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](#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)
```
### 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 form of a list 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 |
|------|-------|-----------------|------------------|---------------|
| 11 | Basic Algebra | 5x + 10 = 10 | 0 | basic_algebra |
| 12 | Logarithm | log2(4) | 2 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 12 * [[8, 7], [2, 0]] =  | [[96,84],[24,0]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (10,9),(1,13)= | (5.5,11.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2+3x-4 | (x+4)(x-1) | factoring |
| 23 | Solve a System of Equations in R^2 | 5x - 5y = 20, -4x - 7y = -38 | x = 6, y = 2 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (12, 2) and (16, 13) | sqrt(137) | distance_two_points |
| 26 | Linear Equations | 19x + -19y = -494, -12x + -2y = 200 | x = -18, y = 8 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 4x + 5 and y = -5/6x - 4 | (-54/29, -71/29) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [7, 11, 10] X [12, 2, -15] =  | [-185, 225, -118] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 5927 dollars, 2% rate of interest and for a time period of 5 years is =  | 592.7 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>4</td><td>-5</td><td>6</td><td>2</td></tr><tr><td>0</td><td>10</td><td>7</td><td>-3</td></tr><tr><td>-6</td><td>-7</td><td>-4</td><td>-1</td></tr></table>and<table><tr><td>6</td><td>-7</td><td>8</td><td>-9</td></tr><tr><td>-7</td><td>-6</td><td>7</td><td>-3</td></tr><tr><td>10</td><td>0</td><td>6</td><td>2</td></tr><tr><td>-6</td><td>-4</td><td>-5</td><td>-1</td></tr></table> | <table><tr><td>107</td><td>-6</td><td>23</td><td>-11</td></tr><tr><td>18</td><td>-48</td><td>127</td><td>-13</td></tr><tr><td>-21</td><td>88</td><td>-116</td><td>68</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 89x^2+190x+87=0 | [-0.67, -1.47] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (-15+15j) * 20j =  | (-300-300j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [-2, 10, -10] . [16, -20, 3] =  | -262 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[55, 61, 1], [28, 67, 9], [53, 91, 33]]) is: | Matrix([[696/24145, -961/24145, 241/24145], [-447/48290, 881/24145, -467/48290], [-1003/48290, -886/24145, 1977/48290]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[18, 97], [57, 84]]) =  |  -4017 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 9310 dollars, 5% rate of interest and for a time period of 9 year is =  | 14442.87 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 9x^2 + 6x + 1 = 0 | simplified solution : ((-0.333, -0.333)), generalized solution : ((-6 + 0)/2*9, (-6 - 0)/2*9) | complex_quadratic |
| 105 | Combine Like terms | 6x^1 + 3x^1 + 9x^1 | 18x^1  | combine_like_terms |
| 111 | Expanding Factored Binomial | (4x+8)(+10x-7) | 40*x^2+52*x-56 | expanding |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 48+14= | 62 | addition |
| 1 | Subtraction | 88-49= | 39 | subtraction |
| 2 | Multiplication | 17*0= | 0 | multiplication |
| 3 | Division | 320/16= | 20.0 | division |
| 6 | Square Root | sqrt(100)= | 10 | square_root |
| 8 | Square | 10^2= | 100 | square |
| 13 | Complex Division | 32/47= | 0.68 | complex_division |
| 16 | Fraction Division | (9/7)/(6/5) | 15/14 | divide_fractions |
| 28 | Fraction Multiplication | (1/6)*(3/10) | 1/20 | fraction_multiplication |
| 31 | Factorial | 2! =  | 2 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 3/1 and 9/1? | < | compare_fractions |
| 47 | Cube Root | cuberoot of 576 upto 2 decimal places is: | 8.32 | cube_root |
| 53 | Exponentiation | 1^8 = | 1 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -97 and 92 =  | 189 | absolute_difference |
| 80 | Percentage of a number | What is 74% of 3? | Required percentage = 2.22% | percentage |
| 90 | isprime | 31 | True | is_prime |
| 97 | Power of Powers | The 20^9^7 =  | 20^63 | power_of_powers |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 1x^1 + 1x^6 | 1x^0 + 6x^5 | power_rule_differentiation |
| 48 | Power Rule Integration | 8x^5 + 8x^9 + 4x^1 + 1x^8 + 8x^1 | (8/5)x^6 + (8/9)x^10 + (4/1)x^2 + (1/8)x^9 + (8/1)x^2 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(sec(x)+2*x^(-2))/dx | tan(x)*sec(x) - 4/x^3 | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 51x^2 + 66x + 69 is =  | 119.0 | definite_integral |
| 110 | Stationary Points | f(x)=3*x^3 + 6*x^2 + 4*x + 3 | (-2/3,19/9) | stationary_points |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 01000= | 10111 | binary_complement_1s |
| 5 | Modulo Division | 99%30= | 9 | modulo_division |
| 14 | Decimal to Binary | Binary of 98= | 1100010 | decimal_to_binary |
| 15 | Binary to Decimal | 0000 | 0 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 16 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 46th Fibonacci number? | 1836311903 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 1000 | 0x8 | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 1111101010 = | 10110 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 450= | 0x1c2 | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 2724 in Octal is:  | 0o5244 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 3 is =  | 14161 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 4899 is =  | 1323 | decimal_to_bcd |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 4 12 16 =  | 0.0 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 37, 10 and 11 exist? | No | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 73 and 50 =  | 57 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 4 and 13 =  | 13.60 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 11 sides | 147.27 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 20m is | 2400 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 16m, 20m, 14m is | 1648 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 26m and radius = 15m is | 3864 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 7m is | 343 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 16m, 7m, 16m is | 1792 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 46m and radius = 12m is | 20809 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 45m and radius = 10m is | 1762 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 19m and radius = 10m is | 1989 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 86 , 102, 52 = | 120 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is sin(30)? | 1/2 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 10 sides =  | 1440 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 12m is | 1809.5573684677208 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 62 m =  | 998305.9919263308 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [355.55, 510.69, 466.34, 362.76, 361.29, 361.07, 460.5, 967.62, 124.59, 627.19, 696.33, 269.54, 766.51, 903.59, 246.94, 158.86] and [928.29, 464.69, 667.73, 869.08, 547.6, 899.66, 562.23, 961.55, 952.5, 111.01, 259.45, 322.58, 893.48, 592.59, 865.67, 790.67] is: | 0.65 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 21 and angle, 120. Find the area of the sector. | Area of sector = 461.81412 | sector_area |
| 86 | Degrees to Radians | Angle 56 in radians is =  | 0.98 | degree_to_rad |
| 87 | Radians to Degrees | Angle 2 in degrees is =  | 114.59 | radian_to_deg |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 17 and height, 35? | CSA of cylinder = 3738.5 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 8 sided polygon with lengths of [100, 106, 97, 63, 31, 97, 21, 24]cm is:  | 539 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 24 | 150.79644737231007 | circumference |
| 108 | Arc length of Angle | Given radius, 23 and angle, 40. Find the arc length of the angle. | Arc length of the angle = 16.05703 | arc_length |
| 112 | Area of Circle | Area of circle with radius 70 | 15400.0 | area_of_circle |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 17 and 4 = | 68 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 1 and 4 =  | 1 | gcd |
| 27 | Prime Factorisation | Find prime factors of 173 | [173] | prime_factors |
| 40 | Common Factors | Common Factors of 79 and 64 =  | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 18 and 1 =  | 1 | hcf |
| 55 | Comparing surds | Fill in the blanks 29^(1/4) _ 91^(1/2) | < | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 781 and SP = 878 is:  | 12.419974391805377 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [12, 84, 588, 4116, 28812, 201684] ,Find the value of a,common ratio,11th term value, sum upto 11th term | The value of a is 12, common ratio is 7 , 11th term is 3389702988 , sum upto 11th term is 3954653484.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 2 numbers 55 and 48 =  | (55*48)^(1/2) = 51.38093031466052 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 18 , 24 , 1 , 31 =  |  4/((1/18) + (1/24) + (1/1) + (1/31)) = 3.5414518048393493 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[943.6989301957527, 942.687709334459, 415.08527238528325, 794.7248710456973] is: | 1607.206020456812 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 18 degrees Celsius to degrees Fahrenheit = | 64.4 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 55 of the AP series: 63, 7, -49 ...  | -2961 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 68 terms of the AP series: -58, 37, 132 ...  | 212466.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 2089 in Roman Numerals is:  | MMLXXXIX | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) =  | 7.28exp(i-1.85) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={2, 3, 4, 5, 8, 9} ,b={9, 5, 6, 7}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {2, 3, 4, 5, 6, 7, 8, 9},Intersection is {9, 5}, a-b is {8, 2, 3, 4},b-a is {6, 7}, Symmetric difference is {2, 3, 4, 6, 7, 8} | set_operation |
| 94 | Base Conversion | Convert DD5D from base 15 to base 10. | 46888 | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 49^2 and 49^2 = 49^(2-2) = 49^0 | 1 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 40^4 and 39^4 = (40/39)^4 = 1.0256410256410255^4 | 1.1065767400162785 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 2037  | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 897 minutes to Hours & Minutes | 14 hours and 57 minutes | minutes_to_hours |
| 106 | signum function | signum of 650 is = | 1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 30.15% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 17 pistons will contain no more than 5 rejected pistons? | 59.15 | binomial_distribution |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 14 objects picked 7 at a time  | 3432 | combinations |
| 42 | Permutations | Number of Permutations from 15 objects picked 4 at a time =   | 32760 | permutation |
| 52 | Probability of a certain sum appearing on faces of dice | If 3 dice are rolled at the same time, the probability of getting a sum of 8 = | 21/216 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [272, 295, 283, 209, 260, 200, 276, 247, 223, 249, 221, 271, 231, 213, 284, 211, 281, 210, 212, 207, 239, 245, 229, 253] with 80% confidence is | (250.11440157643338, 234.96893175689993) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[29, 8, 22, 18, 9, 33, 36, 31, 32, 5, 45, 42, 41, 23, 15] | The Mean is 25.933333333333334 , Standard Deviation is 154.99555555555557, Variance is 12.449721103524993 | data_summary |
| 76 | Mean and Median | Given the series of numbers [63, 37, 98, 21, 76, 85, 23, 47, 2, 44]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 49.6 and Arithmetic median of this series is 45.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 0.59% of population have. Test sensitivity (true positive) is equal to SN= 94.30% whereas test specificity (true negative) SP= 90.17%. What is the probability that this guy really has that disease? | 5.39% | conditional_probability |