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
* [Usage](Usage)
* [Basic Documentation](basic-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)
```
## 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`.

### More complicated worksheets

```
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)
```

## List of Generators
## algebra
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 11 | Basic Algebra | 10x + 1 = 10 | 9/10 | basic_algebra |
| 12 | Logarithm | log3(81) | 4 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 10 * [[1, 8], [10, 2]] =  | [[10,80],[100,20]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (-11,2),(12,-16)= | (0.5,-7.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2+5x-14 | (x+7)(x-2) | factoring |
| 23 | Solve a System of Equations in R^2 | -7x - 4y = -20, 4x - 6y = 28 | x = 4, y = -2 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (-11, -17) and (0, -8) | sqrt(202) | distance_two_points |
| 26 | Linear Equations | -10x + -18y = -404, 12x + -13y = -138 | x = 8, y = 18 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 9/5x + 3 and y = 6/5x + 7 | (20/3, 15) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [-15, -13, -4] X [14, 1, -9] =  | [121, -191, 167] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 3163 dollars, 4% rate of interest and for a time period of 8 years is =  | 1012.16 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>-10</td><td>-10</td><td>0</td></tr><tr><td>-1</td><td>-10</td><td>-9</td></tr><tr><td>2</td><td>7</td><td>1</td></tr></table>and<table><tr><td>-7</td><td>-8</td></tr><tr><td>4</td><td>-1</td></tr><tr><td>8</td><td>-3</td></tr></table> | <table><tr><td>30</td><td>90</td></tr><tr><td>-105</td><td>45</td></tr><tr><td>22</td><td>-26</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 40x^2+179x+77=0 | [-0.48, -3.99] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (-3-9j) * (-17+8j) =  | (123+129j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [-13, -9, 8] . [-8, -14, -10] =  | 150 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[69, 83, 5], [16, 53, 63], [26, 74, 97]]) is: | Matrix([[479/39219, -7681/39219, 292/2307], [86/39219, 6563/39219, -251/2307], [-194/39219, -2948/39219, 137/2307]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[25, 64], [52, 79]]) =  |  -1353 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 9974 dollars, 4% rate of interest and for a time period of 1 year is =  | 10372.96 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 3x^2 + 9x + 4 = 0 | simplified solution : ((-0.543, -2.457)), generalized solution : ((-9 + sqrt(33))/2*3, (-9 - sqrt(33))/2*3) | complex_quadratic |
| 105 | Combine Like terms | 9x^3 + 10x^7 + 1x^6 + 9x^3 + 5x^4 + 1x^2 + 9x^5 + 2x^2 | 3x^2 + 18x^3 + 5x^4 + 9x^5 + 1x^6 + 10x^7  | combine_like_terms |
| 111 | Expanding Factored Binomial | (-7x+3)(-5x) | 35*x^2-15*x | expanding |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 44+29= | 73 | addition |
| 1 | Subtraction | 20-6= | 14 | subtraction |
| 2 | Multiplication | 37*2= | 74 | multiplication |
| 3 | Division | 322/23= | 14 | division |
| 6 | Square Root | sqrt(144)= | 12 | square_root |
| 8 | Square | 18^2= | 324 | square |
| 13 | Complex Division | 20/25= | 0.8 | complex_division |
| 16 | Fraction Division | (2/1)/(2/9) | 9 | divide_fractions |
| 28 | Fraction Multiplication | (10/6)*(10/3) | 50/9 | fraction_multiplication |
| 31 | Factorial | 6! =  | 720 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 2/8 and 10/2? | < | compare_fractions |
| 47 | Cube Root | cuberoot of 343 upto 2 decimal places is: | 7.0 | cube_root |
| 53 | Exponentiation | 10^7 = | 10000000 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -7 and -5 =  | 2 | absolute_difference |
| 80 | Percentage of a number | What is 93% of 68? | Required percentage = 63.24% | percentage |
| 90 | isprime | 60 | False | is_prime |
| 97 | Power of Powers | The 17^2^5 = 17^(2*5) = 17^10 | 2015993900449 | power_of_powers |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 9x^5 | 45x^4 | power_rule_differentiation |
| 48 | Power Rule Integration | 10x^10 + 8x^10 + 7x^6 | (10/10)x^11 + (8/10)x^11 + (7/6)x^7 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(sec(x)+7*x^(-2))/dx | tan(x)*sec(x) - 14/x^3 | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 63x^2 + 37x + 60 is =  | 99.5 | definite_integral |
| 110 | Stationary Points | f(x)=3*x^3 + 5*x^2 | (-10/9,500/243),(0,0) | stationary_points |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 00100100= | 11011011 | binary_complement_1s |
| 5 | Modulo Division | 48%40= | 8 | modulo_division |
| 14 | Decimal to Binary | Binary of 2= | 10 | decimal_to_binary |
| 15 | Binary to Decimal | 11101 | 29 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 11 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 48th Fibonacci number? | 4807526976 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 00110100 | 0x34 | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 11000000 = | 1000000 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 943= | 0x3af | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 1630 in Octal is:  | 0o3136 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 8 is =  | 34644 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 5077 is =  | 13135 | decimal_to_bcd |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 13 2 7 =  | (1.723230794081419e-15+28.142494558940577j) | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 10, 48 and 21 exist? | No | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 24 and 76 =  | 80 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 19 and 8 =  | 20.62 | 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 = 6m is | 216 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 15m, 14m, 13m is | 1174 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 24m and radius = 8m is | 1608 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 17m is | 4913 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 15m, 16m, 9m is | 2160 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 48m and radius = 4m is | 2412 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 41m and radius = 1m is | 131 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 1m and radius = 13m is | 176 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 153 , 48, 31 = | 128 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is cos(90)? | 0 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 6 sides =  | 720 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 8m is | 804.247719318987 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 71 m =  | 1499214.0909853016 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [515.22, 683.73, 303.04] and [503.08, 698.99, 749.7] is: | 0.38 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 26 and angle, 63. Find the area of the sector. | Area of sector = 371.65041 | sector_area |
| 86 | Degrees to Radians | Angle 110 in radians is =  | 1.92 | 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, 36 and height, 49? | CSA of cylinder = 11083.54 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 5 sided polygon with lengths of [47, 53, 3, 94, 41]cm is:  | 238 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 30 | 188.49555921538757 | circumference |
| 108 | Arc length of Angle | Given radius, 46 and angle, 136. Find the arc length of the angle. | Arc length of the angle = 109.18780 | arc_length |
| 112 | Area of Circle | Area of circle with radius 24 | 1810.2857142857142 | area_of_circle |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 5 and 1 = | 5 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 17 and 5 =  | 1 | gcd |
| 27 | Prime Factorisation | Find prime factors of 43 | [43] | prime_factors |
| 40 | Common Factors | Common Factors of 100 and 43 =  | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 19 and 8 =  | 1 | hcf |
| 55 | Comparing surds | Fill in the blanks 21^(1/2) _ 74^(1/1) | < | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 583 and SP = 985 is:  | 68.95368782161235 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [8, 48, 288, 1728, 10368, 62208] ,Find the value of a,common ratio,7th term value, sum upto 11th term | The value of a is 8, common ratio is 6 , 7th term is 373248 , sum upto 11th term is 580475288.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 3 numbers 64 , 32 and 73 =  | (64*32*73)^(1/3) = 53.074299494939964 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 82 , 34 and 66 =  |  3/((1/82) + (1/34) + (1/66)) = 52.855610877058595 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[232.9350882815303, 335.2563860261166, 506.63279598159386, 4.115597138930505, 459.81390060105355, 678.3362850124494, 907.3819064859937, 636.8110397295957, 20.43113538894692, 779.147081565477, 572.3940764483918, 803.6488004919244] is: | 1976.0471832445305 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 100 degrees Celsius to degrees Fahrenheit = | 212.0 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 73 of the AP series: -96, -76, -56 ...  | 1344 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 98 terms of the AP series: -4, -55, -106 ...  | -242795.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 809 in Roman Numerals is:  | DCCCIX | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) =  | 15.26exp(i2.12) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 2, 7} ,b={1, 2, 3, 6}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 3, 6, 7},Intersection is {1, 2}, a-b is {7},b-a is {3, 6}, Symmetric difference is {3, 6, 7} | set_operation |
| 94 | Base Conversion | Convert 10212220 from base 3 to base 15. | C8C | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 9^10 and 9^5 = 9^(10-5) = 9^5 | 59049 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 43^2 and 13^2 = (43/13)^2 = 3.3076923076923075^2 | 10.940828402366863 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 1993  | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 838 minutes to Hours & Minutes | 13 hours and 58 minutes | minutes_to_hours |
| 106 | signum function | signum of 492 is = | 1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 37.97% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 18 pistons will contain no more than 2 rejected pistons? | 1.28 | binomial_distribution |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 17 objects picked 2 at a time  | 136 | combinations |
| 42 | Permutations | Number of Permutations from 20 objects picked 6 at a time =   | 27907200 | 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 3 = | 1/6 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [201, 225, 283, 208, 275, 259, 270, 211, 202, 257, 299, 215, 276, 238, 209, 206, 216, 265, 249, 252, 278, 292, 210, 274, 200, 217, 241, 247, 297, 221, 272, 242, 254, 293, 214, 250, 230, 262, 294, 212] with 80% confidence is | (251.69255044389794, 239.10744955610207) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[12, 42, 30, 24, 38, 23, 40, 21, 15, 18, 13, 7, 41, 39, 40] | The Mean is 26.866666666666667 , Standard Deviation is 142.6488888888889, Variance is 11.943571027497969 | data_summary |
| 76 | Mean and Median | Given the series of numbers [9, 42, 63, 56, 19, 30, 97, 8, 40, 94]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 45.8 and Arithmetic median of this series is 41.0 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.56% of population have. Test sensitivity (true positive) is equal to SN= 98.38% whereas test specificity (true negative) SP= 94.57%. What is the probability that this guy really has that disease? | 22.31% | conditional_probability |