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.

## Usage

The project can be install via pip

```bash
pip install mathgenerator
```

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 | 3x + 9 = 9 | 0 | basic_algebra |
| 12 | Logarithm | log3(6561) | 8 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 10 * [[8, 6], [7, 3]] =  | [[80,60],[70,30]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (3,-15),(-17,1)= | (-7.0,-7.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2-8x+7 | (x-7)(x-1) | factoring |
| 23 | Solve a System of Equations in R^2 | 9x - 9y = -72, -10x - 5y = 20 | x = -4, y = 4 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (0, -14) and (-8, -6) | sqrt(128) | distance_two_points |
| 26 | Linear Equations | -12x + -11y = 138, -1x + -14y = 247 | x = 5, y = -18 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = -2/4x + 8 and y = 1x - 8 | (32/3, 8/3) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [7, -3, 11] X [3, -12, -16] =  | [180, 145, -75] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 1601 dollars, 2% rate of interest and for a time period of 5 years is =  | 160.1 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>10</td><td>-3</td><td>-1</td></tr><tr><td>-3</td><td>-1</td><td>-7</td></tr><tr><td>-3</td><td>-9</td><td>7</td></tr><tr><td>5</td><td>8</td><td>1</td></tr></table>and<table><tr><td>9</td><td>5</td><td>8</td><td>-5</td></tr><tr><td>-1</td><td>4</td><td>3</td><td>7</td></tr><tr><td>-8</td><td>5</td><td>8</td><td>-1</td></tr></table> | <table><tr><td>101</td><td>33</td><td>63</td><td>-70</td></tr><tr><td>30</td><td>-54</td><td>-83</td><td>15</td></tr><tr><td>-74</td><td>-16</td><td>5</td><td>-55</td></tr><tr><td>29</td><td>62</td><td>72</td><td>30</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 96x^2+123x+24=0 | [-0.24, -1.04] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (2-12j) * -10j =  | (-120-20j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [-19, -4, 13] . [-11, -2, -9] =  | 100 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[59, 45, 48], [15, 9, 31], [29, 51, 17]]) is: | Matrix([[17/370, -561/10360, -321/10360], [-23/1110, 389/31080, 1109/31080], [-3/185, 71/1295, 6/1295]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[55, 69], [58, 66]]) =  |  -372 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 7423 dollars, 9% rate of interest and for a time period of 1 year is =  | 8091.07 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation x^2 + 9x + 7 = 0 | simplified solution : ((-0.86, -8.14)), generalized solution : ((-9 + sqrt(53))/2*1, (-9 - sqrt(53))/2*1) | complex_quadratic |
| 105 | Combine Like terms | 4x^1 + 6x^7 + 4x^9 + 3x^6 + 7x^4 + 6x^9 + 3x^7 + 8x^5 + 3x^2 + 1x^5 | 4x^1 + 3x^2 + 7x^4 + 9x^5 + 3x^6 + 9x^7 + 10x^9  | combine_like_terms |
| 111 | Expanding Factored Binomial | (-5x+10)(-6x-8) | 30*x^2-20*x-80 | expanding |
## basic_math
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 0 | Addition | 49+24= | 73 | addition |
| 1 | Subtraction | 90-14= | 76 | subtraction |
| 2 | Multiplication | 65*0= | 0 | multiplication |
| 3 | Division | 153/9= | 17 | division |
| 6 | Square Root | sqrt(121)= | 11 | square_root |
| 8 | Square | 13^2= | 169 | square |
| 13 | Complex Division | 99/25= | 3.96 | complex_division |
| 16 | Fraction Division | (9/5)/(1/10) | 18 | divide_fractions |
| 28 | Fraction Multiplication | (6/1)*(4/9) | 8/3 | fraction_multiplication |
| 31 | Factorial | 4! =  | 24 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 2/3 and 1/8? | > | compare_fractions |
| 47 | Cube Root | cuberoot of 431 upto 2 decimal places is: | 7.55 | cube_root |
| 53 | Exponentiation | 16^9 = | 68719476736 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -48 and -85 =  | 37 | absolute_difference |
| 80 | Percentage of a number | What is 26% of 50? | Required percentage = 13.00% | percentage |
| 90 | isprime | 71 | True | is_prime |
| 97 | Power of Powers | The 44^5^2 = 44^(5*2) = 44^10 | 27197360938418176 | power_of_powers |
## calculus
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 6x^2 + 9x^2 + 2x^8 + 3x^1 | 12x^1 + 18x^1 + 16x^7 + 3x^0 | power_rule_differentiation |
| 48 | Power Rule Integration | 9x^4 + 7x^7 + 6x^6 + 6x^4 | (9/4)x^5 + (7/7)x^8 + (6/6)x^7 + (6/4)x^5 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(sec(x)+4*x^3)/dx | 12*x^2 + tan(x)*sec(x) | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 62x^2 + 2x + 78 is =  | 99.6667 | definite_integral |
| 110 | Stationary Points | f(x)=8*x^2 + 7*x + 1 | (-7/16,-17/32) | stationary_points |
## computer_science
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 10010001= | 01101110 | binary_complement_1s |
| 5 | Modulo Division | 85%29= | 27 | modulo_division |
| 14 | Decimal to Binary | Binary of 17= | 10001 | decimal_to_binary |
| 15 | Binary to Decimal | 0 | 0 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 20 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 48th Fibonacci number? | 4807526976 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 00 | 0x0 | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of  = |  | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 280= | 0x118 | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 1994 in Octal is:  | 0o3712 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 7 is =  | 29299 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 9775 is =  | 26215 | decimal_to_bcd |
## geometry
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 18 18 16 =  | 128.9961239727768 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 48, 40 and 48 exist? | Yes | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 31 and 7 =  | 142 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 16 and 6 =  | 17.09 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 12 sides | 150.0 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 1m is | 6 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 9m, 7m, 6m is | 318 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 20m and radius = 19m is | 4655 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 10m is | 1000 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 16m, 4m, 11m is | 704 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 18m and radius = 13m is | 9556 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 45m and radius = 19m is | 4049 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 38m and radius = 12m is | 5730 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 90 , 59, 150 = | 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 6 sides =  | 720 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 15m is | 2827.4333882308138 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 96 m =  | 3705973.4906218923 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [848.07, 542.12, 669.74, 765.58, 540.05, 31.8, 476.27, 305.45, 148.71, 605.96, 538.21, 613.01, 342.15, 762.78, 849.08, 888.04, 229.57, 673.21, 522.35, 55.69] and [373.43, 892.36, 108.8, 171.3, 283.51, 791.0, 268.17, 870.8, 351.92, 923.46, 732.98, 290.93, 613.57, 487.0, 623.97, 840.61, 901.9, 176.05, 859.64, 227.87] is: | 0.7 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 33 and angle, 218. Find the area of the sector. | Area of sector = 2071.72328 | sector_area |
| 86 | Degrees to Radians | Angle 237 in radians is =  | 4.14 | 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, 5 and height, 31? | CSA of cylinder = 973.89 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 7 sided polygon with lengths of [98, 54, 9, 78, 1, 106, 36]cm is:  | 382 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 93 | 584.3362335677015 | circumference |
| 108 | Arc length of Angle | Given radius, 25 and angle, 190. Find the arc length of the angle. | Arc length of the angle = 82.90314 | arc_length |
| 112 | Area of Circle | Area of circle with radius 34 | 3633.1428571428573 | area_of_circle |
## misc
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 17 and 1 = | 17 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 16 and 9 =  | 1 | gcd |
| 27 | Prime Factorisation | Find prime factors of 86 | [2, 43] | prime_factors |
| 40 | Common Factors | Common Factors of 38 and 100 =  | [1, 2] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 12 and 9 =  | 3 | hcf |
| 55 | Comparing surds | Fill in the blanks 6^(1/4) _ 88^(1/1) | < | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 847 and SP = 880 is:  | 3.896103896103896 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [12, 84, 588, 4116, 28812, 201684] ,Find the value of a,common ratio,7th term value, sum upto 6th term | The value of a is 12, common ratio is 7 , 7th term is 1411788 , sum upto 6th term is 235296.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 4 numbers 72 , 93 , 63 , 5 =  | (72*93*63*5)^(1/4) = 38.10934633766355 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 68 , 62 and 32 =  |  3/((1/68) + (1/62) + (1/32)) = 48.32091690544412 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[696.4519852852237, 658.9333146828044, 483.3976903342588, 222.67348281350618] is: | 1096.5834614726732 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 73 degrees Celsius to degrees Fahrenheit = | 163.4 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 21 of the AP series: -65, 14, 93 ...  | 1515 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 49 terms of the AP series: -84, -125, -166 ...  | -52332.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 1119 in Roman Numerals is:  | MCXIX | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) =  | 13.0exp(i-1.18) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 2, 4, 5, 6, 7, 8} ,b={1, 5, 6, 8, 9, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 4, 5, 6, 7, 8, 9, 10},Intersection is {8, 1, 5, 6}, a-b is {2, 4, 7},b-a is {9, 10}, Symmetric difference is {2, 4, 7, 9, 10} | set_operation |
| 94 | Base Conversion | Convert 9E4F from base 16 to base 15. | C01C | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 37^6 and 37^7 = 37^(6-7) = 37^-1 | 0.02702702702702703 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 50^2 and 11^2 = (50/11)^2 = 4.545454545454546^2 | 20.661157024793393 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 1933  | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 563 minutes to Hours & Minutes | 9 hours and 23 minutes | minutes_to_hours |
| 106 | signum function | signum of -584 is = | -1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 32.97% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 12 pistons will contain no more than 9 rejected pistons? | 99.95 | binomial_distribution |
## statistics
| Id   | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 15 objects picked 5 at a time  | 3003 | combinations |
| 42 | Permutations | Number of Permutations from 14 objects picked 7 at a time =   | 17297280 | 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 5 = | 1/6 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [274, 205, 285, 208, 269, 231, 246, 238, 212, 278, 266, 270, 243, 297, 295, 283, 249, 296, 279, 294, 255, 277, 239, 245, 203, 288, 287, 253] with 80% confidence is | (266.4148171763757, 252.51375425219572) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[26, 34, 33, 32, 45, 26, 50, 42, 40, 15, 5, 48, 48, 11, 6] | The Mean is 30.733333333333334 , Standard Deviation is 223.79555555555558, Variance is 14.959797978433919 | data_summary |
| 76 | Mean and Median | Given the series of numbers [43, 48, 78, 71, 82, 32, 49, 26, 76, 3]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 50.8 and Arithmetic median of this series is 48.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 1.48% of population have. Test sensitivity (true positive) is equal to SN= 98.64% whereas test specificity (true negative) SP= 94.56%. What is the probability that this guy really has that disease? | 21.41% | conditional_probability |