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]`

`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 | 10x + 5 = 5 | 0 | basic_algebra |
| 12 | Logarithm | log3(3) | 1 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 8 * [[10, 5], [3, 9]] =  | [[80,40],[24,72]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (-14,1),(-2,2)= | (-8.0,1.5) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2-2x-15 | (x-5)(x+3) | factoring |
| 23 | Solve a System of Equations in R^2 | -8x - 3y = -31, 4x - 6y = 38 | x = 5, y = -3 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (-4, -6) and (-4, 15) | sqrt(441) | distance_two_points |
| 26 | Linear Equations | 8x + 9y = -202, 5x + -7y = 0 | x = -14, y = -10 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 7/2x + 3 and y = 2/5x + 10 | (70/31, 338/31) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [-18, 12, 1] X [-12, -19, 1] =  | [31, 6, 486] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 4200 dollars, 5% rate of interest and for a time period of 8 years is =  | 1680.0 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>-8</td><td>7</td></tr><tr><td>0</td><td>-5</td></tr><tr><td>-3</td><td>0</td></tr><tr><td>7</td><td>2</td></tr></table>and<table><tr><td>-7</td><td>-4</td></tr><tr><td>6</td><td>-4</td></tr></table> | <table><tr><td>98</td><td>4</td></tr><tr><td>-30</td><td>20</td></tr><tr><td>21</td><td>12</td></tr><tr><td>-37</td><td>-36</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 33x^2+199x+22=0 | [-0.11, -5.92] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (-4-10j) * (4-18j) =  | (-196+32j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [7, -2, 14] . [14, -17, -16] =  | -92 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[81, 23, 19], [73, 75, 49], [7, 71, 93]]) is: | Matrix([[874/55855, -79/22342, -149/111710], [-3223/111710, 370/11171, -1291/111710], [2329/111710, -559/22342, 1099/55855]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[9, 31], [5, 30]]) =  |  115 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 8699 dollars, 9% rate of interest and for a time period of 9 year is =  | 18893.3 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 8x^2 + 8x + 1 = 0 | simplified solution : ((-0.146, -0.854)), generalized solution : ((-8 + sqrt(32))/2*8, (-8 - sqrt(32))/2*8) | complex_quadratic |
| 105 | Combine Like terms | 6x^1 + 5x^1 + 2x^2 | 11x^1 + 2x^2  | combine_like_terms |
| 111 | Expanding Factored Binomial | (3x-1)(+4x-7) | 12*x^2-25*x+7 | expanding |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 46+24= | 70 | addition |
| 1 | Subtraction | 17-10= | 7 | subtraction |
| 2 | Multiplication | 28*0= | 0 | multiplication |
| 3 | Division | 150/6= | 25 | division |
| 6 | Square Root | sqrt(144)= | 12 | square_root |
| 8 | Square | 9^2= | 81 | square |
| 13 | Complex Division | 3/39= | 0.08 | complex_division |
| 16 | Fraction Division | (4/1)/(10/1) | 2/5 | divide_fractions |
| 28 | Fraction Multiplication | (9/7)*(9/6) | 27/14 | fraction_multiplication |
| 31 | Factorial | 0! =  | 1 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 4/10 and 8/9? | < | compare_fractions |
| 47 | Cube Root | cuberoot of 685 upto 2 decimal places is: | 8.82 | cube_root |
| 53 | Exponentiation | 2^7 = | 128 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -43 and 99 =  | 142 | absolute_difference |
| 80 | Percentage of a number | What is 58% of 84? | Required percentage = 48.72% | percentage |
| 90 | isprime | 32 | False | is_prime |
| 97 | Power of Powers | The 34^2^9 =  | 34^18 | power_of_powers |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 6x^10 + 4x^7 + 6x^4 + 2x^2 + 7x^8 | 60x^9 + 28x^6 + 24x^3 + 4x^1 + 56x^7 | power_rule_differentiation |
| 48 | Power Rule Integration | 1x^2 + 8x^8 | (1/2)x^3 + (8/8)x^9 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(exp(x)+9*x^(-2))/dx | exp(x) - 18/x^3 | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 16x^2 + 29x + 67 is =  | 86.8333 | definite_integral |
| 110 | Stationary Points | f(x)=6*x^3 + 8*x^2 + 3*x + 2 | (-4/9 - sqrt(10)/18,6*(-4/9 - sqrt(10)/18)**3 - sqrt(10)/6 + 2/3 + 8*(-4/9 - sqrt(10)/18)**2),(-4/9 + sqrt(10)/18,6*(-4/9 + sqrt(10)/18)**3 + sqrt(10)/6 + 8*(-4/9 + sqrt(10)/18)**2 + 2/3) | stationary_points |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 000= | 111 | binary_complement_1s |
| 5 | Modulo Division | 3%97= | 3 | modulo_division |
| 14 | Decimal to Binary | Binary of 35= | 100011 | decimal_to_binary |
| 15 | Binary to Decimal | 0001100 | 12 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 3 numbers is ? | [0, 1, 1] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 28th Fibonacci number? | 317811 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 110101 | 0x35 | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 11101010 = | 10110 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 858= | 0x35a | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 1377 in Octal is:  | 0o2541 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 3 is =  | 12386 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 4841 is =  | 12149 | decimal_to_bcd |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 20 16 14 =  | 111.24297730643494 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 44, 29 and 14 exist? | No | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 26 and 79 =  | 75 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 9 and 20 =  | 21.93 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 15 sides | 156.0 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 6m is | 216 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 9m, 13m, 1m is | 278 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 44m and radius = 2m is | 578 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 6m is | 216 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 9m, 10m, 17m is | 1530 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 46m and radius = 3m is | 1300 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 15m and radius = 6m is | 417 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 2m and radius = 4m is | 33 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 16 , 182, 51 = | 111 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is cos(0)? | 1 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 7 sides =  | 900 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 4m is | 201.06192982974676 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 95 m =  | 3591364.0018287315 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [971.6, 661.5, 319.66, 602.97, 423.53, 190.72, 120.07, 795.33] and [448.68, 587.18, 139.74, 198.63, 570.02, 430.49, 735.04, 51.89] is: | 0.82 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 12 and angle, 292. Find the area of the sector. | Area of sector = 366.93802 | sector_area |
| 86 | Degrees to Radians | Angle 182 in radians is =  | 3.18 | degree_to_rad |
| 87 | Radians to Degrees | Angle 3 in degrees is =  | 171.89 | radian_to_deg |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 2 and height, 30? | CSA of cylinder = 376.99 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 10 sided polygon with lengths of [64, 97, 94, 42, 33, 71, 98, 104, 50, 47]cm is:  | 700 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 24 | 150.79644737231007 | circumference |
| 108 | Arc length of Angle | Given radius, 39 and angle, 318. Find the arc length of the angle. | Arc length of the angle = 216.45573 | arc_length |
| 112 | Area of Circle | Area of circle with radius 11 | 380.2857142857143 | area_of_circle |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 1 and 5 = | 5 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 3 and 18 =  | 3 | gcd |
| 27 | Prime Factorisation | Find prime factors of 52 | [2, 2, 13] | prime_factors |
| 40 | Common Factors | Common Factors of 13 and 11 =  | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 4 and 14 =  | 2 | hcf |
| 55 | Comparing surds | Fill in the blanks 27^(1/5) _ 4^(1/3) | > | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 198 and SP = 209 is:  | 5.555555555555555 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [6, 66, 726, 7986, 87846, 966306] ,Find the value of a,common ratio,8th term value, sum upto 9th term | The value of a is 6, common ratio is 11 , 8th term is 116923026 , sum upto 9th term is 1414768614.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 2 numbers 79 and 94 =  | (79*94)^(1/2) = 86.17424209124209 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 40 , 14 and 88 =  |  3/((1/40) + (1/14) + (1/88)) = 27.83132530120482 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[261.42719124755655, 829.8065702712056, 82.49007842320133, 333.03044204454835, 102.77960652154705, 201.9111176608831, 309.0507046659713, 610.4565223359361, 41.43497441732025, 690.4630475041106, 925.7944414219104, 349.37781230105634, 204.28488944053746, 377.3045460430586, 370.27260172442533, 215.3422861061215, 881.7450792783372, 736.7449607302535, 186.25288081152647, 512.2187637065] is: | 2199.237457798086 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 55 degrees Celsius to degrees Fahrenheit = | 131.0 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 94 of the AP series: -72, -115, -158 ...  | -4071 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 48 terms of the AP series: 57, -36, -129 ...  | -102168.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 3762 in Roman Numerals is:  | MMMDCCLXII | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) =  | 17.46exp(i1.98) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 2, 5, 6, 7} ,b={1, 2, 5, 7, 8}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 5, 6, 7, 8},Intersection is {1, 2, 5, 7}, a-b is {6},b-a is {8}, Symmetric difference is {6, 8} | set_operation |
| 94 | Base Conversion | Convert 1011000110100000 from base 2 to base 10. | 45472 | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 7^6 and 7^10 = 7^(6-10) = 7^-4 | 0.00041649312786339027 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 49^7 and 10^7 = (49/10)^7 = 4.9^7 | 67822.30728490003 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 2051  | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 86 minutes to Hours & Minutes | 1 hours and 26 minutes | minutes_to_hours |
| 106 | signum function | signum of -742 is = | -1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 39.96% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 16 pistons will contain no more than 3 rejected pistons? | 6.56 | binomial_distribution |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 12 objects picked 7 at a time  | 792 | combinations |
| 42 | Permutations | Number of Permutations from 11 objects picked 6 at a time =   | 332640 | permutation |
| 52 | Probability of a certain sum appearing on faces of dice | If 1 dice are rolled at the same time, the probability of getting a sum of 6 = | 1/6 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [270, 268, 245, 251, 295, 291, 257, 276, 284, 283, 282, 279, 211, 258, 277, 290, 265, 271, 208, 219, 247, 260, 259, 273, 244, 207, 281, 294, 293, 216, 212, 248, 231, 254, 233, 289, 263, 249, 298, 201] with 95% confidence is | (266.9073350347248, 249.69266496527527) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[13, 42, 48, 42, 44, 10, 37, 26, 33, 20, 50, 9, 43, 24, 41] | The Mean is 32.13333333333333 , Standard Deviation is 184.64888888888893, Variance is 13.588557277683638 | data_summary |
| 76 | Mean and Median | Given the series of numbers [26, 66, 31, 85, 23, 25, 42, 19, 46, 92]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 45.5 and Arithmetic median of this series is 36.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 0.05% of population have. Test sensitivity (true positive) is equal to SN= 95.33% whereas test specificity (true negative) SP= 95.03%. What is the probability that this guy really has that disease? | 0.95% | conditional_probability |