What is the 13th Fibonacci number? | 233 | nth_fibonacci_number | `maxN=100`  |
| 64 | [Binary to Hexidecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_hex.py) | 00100 | 0x4 | binary_to_hex | `max_dig=10`  |
| 73 | [Binary 2's Complement](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_2s_complement.py) | 2's complement of 1010 = | 110 | binary_2s_complement | `maxDigits=10`  |
| 79 | [Decimal to Hexadecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_hexadeci.py) | Binary of 461= | 0x1cd | decimal_to_hexadeci | `max_dec=1000`  |
| 84 | [Converts decimal to octal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_octal.py) | The decimal number 1681 in Octal is:  | 0o3221 | decimal_to_octal | `maxDecimal=4096`  |
| 91 | [Binary Coded Decimal to Integer](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/bcd_to_decimal.py) | Integer of Binary Coded Decimal 8 is =  | 33878 | bcd_to_decimal | `maxNumber=10000`  |
| 103 | [Decimal to Binary Coded Decimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_bcd.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_triangle.py) | Area of triangle with side lengths: 8 4 6 =  | 11.62 | area_of_triangle | `maxA=20` `maxB=20`  |
| 19 | [Triangle exists check](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/valid_triangle.py) | Does triangle with sides 3, 48 and 23 exist? | No | valid_triangle | `maxSideLength=50`  |
| 22 | [Third Angle of Triangle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/third_angle_of_triangle.py) | Third angle of triangle with angles 37 and 79 =  | 64 | third_angle_of_triangle | `maxAngle=89`  |
| 25 | [Pythagorean Theorem](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/pythagorean_theorem.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/angle_regular_polygon.py) | Find the angle of a regular polygon with 18 sides | 160.0 | angle_regular_polygon | `minVal=3` `maxVal=20`  |
| 32 | [Surface Area of Cube](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cube.py) | Surface area of cube with side = 16m is | 1536 m^2 | surface_area_cube | `maxSide=20` `unit='m'`  |
| 33 | [Surface Area of Cuboid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cuboid.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cylinder.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cube.py) | Volume of cube with side = 12m is | 1728 m^3 | volume_cube | `maxSide=20` `unit='m'`  |
| 36 | [Volume of Cuboid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cuboid.py) | Volume of cuboid with sides = 12m, 11m, 10m is | 1320 m^3 | volume_cuboid | `maxSide=20` `unit='m'`  |
| 37 | [Volume of cylinder](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cylinder.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cone.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cone.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/fourth_angle_of_quadrilateral.py) | Fourth angle of quadrilateral with angles 98 , 38, 15 = | 209 | fourth_angle_of_quadrilateral | `maxAngle=180`  |
| 57 | [Trigonometric Values](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/basic_trigonometry.py) | What is tan(60)? | √3 | basic_trigonometry | `angles=[0, 30, 45, 60, 90]` `functions=['sin', 'cos', 'tan']`  |
| 58 | [Sum of Angles of Polygon](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/sum_of_polygon_angles.py) | Sum of angles of polygon with 4 sides =  | 360 | sum_of_polygon_angles | `maxSides=12`  |
| 60 | [Surface Area of Sphere](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_sphere.py) | Surface area of Sphere with radius = 15m is | 2827.4333882308138 m^2 | surface_area_sphere | `maxSide=20` `unit='m'`  |
| 61 | [Volume of Sphere](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_sphere.py) | Volume of sphere with radius 74 m =  | 1697398.3219443604 m^3 | volume_sphere | `maxRadius=100`  |
| 70 | [Angle between 2 vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/angle_btw_vectors.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/sector_area.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/degree_to_rad.py) | Angle 168 in radians is =  | 2.93 | degree_to_rad | `max_deg=360`  |
| 87 | [Radians to Degrees](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/radian_to_deg.py) | Angle 1 in degrees is =  | 57.3 | radian_to_deg | `max_rad=3`  |
| 95 | [Curved surface area of a cylinder](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/curved_surface_area_cylinder.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/perimeter_of_polygons.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/circumference.py) | Circumference of circle with radius 98 | 615.7521601035994 | circumference | `maxRadius=100`  |
| 108 | [Arc length of Angle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/arc_length.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_circle.py) | Area of circle with radius 47 | 6942.571428571429 | area_of_circle | `maxRadius=100`  |
| 113 | [Volume of frustum](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_frustum.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/equation_of_line_from_two_points.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_circle_given_center_and_point.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_hemisphere.py) | Volume of hemisphere with radius 7 m =  | 718.378 m^3 | volume_hemisphere | `maxRadius=100`  |
| 122 | [Volume of pyramid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_pyramid.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_pyramid.py) | 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)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/lcm.py) | LCM of 7 and 20 = | 140 | lcm | `maxVal=20`  |
| 10 | [GCD (Greatest Common Denominator)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/gcd.py) | GCD of 16 and 2 =  | 2 | gcd | `maxVal=20`  |
| 27 | [Prime Factorisation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/prime_factors.py) | Find prime factors of 13 | [13] | prime_factors | `minVal=1` `maxVal=200`  |
| 40 | [Common Factors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/common_factors.py) | Common Factors of 58 and 85 =  | [1] | common_factors | `maxVal=100`  |
| 51 | [HCF (Highest Common Factor)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/hcf.py) | HCF of 15 and 13 =  | 1 | hcf | `maxVal=20`  |
| 55 | [Comparing surds](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/surds_comparison.py) | Fill in the blanks 52^(1/6) _ 49^(1/9) | > | surds_comparison | `maxValue=100` `maxRoot=10`  |
| 63 | [Profit or Loss Percent](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/profit_loss_percent.py) | Loss percent when CP = 899 and SP = 190 is:  | 78.86540600667408 | profit_loss_percent | `maxCP=1000` `maxSP=1000`  |
| 66 | [Geometric Progression](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/geometric_progression.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/geometric_mean.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/harmonic_mean.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/euclidian_norm.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/celsius_to_fahrenheit.py) | Convert 91 degrees Celsius to degrees Fahrenheit = | 195.8 | celsius_to_fahrenheit | `maxTemp=100`  |
| 82 | [AP Term Calculation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/arithmetic_progression_term.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/arithmetic_progression_sum.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/decimal_to_roman_numerals.py) | The number 0 in Roman Numerals is:  | MCCLXXVII | decimal_to_roman_numerals | `maxDecimal=4000`  |
| 92 | [Complex To Polar Form](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/complex_to_polar.py) | 18.44(-12.0theta + i-14.0theta) | -2.28 | complex_to_polar | `minRealImaginaryNum=-20, maxRealImaginaryNum=20`  |
| 93 | [Union,Intersection,Difference of Two Sets](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/set_operation.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/base_conversion.py) | Convert 1A1A9 from base 12 to base 2. | 1001010110010001 | base_conversion | `maxNum=60000` `maxBase=16`  |
| 98 | [Quotient of Powers with Same Base](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/quotient_of_power_same_base.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/quotient_of_power_same_power.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/is_leap_year.py) | Year 1910  | is not a leap year | is_leap_year | `minNumber=1900` `maxNumber=2099`  |
| 102 | [Minute to Hour conversion](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/minutes_to_hours.py) | Convert 614 minutes to Hours & Minutes | 10 hours and 14 minutes | minutes_to_hours | `maxMinutes=999`  |
| 106 | [signum function](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/signum_function.py) | signum of -726 is = | -1 | signum_function | `min=-999` `max=999`  |
| 109 | [Binomial distribution](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/binomial_distribution.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/Factors.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/product_of_scientific_notations.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/combinations.py) | Number of combinations from 15 objects picked 3 at a time  | 455 | combinations | `maxlength=20`  |
| 42 | [Permutations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/permutation.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/dice_sum_probability.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/confidence_interval.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/data_summary.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/mean_median.py) | 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](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/conditional_probability.py) | 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 | ``  |