# 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)
* [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)
```
## 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 | 4x + 7 = 7 | 0 | basic_algebra |
| 12 | Logarithm | log3(6561) | 8 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 10 * [[3, 9], [5, 7]] =  | [[30,90],[50,70]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (-12,-6),(19,-10)= | (3.5,-8.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2+18x+80 | (x+8)(x+10) | factoring |
| 23 | Solve a System of Equations in R^2 | 8x + 6y = 72, -3x + 3y = -6 | x = 6, y = 4 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (17, -8) and (-9, -14) | sqrt(712) | distance_two_points |
| 26 | Linear Equations | -1x + 1y = -27, 11x + -17y = 405 | x = 9, y = -18 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -9/4x + 2 and y = -9x - 1 | (-4/9, 3) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [-19, 19, 20] X [-12, 20, -4] =  | [-476, -316, -152] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 7547 dollars, 10% rate of interest and for a time period of 8 years is =  | 6037.6 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>-7</td><td>-4</td></tr><tr><td>-4</td><td>-9</td></tr><tr><td>-3</td><td>7</td></tr></table>and<table><tr><td>10</td><td>-2</td><td>4</td></tr><tr><td>-6</td><td>-5</td><td>2</td></tr></table> | <table><tr><td>-46</td><td>34</td><td>-36</td></tr><tr><td>14</td><td>53</td><td>-34</td></tr><tr><td>-72</td><td>-29</td><td>2</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 66x^2+187x+25=0 | [-0.14, -2.69] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (-1+5j) * (-18+20j) =  | (-82-110j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [1, -1, -14] . [17, 6, 20] =  | -269 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[37, 76, 39], [67, 82, 13], [61, 73, 79]]) is: | Matrix([[-1843/47252, 3157/141756, 1105/70878], [375/11813, -136/35439, -533/35439], [37/47252, -645/47252, 343/23626]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[91, 18], [68, 24]]) =  |  960 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 2610 dollars, 5% rate of interest and for a time period of 1 year is =  | 2740.5 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 4x^2 + 4x + 1 = 0 | simplified solution : ((-0.5, -0.5)), generalized solution : ((-4 + 0)/2*4, (-4 - 0)/2*4) | complex_quadratic |
| 105 | Combine Like terms | 1x^2 + 7x^2 + 6x^4 + 5x^4 + 5x^2 | 13x^2 + 11x^4  | combine_like_terms |
| 111 | Expanding Factored Binomial | (-5x-10)(+5x+9) | -25*x^2-95*x-90 | expanding |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 49+48= | 97 | addition |
| 1 | Subtraction | 61-29= | 32 | subtraction |
| 2 | Multiplication | 14*1= | 14 | multiplication |
| 3 | Division | 57/19= | 3 | division |
| 6 | Square Root | sqrt(1)= | 1 | square_root |
| 8 | Square | 6^2= | 36 | square |
| 13 | Complex Division | 25/4= | 6.25 | complex_division |
| 16 | Fraction Division | (3/2)/(1/4) | 6 | divide_fractions |
| 28 | Fraction Multiplication | (8/3)*(1/4) | 2/3 | fraction_multiplication |
| 31 | Factorial | 5! =  | 120 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 9/8 and 5/4? | < | compare_fractions |
| 47 | Cube Root | cuberoot of 658 upto 2 decimal places is: | 8.7 | cube_root |
| 53 | Exponentiation | 15^10 = | 576650390625 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -6 and -50 =  | 44 | absolute_difference |
| 80 | Percentage of a number | What is 55% of 14? | Required percentage = 7.70% | percentage |
| 90 | isprime | 71 | True | is_prime |
| 97 | Power of Powers | The 12^6^4 = 12^(6*4) = 12^24 | 79496847203390844133441536 | power_of_powers |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 9x^10 + 6x^10 + 1x^6 + 10x^3 | 90x^9 + 60x^9 + 6x^5 + 30x^2 | power_rule_differentiation |
| 48 | Power Rule Integration | 3x^10 + 5x^6 + 10x^6 | (3/10)x^11 + (5/6)x^7 + (10/6)x^7 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(ln(x)+5*x^2)/dx | 10*x + 1/x | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 80x^2 + 100x + 5 is =  | 81.6667 | definite_integral |
| 110 | Stationary Points | f(x)=10*x^3 + 9*x^2 + 3 | (-3/5,102/25),(0,3) | stationary_points |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 010000= | 101111 | binary_complement_1s |
| 5 | Modulo Division | 87%99= | 87 | modulo_division |
| 14 | Decimal to Binary | Binary of 3= | 11 | decimal_to_binary |
| 15 | Binary to Decimal | 0010110100 | 180 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 7 numbers is ? | [0, 1, 1, 2, 3, 5, 8] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 47th Fibonacci number? | 2971215073 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 000011010 | 0x1a | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 10011 = | 1101 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 978= | 0x3d2 | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 2183 in Octal is:  | 0o4207 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 6 is =  | 26179 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 8980 is =  | 2314 | decimal_to_bcd |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 10 8 8 =  | 31.22498999199199 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 3, 49 and 40 exist? | No | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 40 and 55 =  | 85 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 10 and 8 =  | 12.81 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 13 sides | 152.31 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 11m is | 726 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 2m, 9m, 3m is | 102 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 10m and radius = 5m is | 471 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 14m is | 2744 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 19m, 4m, 20m is | 1520 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 42m and radius = 17m is | 38132 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 45m and radius = 1m is | 144 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 4m and radius = 11m is | 506 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 81 , 55, 163 = | 61 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is sin(60)? | √3/2 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 9 sides =  | 1260 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 6m is | 452.3893421169302 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 80 m =  | 2144660.584850632 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [956.55, 864.51, 874.49, 333.53, 113.01, 10.44, 653.97, 374.14, 904.82, 608.05, 99.98, 572.65, 354.05, 655.03, 327.04, 853.25, 319.43, 678.41] and [15.79, 792.32, 392.52, 370.7, 283.13, 531.51, 389.19, 480.01, 188.33, 278.59, 964.88, 541.74, 303.95, 941.8, 96.12, 76.43, 864.81, 112.41] is: | 0.88 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 35 and angle, 335. Find the area of the sector. | Area of sector = 3581.19746 | sector_area |
| 86 | Degrees to Radians | Angle 147 in radians is =  | 2.57 | 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, 48 and height, 55? | CSA of cylinder = 16587.61 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 10 sided polygon with lengths of [104, 52, 101, 64, 71, 4, 34, 86, 81, 30]cm is:  | 627 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 12 | 75.39822368615503 | circumference |
| 108 | Arc length of Angle | Given radius, 42 and angle, 156. Find the arc length of the angle. | Arc length of the angle = 114.35397 | arc_length |
| 112 | Area of Circle | Area of circle with radius 39 | 4780.285714285714 | area_of_circle |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 6 and 20 = | 60 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 2 and 2 =  | 2 | gcd |
| 27 | Prime Factorisation | Find prime factors of 100 | [2, 2, 5, 5] | prime_factors |
| 40 | Common Factors | Common Factors of 84 and 41 =  | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 3 and 20 =  | 1 | hcf |
| 55 | Comparing surds | Fill in the blanks 20^(1/4) _ 26^(1/6) | > | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 235 and SP = 844 is:  | 259.1489361702128 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [7, 42, 252, 1512, 9072, 54432] ,Find the value of a,common ratio,9th term value, sum upto 8th term | The value of a is 7, common ratio is 6 , 9th term is 11757312 , sum upto 8th term is 2351461.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 2 numbers 74 and 4 =  | (74*4)^(1/2) = 17.204650534085253 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 41 , 30 , 67 , 10 =  |  4/((1/41) + (1/30) + (1/67) + (1/10)) = 23.168400337362947 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[88.31792181152476, 63.99729325678627, 241.6129026822925, 248.43562116710117, 359.69249783374147, 165.59992609948227, 105.69265168153541] is: | 547.6912694265379 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 47 degrees Celsius to degrees Fahrenheit = | 116.60000000000001 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 72 of the AP series: 50, 91, 132 ...  | 2961 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 96 terms of the AP series: -11, 58, 127 ...  | 313584.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 3140 in Roman Numerals is:  | MMMCXL | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) =  | 17.12exp(i1.69) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={8, 4, 7} ,b={1, 2, 5, 7}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 4, 5, 7, 8},Intersection is {7}, a-b is {8, 4},b-a is {1, 2, 5}, Symmetric difference is {1, 2, 4, 5, 8} | set_operation |
| 94 | Base Conversion | Convert B76F from base 16 to base 10. | 46959 | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 2^10 and 2^5 = 2^(10-5) = 2^5 | 32 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 20^3 and 13^3 = (20/13)^3 = 1.5384615384615385^3 | 3.641329085116068 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 1988  | is a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 860 minutes to Hours & Minutes | 14 hours and 20 minutes | minutes_to_hours |
| 106 | signum function | signum of -220 is = | -1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 35.73% 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 2 rejected pistons? | 7.57 | binomial_distribution |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 13 objects picked 7 at a time  | 1716 | combinations |
| 42 | Permutations | Number of Permutations from 20 objects picked 5 at a time =   | 1860480 | 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 16 = | 6/216 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [248, 294, 218, 252, 232, 271, 263, 213, 282, 244, 202, 270, 268, 257, 215, 262, 250, 239, 223, 253] with 80% confidence is | (254.68566484458836, 240.91433515541166) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[45, 33, 42, 7, 43, 38, 28, 26, 20, 48, 44, 46, 12, 39, 25] | The Mean is 33.06666666666667 , Standard Deviation is 154.9955555555556, Variance is 12.449721103524993 | data_summary |
| 76 | Mean and Median | Given the series of numbers [12, 81, 93, 55, 5, 46, 35, 6, 91, 50]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 47.4 and Arithmetic median of this series is 48.0 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 0.52% of population have. Test sensitivity (true positive) is equal to SN= 98.31% whereas test specificity (true negative) SP= 96.83%. What is the probability that this guy really has that disease? | 13.95% | conditional_probability |