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* Improve combine_like_terms * Lint fix * add some latex to readme * give compound_interest latex formatting * fix compound interest readme * update combine_like_terms readme * combine_like_terms add delimiters * Convert some alebra output to latex * Add missing right] to latex * Fix makeReadme script * Correct det 2x2 latex * use bmatrix for det 2x2 * update readme and bump version * Make latex matrix one line * made latex for most of algebra * more latex migrations * convert basic_math to latex * re-generate readme * fix double exponent * latex for most of calculus * Improved stationary points gen * made cs latex * Transform geometry to latex * texify misc outputs * texify statistics * regenerate readme * Add tex markers to linear_equations * add list_to_tex for mult_int_22 * upgrade readme * update list_to_tex * add end to list_to_tex * tweak list_to_tex, update readme * Update README.md * Update README.md * lint fixes * lint fix * Remove tests * texify system_of_equations * update system_of_equations tex * regen readme * texify complex_quadratic * update complex_quadratic * regen readme * sqrt to complex_quadratic * complex_quadratic texify * Update README.md * Update README.md * make latexbuilder * regen readme * fix bmatrix * bmatrix conversions * update readme * use times symbol * improve tex of prod_sci_notations * Add missing delim to prod of sci notations * Add missing curly brack to prod-sci-not * lint fixes * texify differentiation * texify stationary points * changed differentation to trig_differentiation * texify stationary points * update readme * Remove left right from stat_points * texify angle_btw_vectors * update readme * add spaces to mod operator * Swap \\% with \\percent * update readme * Replace //percent with non-math % * fix leftover \\percent * latexify vector_cross * change tex multiply to times * update readme * lint fixes * lint fix
222 lines
36 KiB
Markdown
222 lines
36 KiB
Markdown
# mathgenerator
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A math problem generator, created for the purpose of giving teachers and students the means to easily get access to random math exercises to suit their needs.
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To try out generators, go to <https://lukew3.github.io/mathgenerator>
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See [CONTRIBUTING.md](https://github.com/lukew3/mathgenerator/blob/main/CONTRIBUTING.md) for information about how to contribute.
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## Table of Contents
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* [Installation](#installation)
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* [Usage](#usage)
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* [List of Generators](#list-of-generators)
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* [algebra](#algebra)
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* [basic_math](#basic_math)
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* [calculus](#calculus)
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* [computer_science](#computer_science)
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* [geometry](#geometry)
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* [misc](#misc)
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* [statistics](#statistics)
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## Installation
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The project can be install via pip
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```bash
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pip install mathgenerator
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```
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## Usage
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Here is an example of how you would generate an addition problem:
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```python
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import mathgenerator
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#generate an addition problem
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problem, solution = mathgenerator.addition()
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#another way to generate an addition problem using genById()
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problem, solution = mathgenerator.genById(0)
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```
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You may prefer to use `import mathgenerator as mg` and run functions like `mg.addition()` so that you don't have to type as much.
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<!--
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### Creating a worksheet
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If you wish to create a worksheet, you can use the [worksheetgen](https://github.com/lukew3/worksheetgen) package. Install this with `pip install worksheetgen`. Here is an example of how a worksheet would be generated.
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```
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from mathgenerator import mathgen
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from worksheetgen.wg import Worksheet
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ws = Worksheet("Worksheet title")
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with ws.section('Section 1', description='These are instructions')
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# Writes 10 problems generated with id 1, [0] at the end specifies to take problem, and not solution.
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for _ in range(10):
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ws.add_problem(mathgen.genById(1)[0])
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ws.write_pdf()
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```
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This creates the pdf `ws.pdf` in your current directory
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-->
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Problem/solution pairs are generated with either:
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* `mathgenerator.<generator_name>()` - generates a problem, solution set from the given generator name.
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* `mathgenerator.genById(id)` - generates a problem, solution set with generator id provided by the `id` parameter
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<!--
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#### `format` kwarg
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* Pass `format=latex` to return problem and solution set as latex. If latex is not available for that generator, the problem will return the string "Latex unavailable"
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* Pass `format=raw` to return just the raw data for each generator. An array of each variable necessary to the generator is returned.
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* If you don't pass a value to the format kwarg, the generator will return a problem and answer in asciimath format.
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-->
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You can also use `getGenList()` to return a list of all generators included in the library in the format:
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```
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[id, title, gen_func, funcname, subjectname, kwargs]
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```
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## List of Generators
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## algebra
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| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
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|------|-------|-----------------|------------------|---------------|--------|
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| 11 | [Basic Algebra](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/basic_algebra.py) | $9x + 9 = 9$ | $0$ | basic_algebra | `maxVariable=10` |
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| 12 | [Logarithm](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/log.py) | $log_{2}(256)=$ | $8$ | log | `maxBase=3` `maxVal=8` |
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| 17 | [Integer Multiplication with 2x2 Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_int_to_22_matrix.py) | $2 * \begin{bmatrix} 8 & 0 \\ 10 & 10 \end{bmatrix} =$ | $\begin{bmatrix} 16 & 0 \\ 20 & 20 \end{bmatrix}$ | multiply_int_to_22_matrix | `maxMatrixVal=10` `maxRes=100` |
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| 20 | [Midpoint of the two point](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/midpoint_of_two_points.py) | The midpoint of $(7,5)$ and $(-17,14) = $ | $(-5.0,9.5)$ | midpoint_of_two_points | `maxValue=20` |
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| 21 | [Factoring Quadratic](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/factoring.py) | $x^2-2x$ | $(x)(x-2)$ | factoring | `range_x1=10` `range_x2=10` |
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| 23 | [Solve a System of Equations in R^2](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/system_of_equations.py) | Given $4x - 6y = 36$ and $9x - 2y = 12$, solve for $x$ and $y$. | $x = 0$, $y = -6$ | system_of_equations | `range_x=10` `range_y=10` `coeff_mult_range=10` |
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| 24 | [Distance between 2 points](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/distance_two_points.py) | Find the distance between $(7, -15)$ and $(0, -1)$ | $\sqrt{245}$ | distance_two_points | `maxValXY=20` `minValXY=-20` |
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| 26 | [Linear Equations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/linear_equations.py) | Given the equations $-3x + 10y = -140$ and $-3x + -4y = -28$, solve for $x$ and $y$ | $x = 20$, $y = -8$ | linear_equations | `n=2` `varRange=20` `coeffRange=20` |
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| 41 | [Intersection of Two Lines](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/intersection_of_two_lines.py) | Find the point of intersection of the two lines: $y = 9/3x - 6$ and $y = 1/3x + 6$ | $(9/2, 15/2)$ | intersection_of_two_lines | `minM=-10` `maxM=10` `minB=-10` `maxB=10` `minDenominator=1` `maxDenominator=6` |
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| 43 | [Cross Product of 2 Vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/vector_cross.py) | $[-18, 0, 20] \times [-16, -5, 0] = $ | $[100, -320, 90]$ | vector_cross | `minVal=-20` `maxVal=20` |
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| 45 | [Simple Interest](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/simple_interest.py) | Simple interest for a principle amount of $9080$ dollars, $3$% rate of interest and for a time period of $6$ years is $=$ | $1634.4$ | simple_interest | `maxPrinciple=10000` `maxRate=10` `maxTime=10` |
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| 46 | [Multiplication of two matrices](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/matrix_multiplication.py) | Multiply$\begin{bmatrix}0&-1&-9&1\\-10&4&3&-10\end{bmatrix}$and$\begin{bmatrix}-4&-2&-4\\8&-1&2\\-2&6&-5\\-10&7&5\end{bmatrix}$ | $\begin{bmatrix}0&-46&48\\166&-36&-17\end{bmatrix}$ | matrix_multiplication | `maxVal=100` `max_dim=10` |
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| 50 | [Quadratic Equation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/quadratic_equation.py) | What are the zeros of the quadratic equation $24x^2+103x+26=0$ | ${-0.27, -4.02}$ | quadratic_equation | `maxVal=100` |
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| 65 | [Multiplication of 2 complex numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_complex_numbers.py) | $(17+1j) * (17-1j) = $ | $(290+0j)$ | multiply_complex_numbers | `minRealImaginaryNum=-20` `maxRealImaginaryNum=20` |
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| 72 | [Dot Product of 2 Vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/vector_dot.py) | $[9, 14, -19]\cdot[-8, -9, 10]=$ | $-388$ | vector_dot | `minVal=-20` `maxVal=20` |
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| 74 | [Inverse of a Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/invert_matrix.py) | Inverse of Matrix $\begin{bmatrix} 0 & 0 & 1 \\ 1 & 3 & 3 \\ 1 & 2 & 2 \end{bmatrix}$ is: | \begin{bmatrix} 0 & -2 & 3 \\ -1 & 1 & -1 \\ 1 & 0 & 0 \end{bmatrix} | invert_matrix | `SquareMatrixDimension=3` `MaxMatrixElement=99` `OnlyIntegerElementsInInvertedMatrix=True` |
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| 77 | [Determinant to 2x2 Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/int_matrix_22_determinant.py) | $\det \begin{bmatrix} 24 & 94 \\ 21 & 29 \end{bmatrix}= $ | $-1278$ | int_matrix_22_determinant | `maxMatrixVal=100` |
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| 78 | [Compound Interest](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/compound_interest.py) | Compound interest for a principle amount of $2004$ dollars, $1$% rate of interest and for a time period of $5$ years is $=$ | $2106.22$ | compound_interest | `maxPrinciple=10000` `maxRate=10` `maxTime=10` |
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| 100 | [complex Quadratic Equation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/complex_quadratic.py) | Find the roots of given Quadratic Equation $7x^2 + 7x + 1 = 0$ | $((-0.173, -0.827)) = (\frac{-7 + \sqrt{21}}{2*7}, (\frac{-7 - \sqrt{21}}{2*7})$ | complex_quadratic | `prob_type=0` `max_range=10` |
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| 105 | [Combine Like terms](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/combine_like_terms.py) | $4x^{13} + 1x^{16}$ | $4x^{13} + 1x^{16}$ | combine_like_terms | `maxCoef=10` `maxExp=20` `maxTerms=10` |
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| 111 | [Expanding Factored Binomial](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/expanding.py) | $(-10x-2)(-1x+6)$ | $10x^2-58x-12$ | expanding | `range_x1=10` `range_x2=10` `range_a=10` `range_b=10` |
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## basic_math
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| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
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|------|-------|-----------------|------------------|---------------|--------|
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| 0 | [Addition](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/addition.py) | $40+14=$ | $54$ | addition | `maxSum=99` `maxAddend=50` |
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| 1 | [Subtraction](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/subtraction.py) | $12-2=$ | $10$ | subtraction | `maxMinuend=99` `maxDiff=99` |
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| 2 | [Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/multiplication.py) | $7\cdot8$ | $56$ | multiplication | `maxMulti=12` |
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| 3 | [Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/division.py) | $92\div23=$ | $4$ | division | `maxA=25` `maxB=25` |
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| 6 | [Square Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square_root.py) | $\sqrt{1}=$ | $1$ | square_root | `minNo=1` `maxNo=12` |
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| 8 | [Square](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square.py) | $9^2=$ | $81$ | square | `maxSquareNum=20` |
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| 13 | [Fraction to Decimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/fraction_to_decimal.py) | $84\div6=$ | $14.0$ | fraction_to_decimal | `maxRes=99` `maxDivid=99` |
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| 16 | [Fraction Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/divide_fractions.py) | $\frac{6}{7}\div\frac{9}{5}=$ | $\frac{10}{21}$ | divide_fractions | `maxVal=10` |
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| 28 | [Fraction Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/fraction_multiplication.py) | $\frac{3}{9}\cdot\frac{7}{6}=$ | $\frac{7}{18}$ | fraction_multiplication | `maxVal=10` |
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| 31 | [Factorial](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/factorial.py) | $5! =$ | $120$ | factorial | `maxInput=6` |
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| 44 | [Compare Fractions](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/compare_fractions.py) | Which symbol represents the comparison between $\frac{3}{5}$ and $\frac{3}{9}$? | > | compare_fractions | `maxVal=10` |
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| 47 | [Cube Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/cube_root.py) | What is the cube root of: $\sqrt[3]{30}=$ to 2 decimal places? | $3.11$ | cube_root | `minNo=1` `maxNo=1000` |
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| 53 | [Exponentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/exponentiation.py) | $4^1 =$ | $4$ | exponentiation | `maxBase=20` `maxExpo=10` |
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| 71 | [Absolute difference between two numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/absolute_difference.py) | $|22--59|=$ | $81$ | absolute_difference | `maxA=100` `maxB=100` |
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| 80 | [Percentage of a number](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage.py) | What is $5$% of $18$? | $0.90$ | percentage | `maxValue=99` `maxpercentage=99` |
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| 90 | [isprime](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/is_prime.py) | Is $73$ prime? | Yes | is_prime | `max_num=100` |
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| 97 | [Power of Powers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/power_of_powers.py) | Simplify $31^{8^{2}}$ | $31^{16}$ | power_of_powers | `maxBase=50` `maxPower=10` |
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| 118 | [Percentage difference](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage_difference.py) | What is the percentage difference between $66$ and $7$? | $161.64$% | percentage_difference | `maxValue=200` `minValue=0` |
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| 119 | [Percentage error](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage_error.py) | Find the percentage error when observed value equals $-44$ and exact value equals $-26$. | $69.23\%$ | percentage_error | `maxValue=100` `minValue=-100` |
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| 120 | [Greatest Common Divisor of N Numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/greatest_common_divisor.py) | $GCD(860597057,541815762)=$ | $1$ | greatest_common_divisor | `numbersCount=2` `maximalNumberLimit=10**9` |
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| 124 | [Is Composite](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/is_composite.py) | Is $144$ composite? | Yes | is_composite | `maxNum=250` |
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## calculus
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| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
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|------|-------|-----------------|------------------|---------------|--------|
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| 7 | [Power Rule Differentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/power_rule_differentiation.py) | $2x^{6} + 5x^{4} + 6x^{4} + 9x^{4}$ | $12x^{5} + 20x^{3} + 24x^{3} + 36x^{3}$ | power_rule_differentiation | `maxCoef=10` `maxExp=10` `maxTerms=5` |
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| 48 | [Power Rule Integration](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/power_rule_integration.py) | $8x^{1} + 1x^{9} + 5x^{1}$ | $\frac{8}{1}x^{2} + \frac{1}{9}x^{10} + \frac{5}{1}x^{2} + C$ | power_rule_integration | `maxCoef=10` `maxExp=10` `maxTerms=5` |
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| 88 | [Trigonometric Differentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/trig_differentiation.py) | $\frac{d}{dx}(\sin)=$ | $\cos$ | trig_differentiation | |
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| 89 | [Definite Integral of Quadratic Equation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/definite_integral.py) | The definite integral within limits $0$ to $1$ of the equation $24x^2 + 93x + 13 = $ | $67.5$ | definite_integral | `max_coeff=100` |
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| 110 | [Stationary Points](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/stationary_points.py) | $f(x)=10*x^3 + 8*x^2 + 2*x + 5$ | ${- \frac{1}{3}, - \frac{1}{5}}$ | stationary_points | `maxExp=3` `maxCoef=10` |
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## computer_science
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| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
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|------|-------|-----------------|------------------|---------------|--------|
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| 4 | [Binary Complement 1s](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_complement_1s.py) | $010 = $ | $101$ | binary_complement_1s | `maxDigits=10` |
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| 5 | [Modulo Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/modulo_division.py) | $84$ % $20 = $ | $4$ | modulo_division | `maxRes=99` `maxModulo=99` |
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| 14 | [Decimal to Binary](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_binary.py) | Binary of $49 = $ | $110001$ | decimal_to_binary | `max_dec=99` |
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| 15 | [Binary to Decimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_decimal.py) | $00$ | $0$ | binary_to_decimal | `max_dig=10` |
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| 56 | [Fibonacci Series](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/fibonacci_series.py) | The Fibonacci Series of the first ${n}$ numbers is ? | $0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89$ | fibonacci_series | `minNo=1` |
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| 62 | [nth Fibonacci number](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/nth_fibonacci_number.py) | What is the 74th Fibonacci number? | $1304969544928660$ | nth_fibonacci_number | `maxN=100` |
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| 64 | [Binary to Hexidecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_hex.py) | $11010100$ | $0xd4$ | binary_to_hex | `max_dig=10` |
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| 73 | [Binary 2's Complement](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_2s_complement.py) | 2's complement of $1 = $ | $1$ | binary_2s_complement | `maxDigits=10` |
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| 79 | [Decimal to Hexadecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_hexadeci.py) | Binary of $639 = $ | $0x27f$ | decimal_to_hexadeci | `max_dec=1000` |
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| 84 | [Converts decimal to octal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_octal.py) | The decimal number ${x}$ in Octal is: | $0o5206$ | decimal_to_octal | `maxDecimal=4096` |
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| 91 | [Binary Coded Decimal to Integer](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/bcd_to_decimal.py) | Integer of Binary Coded Decimal $3$ is $=$ | $12440$ | bcd_to_decimal | `maxNumber=10000` |
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| 103 | [Decimal to Binary Coded Decimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_bcd.py) | BCD of Decimal Number $6981 = $ | $11145$ | decimal_to_bcd | `maxNumber=10000` |
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## geometry
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| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
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|------|-------|-----------------|------------------|---------------|--------|
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| 18 | [Area of Triangle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_triangle.py) | Area of triangle with side lengths: $5, 15 11 = $ | $19.14$ | area_of_triangle | `maxA=20` `maxB=20` |
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| 19 | [Triangle exists check](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/valid_triangle.py) | Does triangle with sides $20, 17$ and $29$ exist? | $Yes$ | valid_triangle | `maxSideLength=50` |
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| 22 | [Third Angle of Triangle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/third_angle_of_triangle.py) | Third angle of triangle with angles $1$ and $86 = $ | $93$ | third_angle_of_triangle | `maxAngle=89` |
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| 25 | [Pythagorean Theorem](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/pythagorean_theorem.py) | What is the hypotenuse of a right triangle given the other two sides have lengths $18$ and $9$? | $20.12$ | pythagorean_theorem | `maxLength=20` |
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| 29 | [Angle of a Regular Polygon](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/angle_regular_polygon.py) | Find the angle of a regular polygon with $7$ sides | $128.57$ | angle_regular_polygon | `minVal=3` `maxVal=20` |
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|
| 32 | [Surface Area of Cube](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cube.py) | Surface area of cube with side $= 17m$ is | $1734 m^2$ | surface_area_cube | `maxSide=20` `unit='m'` |
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| 33 | [Surface Area of Cuboid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cuboid.py) | Surface area of cuboid with sides of lengths: $9m, 11m, 20m$ is | $998 m^2$ | surface_area_cuboid | `maxSide=20` `unit='m'` |
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|
| 34 | [Surface Area of Cylinder](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cylinder.py) | Surface area of cylinder with height $= 25m$ and radius $= 18m$ is | $4863 m^2$ | surface_area_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'` |
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| 35 | [Volume of Cube](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cube.py) | Volume of cube with a side length of $13m$ is | $2197 m^3$ | volume_cube | `maxSide=20` `unit='m'` |
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| 36 | [Volume of Cuboid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cuboid.py) | Volume of cuboid with sides = $2m, 6m, 18m$ is | $216 m^3$ | volume_cuboid | `maxSide=20` `unit='m'` |
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| 37 | [Volume of cylinder](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cylinder.py) | Volume of cylinder with height $= 28m$ and radius $= 5m$ is | $2199 m^3$ | volume_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'` |
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| 38 | [Surface Area of cone](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_cone.py) | Surface area of cone with height $= 37m$ and radius $= 15m$ is | $2588 m^2$ | surface_area_cone | `maxRadius=20` `maxHeight=50` `unit='m'` |
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| 39 | [Volume of cone](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cone.py) | Volume of cone with height $= 17m$ and radius $= 1m$ is | $17 m^3$ | volume_cone | `maxRadius=20` `maxHeight=50` `unit='m'` |
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| 49 | [Fourth Angle of Quadrilateral](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/fourth_angle_of_quadrilateral.py) | Fourth angle of quadrilateral with angles $108 , 35, 117 =$ | $100$ | fourth_angle_of_quadrilateral | `maxAngle=180` |
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| 57 | [Trigonometric Values](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/basic_trigonometry.py) | $\tan(0) = $ | $0$ | basic_trigonometry | `angles=[0, 30, 45, 60, 90]` `functions=['sin', 'cos', 'tan']` |
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|
| 58 | [Sum of Angles of Polygon](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/sum_of_polygon_angles.py) | What is the sum of interior angles of a polygon with $5$ sides? | $540$ | sum_of_polygon_angles | `maxSides=12` |
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| 60 | [Surface Area of Sphere](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_sphere.py) | Surface area of Sphere with radius $= 14m$ is | $2463.0086404143976 m^2$ | surface_area_sphere | `maxSide=20` `unit='m'` |
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|
| 61 | [Volume of Sphere](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_sphere.py) | Volume of sphere with radius $12 m = $ | $7238.229473870882 m^3$ | volume_sphere | `maxRadius=100` |
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| 70 | [Angle between 2 vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/angle_btw_vectors.py) | angle between the vectors $[90.18, 778.39, 6.95, 189.4, 402.86]$ and $[937.62, 966.01, 986.87, 311.51, 725.29]$ is: | $0.77$ radians | angle_btw_vectors | `maxEltAmt=20` |
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|
| 75 | [Area of a Sector](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/sector_area.py) | What is the area of a sector with radius $27$ and angle $340$ degrees? | $2162.99$ | sector_area | `maxRadius=49` `maxAngle=359` |
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| 86 | [Degrees to Radians](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/degree_to_rad.py) | Angle $50$ degrees in radians is: | $0.87$ | degree_to_rad | `max_deg=360` |
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| 87 | [Radians to Degrees](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/radian_to_deg.py) | Angle $1.14$ radians in degrees is: | $65.32$ | radian_to_deg | `max_rad=6.28` |
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| 95 | [Curved surface area of a cylinder](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/curved_surface_area_cylinder.py) | What is the curved surface area of a cylinder of radius, $42$ and height, $28$? | $7389.03$ | curved_surface_area_cylinder | `maxRadius=49` `maxHeight=99` |
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| 96 | [Perimeter of Polygons](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/perimeter_of_polygons.py) | The perimeter of a $11$ sided polygon with lengths of $16, 109, 106, 37, 3, 59, 49, 1, 88, 43, 42$cm is: | $553$ | perimeter_of_polygons | `maxSides=12` `maxLength=120` |
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| 104 | [Circumference](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/circumference.py) | Circumference of circle with radius $37 = $ | $232.48$ | circumference | `maxRadius=100` |
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| 108 | [Arc length of Angle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/arc_length.py) | Given radius, $49$ and angle, $13$. Find the arc length of the angle. | Arc length of the angle $= 11.11775$ | arc_length | `maxRadius=49` `maxAngle=359` |
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| 112 | [Area of Circle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_circle.py) | Area of circle with radius $92=$ | $26590.44$ | area_of_circle | `maxRadius=100` |
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| 113 | [Volume of frustum](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_frustum.py) | Volume of frustum with height $= 33m$ and $r1 = 7m$ is and $r2 = 7m$ is | $6669.0 m^3$ | volume_frustum | `maxR1=20` `maxR2=20` `maxHeight=50` `unit='m'` |
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| 114 | [Equation of line from two points](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/equation_of_line_from_two_points.py) | What is the equation of the line between points $(20,7)$ and $(-12,12)$ in slope-intercept form? | $32y = -5x + 324$ | equation_of_line_from_two_points | `maxCoordinate=20` `minCoordinate=-20` |
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| 115 | [Area of Circle given center and a point on circle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_circle_given_center_and_point.py) | Area of circle with center $(-8,9)$ and passing through $(-4.0, 9.0)$ is | $50.27$ | area_of_circle_given_center_and_point | `maxCoordinate = 10` `maxRadius=10` |
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| 117 | [Volume of Hemisphere](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_hemisphere.py) | Volume of hemisphere with radius $25 m =$ | $32724.923 m^3$ | volume_hemisphere | `maxRadius=100` |
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| 122 | [Volume of pyramid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_pyramid.py) | Volume of pyramid with base length $= 3 m$, base width $= 1 m$ and height $= 2 m$ is | $2.0 m^3$ | volume_pyramid | `maxLength=20` `maxWidth=20` `maxHeight=50` `unit='m'` |
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| 123 | [Surface area of pyramid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/surface_area_pyramid.py) | Surface area of pyramid with base length $= 6m$, base width $= 6m$, and height $= 4m$ is | $96 m^2$ | surface_area_pyramid | `unit='m'` |
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| 125 | [Complementary and Supplementary Angle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/complementary_and_supplementary_angle.py) | The supplementary angle of 48 = | 132 | complementary_and_supplementary_angle | `maxSupp=180` `maxComp=90` |
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|
## misc
|
|
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|
|
|------|-------|-----------------|------------------|---------------|--------|
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| 9 | [LCM (Least Common Multiple)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/lcm.py) | LCM of $11$ and $12 =$ | $132$ | lcm | `maxVal=20` |
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| 10 | [GCD (Greatest Common Denominator)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/gcd.py) | GCD of $20$ and $9 = $ | $1$ | gcd | `maxVal=20` |
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| 27 | [Prime Factorisation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/prime_factors.py) | Find prime factors of $84$ | $2, 2, 3, 7$ | prime_factors | `minVal=1` `maxVal=200` |
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| 40 | [Common Factors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/common_factors.py) | Common Factors of $7$ and $44 = $ | $[1]$ | common_factors | `maxVal=100` |
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| 51 | [HCF (Highest Common Factor)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/hcf.py) | HCF of $13$ and $5 = $ | $1$ | hcf | `maxVal=20` |
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| 55 | [Comparing surds](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/surds_comparison.py) | Fill in the blanks $23^{\frac{1}{9}}$ _ $63^{\frac{1}{2}}$ | $<$ | surds_comparison | `maxValue=100` `maxRoot=10` |
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| 63 | [Profit or Loss Percent](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/profit_loss_percent.py) | Profit percent when $CP = 145$ and $SP = 782$ is: | $439.31$ | profit_loss_percent | `maxCP=1000` `maxSP=1000` |
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| 66 | [Geometric Progression](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/geometric_progression.py) | For the given GP $[3, 36, 432, 5184, 62208, 746496]$. Find the value of a common ratio, 10th term value, sum upto 10th term | The value of a is $3$, common ratio is $12$ , 10th term is $15479341056$, sum upto 10th term is $16886553879.0$ | geometric_progression | `number_values=6` `min_value=2` `max_value=12` `n_term=7` `sum_term=5` |
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| 67 | [Geometric Mean of N Numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/geometric_mean.py) | Geometric mean of $3$ numbers $[15, 90, 74] = $ | $46.4$ | geometric_mean | `maxValue=100` `maxCount=4` |
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| 68 | [Harmonic Mean of N Numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/harmonic_mean.py) | Harmonic mean of $4$ numbers $4, 94, 70, 14 = $ | $40.42123738481791$ | harmonic_mean | `maxValue=100` `maxNum=4` |
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| 69 | [Euclidian norm or L2 norm of a vector](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/euclidian_norm.py) | Euclidian norm or L2 norm of the vector $[667.6348977529038, 679.4272834518646, 255.59424823283462, 642.7158651607829, 619.0578738657584, 693.3434890856785, 107.39417747607006]$ is: | $1503.75$ | euclidian_norm | `maxEltAmt=20` |
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| 81 | [Celsius To Fahrenheit](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/celsius_to_fahrenheit.py) | Convert $2$ degrees Celsius to degrees Fahrenheit | $35.6$ | celsius_to_fahrenheit | `maxTemp=100` |
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| 82 | [AP Term Calculation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/arithmetic_progression_term.py) | Find term number $67$ of the AP series: $56, 133, 210 ... $ | $5138$ | arithmetic_progression_term | `maxd=100` `maxa=100` `maxn=100` |
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| 83 | [AP Sum Calculation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/arithmetic_progression_sum.py) | Find the sum of first $54$ terms of the AP series: $83, 42, 1 ... $ | $-54189.0$ | arithmetic_progression_sum | `maxd=100` `maxa=100` `maxn=100` |
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| 85 | [Converts decimal to Roman Numerals](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/decimal_to_roman_numerals.py) | The number $0$ in Roman Numerals is: | $MMCCCLVI$ | decimal_to_roman_numerals | `maxDecimal=4000` |
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| 92 | [Complex To Polar Form](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/complex_to_polar.py) | $17.12(2.0\theta + i17.0\theta)$ | $1.45$ | complex_to_polar | `minRealImaginaryNum=-20, maxRealImaginaryNum=20` |
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| 93 | [Union,Intersection,Difference of Two Sets](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/set_operation.py) | Given the two sets $a={2, 6, 8, 9, 10}$, $b={8, 10, 4}. Find the Union, intersection, a-b, b-a, and symmetric difference | Union is ${2, 4, 6, 8, 9, 10}$. Intersection is ${8, 10}$, a-b is ${9, 2, 6}$, b-a is ${4}$. Symmetric difference is ${2, 4, 6, 9}$. | set_operation | `minval=3` `maxval=7` `n_a=4` `n_b=5` |
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| 94 | [Base Conversion](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/base_conversion.py) | Convert $56371$ from base $10$ to base $5$. | $3300441$ | base_conversion | `maxNum=60000` `maxBase=16` |
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| 98 | [Quotient of Powers with Same Base](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/quotient_of_power_same_base.py) | The Quotient of $17^{1}$ and $17^{9} = $17^{1-9} = 17^{-8}$ | $1.4335360832968505e-10$ | quotient_of_power_same_base | `maxBase=50` `maxPower=10` |
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| 99 | [Quotient of Powers with Same Power](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/quotient_of_power_same_power.py) | The Quotient of $33^{4}$ and $23^{4} = (33/23)^4 = 1.434782608695652^{4}$ | $4.237838629793346$ | quotient_of_power_same_power | `maxBase=50` `maxPower=10` |
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| 101 | [Leap Year or Not](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/is_leap_year.py) | Is 1906 a leap year? | 1906 is not a leap year | is_leap_year | `minNumber=1900` `maxNumber=2099` |
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| 102 | [Minute to Hour conversion](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/minutes_to_hours.py) | Convert $381$ minutes to hours & minutes | $6$ hours and $21$ minutes | minutes_to_hours | `maxMinutes=999` |
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| 106 | [signum function](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/signum_function.py) | signum of 985 is = | $1$ | signum_function | `min=-999` `max=999` |
|
|
| 109 | [Binomial distribution](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/binomial_distribution.py) | A manufacturer of metal pistons finds that, on average, $34.46$% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of $10$ pistons will contain no more than $8$ rejected pistons? | $99.95$ | binomial_distribution | `` |
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| 116 | [Factors of a number](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/factors.py) | Factors of $949 = $ | $[1, 13, 73, 949]$ | factors | `maxVal=1000` |
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| 121 | [Product of scientific notations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/product_of_scientific_notations.py) | Product of scientific notations $7.83 \times 10^{-39}$ and $6.12 \times 10^{-95} = $ | $4.79 \times 10^{-133}$ | product_of_scientific_notations | `minExpVal=-100` `maxExpVal=100` |
|
|
## statistics
|
|
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|
|
|------|-------|-----------------|------------------|---------------|--------|
|
|
| 30 | [Combinations of Objects](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/combinations.py) | Find the number of combinations from $14$ objects picked $6$ at a time. | $3003$ | combinations | `maxlength=20` |
|
|
| 42 | [Permutations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/permutation.py) | Number of Permutations from $17$ objects picked $6$ at a time is: | $8910720$ | permutation | `maxlength=20` |
|
|
| 52 | [Probability of a certain sum appearing on faces of dice](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/dice_sum_probability.py) | If $3$ dice are rolled at the same time, the probability of getting a sum of $3 =$ | \frac{1}{216} | dice_sum_probability | `maxDice=3` |
|
|
| 54 | [Confidence interval For sample S](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/confidence_interval.py) | The confidence interval for sample $[226, 260, 221, 245, 282, 274, 207, 299, 257, 211, 233, 239, 206, 208, 242, 224, 265, 287, 230, 276, 256, 237, 215, 291, 216, 251, 255, 229, 279, 275, 210, 203, 220, 292]$ with $95$% confidence is | $(254.41804694839914, 235.052541286895)$ | confidence_interval | `` |
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|
| 59 | [Mean,Standard Deviation,Variance](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/data_summary.py) | Find the mean,standard deviation and variance for the data $48, 38, 10, 5, 24, 46, 50, 17, 20, 13, 17, 14, 5, 20, 34$ | The Mean is $24.066666666666666$, Standard Deviation is $220.0622222222222$, Variance is $14.834494336586678$ | data_summary | `number_values=15` `minval=5` `maxval=50` |
|
|
| 76 | [Mean and Median](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/mean_median.py) | Given the series of numbers $[6, 30, 32, 39, 42, 65, 72, 80, 84, 85]$. Find the arithmatic mean and mdian of the series | Arithmetic mean of the series is $53.5$ and Arithmetic median of this series is $53.5$ | mean_median | `maxlen=10` |
|
|
| 107 | [Conditional Probability](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/conditional_probability.py) | Someone tested positive for a nasty disease which only $1.26\%$ of the population have. Test sensitivity (true positive) is equal to $SN=93.71$% whereas test specificity (true negative) $SP=90.62\%$. What is the probability that this guy really has that disease? | $11.31$% | conditional_probability | `` |
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