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.com/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

worksheet = Worksheet("Worksheet title")
worksheet.add_instruction("Instructions")
# Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.
for _ in range(10):
	worksheet.add_problem(mathgen.genById(1)[0])
worksheet.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) | 4x + 8 = 10 | 1/2 | basic_algebra | `maxVariable=10`  |
| 12 | [Logarithm](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/log.py) | log2(8) | 3 | 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) | 6 * [[3, 3], [7, 2]] =  | [[18,18],[42,12]] | 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) | (-10,11),(-4,-12)= | (-7.0,-0.5) | midpoint_of_two_points | `maxValue=20`  |
| 21 | [Factoring Quadratic](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/factoring.py) | x^2+4x-21 | (x+7)(x-3) | 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) | -x + 8y = -35, -4x + 5y = -32 | x = 3, y = -4 | 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 (-4, 5) and (-19, 11) | sqrt(261) | distance_two_points | `maxValXY=20` `minValXY=-20`  |
| 26 | [Linear Equations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/linear_equations.py) | 3x + 6y = 18, -14x + 11y = -279 | x = 16, 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 = 0/5x + 10 and y = -5/2x + 5 | (-2, 10) | 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) | [-2, -13, 7] X [9, -17, 8] =  | [15, 79, 151] | 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 2145 dollars, 7% rate of interest and for a time period of 7 years is =  | 1051.05 | 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>-8</td><td>-7</td></tr><tr><td>10</td><td>2</td></tr><tr><td>-7</td><td>-8</td></tr><tr><td>-7</td><td>-10</td></tr></table>and<table><tr><td>9</td><td>2</td><td>2</td><td>1</td></tr><tr><td>-1</td><td>3</td><td>-1</td><td>-6</td></tr></table> | <table><tr><td>-65</td><td>-37</td><td>-9</td><td>34</td></tr><tr><td>88</td><td>26</td><td>18</td><td>-2</td></tr><tr><td>-55</td><td>-38</td><td>-6</td><td>41</td></tr><tr><td>-53</td><td>-44</td><td>-4</td><td>53</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 10x^2+51x+46=0 | [-1.17, -3.93] | quadratic_equation | `maxVal=100`  |
| 65 | [Multiplication of 2 complex numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_complex_numbers.py) | (-4+11j) * (5-9j) =  | (79+91j) | 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) | [-12, 11, 13] . [-4, 9, -13] =  | -22 | 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([[25, 98, 43], [11, 56, 70], [27, 19, 89]]) is: | Matrix([[1218/41533, -2635/41533, 1484/41533], [911/124599, 1064/124599, -1277/124599], [-1303/124599, 2171/124599, 322/124599]]) | 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([[11, 84], [38, 41]]) =  |  -2741 | 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 4581 dollars, 4% rate of interest and for a time period of 6 year is =  | 5796.43 | 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 9x^2 + 7x + 1 = 0 | simplified solution : ((-0.189, -0.589)), generalized solution : ((-7 + sqrt(13))/2*9, (-7 - sqrt(13))/2*9) | 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) | 8x^4 + 4x^4 + 6x^1 + 9x^4 + 7x^5 + 10x^3 | 6x^1 + 10x^3 + 21x^4 + 7x^5  | 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-3)(x+4) | *x^2-3*x-12 | 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) | 16+43= | 59 | addition | `maxSum=99` `maxAddend=50`  |
| 1 | [Subtraction](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/subtraction.py) | 85-8= | 77 | subtraction | `maxMinuend=99` `maxDiff=99`  |
| 2 | [Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/multiplication.py) | 1*4= | 4 | multiplication | `maxMulti=12`  |
| 3 | [Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/division.py) | 9/9= | 1 | division | `maxA=25` `maxB=25`  |
| 6 | [Square Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square_root.py) | sqrt(4)= | 2 | square_root | `minNo=1` `maxNo=12`  |
| 8 | [Square](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square.py) | 17^2= | 289 | square | `maxSquareNum=20`  |
| 13 | [Complex Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/complex_division.py) | 21/59= | 0.36 | complex_division | `maxRes=99` `maxDivid=99`  |
| 16 | [Fraction Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/divide_fractions.py) | (5/2)/(3/10) | 25/3 | divide_fractions | `maxVal=10`  |
| 28 | [Fraction Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/fraction_multiplication.py) | (5/1)*(10/4) | 25/2 | fraction_multiplication | `maxVal=10`  |
| 31 | [Factorial](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/factorial.py) | 2! =  | 2 | 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 8/2 and 9/8? | > | 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 396 up to 2 decimal places? | 7.34 | cube_root | `minNo=1` `maxNo=1000`  |
| 53 | [Exponentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/exponentiation.py) | 2^7 = | 128 | 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) | |37--95|= | 132 | 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 99% of 76? | 75.24 | percentage | `maxValue=99` `maxpercentage=99`  |
| 90 | [isprime](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/is_prime.py) | Is 61 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 49^8^2= | 49^16 | power_of_powers | `maxBase=50` `maxPower=10`  |
## 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 + 9x^7 + 6x^4 | 2x^0 + 63x^6 + 24x^3 | 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) | 5x^2 + 3x^10 + 4x^1 | (5/2)x^3 + (3/10)x^11 + (4/1)x^2 + 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(ln(x)+2*x^(-3))/dx | 1/x - 6/x^4 | 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 100x^2 + 80x + 22 is =  | 95.3333 | definite_integral | `max_coeff=100`  |
| 110 | [Stationary Points](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/stationary_points.py) | f(x)=3*x^3 + 6*x^2 + 9*x + 1 |  | 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) | 1= | 0 | binary_complement_1s | `maxDigits=10`  |
| 5 | [Modulo Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/modulo_division.py) | 51%46= | 5 | 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 58= | 111010 | 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) | 0110001111 | 399 | 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 78th Fibonacci number? | 8944394323791488 | nth_fibonacci_number | `maxN=100`  |
| 64 | [Binary to Hexidecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_hex.py) | 111011 | 0x3b | 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 11010 = | 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 456= | 0x1c8 | 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 3211 in Octal is:  | 0o6213 | 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 7 is =  | 29237 | 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 5763 is =  | 1683 | 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: 15 18 11 =  | 82.3164625090267 | area_of_triangle | `maxA=20` `maxB=20` `maxC=20`  |
| 19 | [Triangle exists check](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/valid_triangle.py) | Does triangle with sides 16, 30 and 26 exist? | Yes | 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 75 and 64 =  | 41 | 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 6 =  | 9.22 | 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 19 sides | 161.05 | 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 = 7m is | 294 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 = 9m, 6m, 3m is | 198 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 = 35m and radius = 1m is | 226 m^2 | surface_area_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'`  |
| 35 | [Volum of Cube](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cube.py) | Volume of cube with side = 19m is | 6859 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 = 14m, 18m, 8m is | 2016 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 = 2m and radius = 4m is | 100 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 = 10m and radius = 1m is | 34 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 = 41m and radius = 2m is | 171 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 47 , 186, 23 = | 104 | 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(90)? | ∞ | 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 8 sides =  | 1080 | 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 = 2m is | 50.26548245743669 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 70 m =  | 1436755.040241732 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 [809.39, 750.64, 808.48] and [99.52, 21.47, 323.85] is: | 0.69 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, 38 and angle, 119. Find the area of the sector. | Area of sector = 1499.55199 | 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 187 in radians is =  | 3.26 | 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 2 in degrees is =  | 114.59 | 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, 25 and height, 26? | CSA of cylinder = 4084.07 | 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 11 sided polygon with lengths of [39, 70, 58, 27, 85, 119, 47, 59, 113, 38, 45]cm is:  | 700 | 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 76 | 477.5220833456485 | circumference | `maxRadius=100`  |
| 108 | [Arc length of Angle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/arc_length.py) | Given radius, 30 and angle, 240. Find the arc length of the angle. | Arc length of the angle = 125.66371 | 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 37 | 4302.571428571428 | area_of_circle | `maxRadius=100`  |
## 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 19 and 2 = | 38 | lcm | `maxVal=20`  |
| 10 | [GCD (Greatest Common Denominator)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/gcd.py) | GCD of 16 and 6 =  | 2 | gcd | `maxVal=20`  |
| 27 | [Prime Factorisation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/prime_factors.py) | Find prime factors of 78 | [2, 3, 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 21 and 77 =  | [1, 7] | common_factors | `maxVal=100`  |
| 51 | [HCF (Highest Common Factor)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/hcf.py) | HCF of 17 and 3 =  | 1 | hcf | `maxVal=20`  |
| 55 | [Comparing surds](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/surds_comparison.py) | Fill in the blanks 58^(1/5) _ 18^(1/8) | > | 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 = 821 and SP = 113 is:  | 86.23629719853837 | 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 [5, 15, 45, 135, 405, 1215] ,Find the value of a,common ratio,10th term value, sum upto 11th term | The value of a is 5, common ratio is 3 , 10th term is 98415 , sum upto 11th term is 442865.0 | 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 4 numbers 76 , 17 , 48 , 57 =  | (76*17*48*57)^(1/4) = 43.36053695794891 | 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 4 numbers 12 , 23 , 94 , 96 =  |  4/((1/12) + (1/23) + (1/94) + (1/96)) = 27.0514173998045 | 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[802.4475305377166, 660.7012519538307, 370.72333556197833, 54.54747734093479, 367.379416204208, 945.4792894951261, 219.91075384694793, 302.48678829534293] is: | 1545.8386466508773 | euclidian_norm | `maxEltAmt=20`  |
| 81 | [Celsius To Fahrenheit](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/celsius_to_fahrenheit.py) | Convert 6 degrees Celsius to degrees Fahrenheit = | 42.8 | 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 67 of the AP series: -19, -81, -143 ...  | -4111 | 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 45 terms of the AP series: 58, 32, 6 ...  | -23130.0 | 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:  | MMMDCCCXXXV | 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) | 17.12(2.0theta + i-17.0theta) | -1.45 | 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={8, 9, 5} ,b={10, 3, 6, 7}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {3, 5, 6, 7, 8, 9, 10},Intersection is set(), a-b is {8, 9, 5},b-a is {10, 3, 6, 7}, Symmetric difference is {3, 5, 6, 7, 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 E87 from base 16 to base 10. | 3719 | 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 31^8 and 31^8 = 31^(8-8) = 31^0 | 1 | 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 24^1 and 19^1 = (24/19)^1 = 1.263157894736842^1 | 1.263157894736842 | 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 2086  | 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 680 minutes to Hours & Minutes | 11 hours and 20 minutes | minutes_to_hours | `maxMinutes=999`  |
| 106 | [signum function](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/signum_function.py) | signum of -93 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, 40.52% 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 2 rejected pistons? | 0.32 | binomial_distribution | ``  |
## 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 17 objects picked 0 at a time  | 1 | combinations | `maxlength=20`  |
| 42 | [Permutations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/permutation.py) | Number of Permutations from 16 objects picked 8 at a time =   | 518918400 | 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 3 dice are rolled at the same time, the probability of getting a sum of 5 = | 6/216 | 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 [272, 287, 274, 273, 266, 212, 242, 258, 291, 243, 248, 240, 236, 232, 249, 207, 271, 251, 206, 282, 295, 283, 238, 210, 234, 288, 268, 229, 289, 219, 294, 264, 215] with 95% confidence is | (262.9335851189468, 244.09671791135625) | 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[50, 29, 15, 50, 26, 25, 12, 16, 31, 38, 31, 5, 7, 42, 36] | The Mean is 27.533333333333335 , Standard Deviation is 193.0488888888889, Variance is 13.894203427648845 | 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 [6, 9, 17, 22, 26, 35, 37, 58, 75, 83]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 36.8 and Arithmetic median of this series is 30.5 | 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 0.18% of population have. Test sensitivity (true positive) is equal to SN= 93.38% whereas test specificity (true negative) SP= 93.15%. What is the probability that this guy really has that disease? | 2.4% | conditional_probability | ``  |