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 | 3x + 8 = 10 | 2/3 | basic_algebra |
| 12 | Logarithm | log3(3) | 1 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 2 * [[6, 4], [10, 9]] =  | [[12,8],[20,18]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (3,-15),(8,11)= | (5.5,-2.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2-17x+70 | (x-7)(x-10) | factoring |
| 23 | Solve a System of Equations in R^2 | -2x + 6y = 2, -2x - y = 23 | x = -10, y = -3 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (-6, -8) and (-13, 16) | sqrt(625) | distance_two_points |
| 26 | Linear Equations | 8x + -13y = -111, 11x + -7y = 54 | x = 17, y = 19 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -9/4x + 9 and y = 0/6x - 8 | (68/9, -8) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [9, -10, 20] X [-9, 8, 15] =  | [-310, -315, -18] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 4798 dollars, 8% rate of interest and for a time period of 4 years is =  | 1535.36 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>6</td><td>-10</td><td>0</td></tr><tr><td>6</td><td>-4</td><td>1</td></tr><tr><td>-9</td><td>7</td><td>-10</td></tr></table>and<table><tr><td>-3</td><td>0</td><td>-9</td><td>-10</td></tr><tr><td>7</td><td>9</td><td>-2</td><td>-2</td></tr><tr><td>4</td><td>-10</td><td>-8</td><td>2</td></tr></table> | <table><tr><td>-88</td><td>-90</td><td>-34</td><td>-40</td></tr><tr><td>-42</td><td>-46</td><td>-54</td><td>-50</td></tr><tr><td>36</td><td>163</td><td>147</td><td>56</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 100x^2+147x+38=0 | [-0.33, -1.14] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (-1+16j) * (7-13j) =  | (201+125j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [-19, 13, -18] . [-12, -6, -7] =  | 276 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[6, 24, 41], [7, 69, 75], [58, 3, 86]]) is: | Matrix([[-1903/13005, 647/13005, 343/13005], [-3748/39015, 1862/39015, 163/39015], [1327/13005, -458/13005, -82/13005]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[95, 84], [5, 32]]) =  |  2620 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 9340 dollars, 8% rate of interest and for a time period of 6 year is =  | 14821.41 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 2x^2 + 7x + 5 = 0 | simplified solution : ((-1.0, -2.5)), generalized solution : ((-7 + 3)/2*2, (-7 - 3)/2*2) | complex_quadratic |
| 105 | Combine Like terms | 8x^2 + 7x^2 + 1x^2 | 16x^2  | combine_like_terms |
| 111 | Expanding Factored Binomial | (-7x-9)(-10x-1) | 70*x^2+97*x+9 | expanding |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 13+25= | 38 | addition |
| 1 | Subtraction | 24-15= | 9 | subtraction |
| 2 | Multiplication | 2*28= | 56 | multiplication |
| 3 | Division | 396/22= | 18 | division |
| 6 | Square Root | sqrt(64)= | 8 | square_root |
| 8 | Square | 14^2= | 196 | square |
| 13 | Complex Division | 19/29= | 0.66 | complex_division |
| 16 | Fraction Division | (5/3)/(9/2) | 10/27 | divide_fractions |
| 28 | Fraction Multiplication | (8/3)*(4/1) | 32/3 | fraction_multiplication |
| 31 | Factorial | 1! =  | 1 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 6/9 and 1/8? | > | compare_fractions |
| 47 | Cube Root | cuberoot of 5 upto 2 decimal places is: | 1.71 | cube_root |
| 53 | Exponentiation | 13^4 = | 28561 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -51 and -94 =  | 43 | absolute_difference |
| 80 | Percentage of a number | What is 71% of 88? | Required percentage = 62.48% | percentage |
| 90 | isprime | 13 | True | is_prime |
| 97 | Power of Powers | The 10^5^10 = 10^(5*10) = 10^50 | 100000000000000000000000000000000000000000000000000 | power_of_powers |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 6x^2 + 4x^10 + 6x^1 + 3x^7 | 12x^1 + 40x^9 + 6x^0 + 21x^6 | power_rule_differentiation |
| 48 | Power Rule Integration | 6x^1 + 6x^1 + 4x^8 + 9x^6 | (6/1)x^2 + (6/1)x^2 + (4/8)x^9 + (9/6)x^7 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(exp(x)+4*x^3)/dx | 12*x^2 + exp(x) | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 14x^2 + 94x + 74 is =  | 125.6667 | definite_integral |
| 110 | Stationary Points | f(x)=2*x^2 + 10*x + 5 | (-5/2,-15/2) | stationary_points |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 11001011= | 00110100 | binary_complement_1s |
| 5 | Modulo Division | 94%91= | 3 | modulo_division |
| 14 | Decimal to Binary | Binary of 51= | 110011 | decimal_to_binary |
| 15 | Binary to Decimal | 111111 | 63 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 12 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 99th Fibonacci number? | 218922995834555891712 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 0001111 | 0xf | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 110010011 = | 1101101 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 916= | 0x394 | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 3202 in Octal is:  | 0o6202 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 1 is =  | 4151 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 8449 is =  | 2101 | decimal_to_bcd |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 1 15 20 =  | (2.623718239906474e-15+42.8485705712571j) | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 40, 33 and 15 exist? | Yes | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 35 and 10 =  | 135 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 20 and 9 =  | 21.93 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 20 sides | 162.0 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 8m is | 384 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 16m, 9m, 9m is | 738 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 8m and radius = 7m is | 659 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 3m is | 27 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 15m, 13m, 8m is | 1560 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 24m and radius = 12m is | 10857 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 4m and radius = 8m is | 425 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 21m and radius = 14m is | 4310 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 100 , 102, 61 = | 97 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is tan(0)? | 0 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 12 sides =  | 1800 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 2m is | 50.26548245743669 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 87 m =  | 2758330.916222452 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [395.2, 94.94, 487.59, 915.24, 212.71, 151.62, 941.03, 166.04, 137.63, 142.14] and [959.66, 406.65, 510.24, 773.64, 637.71, 431.66, 300.24, 482.26, 290.31, 299.93] is: | 0.69 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 5 and angle, 124. Find the area of the sector. | Area of sector = 27.05260 | sector_area |
| 86 | Degrees to Radians | Angle 267 in radians is =  | 4.66 | degree_to_rad |
| 87 | Radians to Degrees | Angle 1 in degrees is =  | 57.3 | radian_to_deg |
| 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 34 and height, 64? | CSA of cylinder = 13672.21 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 5 sided polygon with lengths of [17, 118, 88, 80, 100]cm is:  | 403 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 92 | 578.0530482605219 | circumference |
| 108 | Arc length of Angle | Given radius, 45 and angle, 198. Find the arc length of the angle. | Arc length of the angle = 155.50884 | arc_length |
| 112 | Area of Circle | Area of circle with radius 66 | 13690.285714285714 | area_of_circle |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 3 and 12 = | 12 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 3 and 9 =  | 3 | gcd |
| 27 | Prime Factorisation | Find prime factors of 190 | [2, 5, 19] | prime_factors |
| 40 | Common Factors | Common Factors of 43 and 94 =  | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 18 and 11 =  | 1 | hcf |
| 55 | Comparing surds | Fill in the blanks 64^(1/8) _ 38^(1/7) | > | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 193 and SP = 876 is:  | 353.8860103626943 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [6, 42, 294, 2058, 14406, 100842] ,Find the value of a,common ratio,6th term value, sum upto 8th term | The value of a is 6, common ratio is 7 , 6th term is 100842 , sum upto 8th term is 5764800.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 3 numbers 38 , 65 and 39 =  | (38*65*39)^(1/3) = 45.840975768757424 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 14 , 20 and 53 =  |  3/((1/14) + (1/20) + (1/53)) = 21.38328530259366 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[317.9880634312611, 628.8368810535857, 407.8183503281746, 822.4501014932654, 319.1817378122325, 161.7987092039548, 908.7922300469593, 4.453912375814051, 796.3181726847199, 696.9354536922802, 651.7673559381681, 511.34562947699845, 824.5863614061724, 76.39867279289648, 489.9631394752603, 607.379368438552, 787.6619389442924, 846.7945116397568, 135.6457464412647] is: | 2598.078695453033 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 19 degrees Celsius to degrees Fahrenheit = | 66.2 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 30 of the AP series: -8, -106, -204 ...  | -2850 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 72 terms of the AP series: 88, 44, 0 ...  | -106128.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 3688 in Roman Numerals is:  | MMMDCLXXXVIII | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) =  | 17.89exp(i0.46) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={2, 3, 5, 7} ,b={1, 5, 8, 9, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 3, 5, 7, 8, 9, 10},Intersection is {5}, a-b is {2, 3, 7},b-a is {8, 1, 10, 9}, Symmetric difference is {1, 2, 3, 7, 8, 9, 10} | set_operation |
| 94 | Base Conversion | Convert AA69 from base 13 to base 2. | 101110011000011 | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 34^9 and 34^6 = 34^(9-6) = 34^3 | 39304 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 26^2 and 36^2 = (26/36)^2 = 0.7222222222222222^2 | 0.5216049382716049 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 2061  | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 409 minutes to Hours & Minutes | 6 hours and 49 minutes | minutes_to_hours |
| 106 | signum function | signum of -824 is = | -1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 31.21% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 14 pistons will contain no more than 1 rejected pistons? | 3.91 | binomial_distribution |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 19 objects picked 3 at a time  | 969 | combinations |
| 42 | Permutations | Number of Permutations from 14 objects picked 4 at a time =   | 24024 | 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 5 = | 6/216 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [228, 226, 239, 289, 229, 209, 230, 213, 236, 235, 206, 243, 272, 293, 264, 201, 214, 207, 257, 240, 299, 283, 262, 284, 260, 222, 237, 273, 220, 247, 276, 271, 245, 259, 277, 290, 238] with 80% confidence is | (253.74831626949535, 242.14357562239653) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[47, 10, 22, 19, 42, 37, 17, 15, 31, 48, 40, 16, 18, 28, 19] | The Mean is 27.266666666666666 , Standard Deviation is 149.2622222222222, Variance is 12.21729193488566 | data_summary |
| 76 | Mean and Median | Given the series of numbers [43, 64, 56, 77, 71, 20, 76, 72, 92, 10]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 58.1 and Arithmetic median of this series is 67.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.24% of population have. Test sensitivity (true positive) is equal to SN= 90.15% whereas test specificity (true negative) SP= 93.47%. What is the probability that this guy really has that disease? | 14.77% | conditional_probability |