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## algebra ## algebra
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------| |------|-------|-----------------|------------------|---------------|--------|
| 11 | [Basic Algebra](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/basic_algebra.py) | 10x + 4 = 10 | 3/5 | basic_algebra | `maxVariable=10` |
| 12 | [Logarithm](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/log.py) | log3(6561) | 8 | log | `maxBase=3` `maxVal=8` |
| 17 | [Integer Multiplication with 2x2 Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_int_to_22_matrix.py) | 7 * [[6, 0], [10, 0]] = | [[42,0],[70,0]] | multiply_int_to_22_matrix | `maxMatrixVal=10` `maxRes=100` |
| 20 | [Midpoint of the two point](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/midpoint_of_two_points.py) | (-1,11),(-14,15)= | (-7.5,13.0) | midpoint_of_two_points | `maxValue=20` |
| 21 | [Factoring Quadratic](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/factoring.py) | x^2-4x-5 | (x-5)(x+1) | factoring | `range_x1=10` `range_x2=10` |
| 23 | [Solve a System of Equations in R^2](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/system_of_equations.py) | -8x + 9y = -32, -2x - 3y = 34 | x = -5, y = -8 | system_of_equations | `range_x=10` `range_y=10` `coeff_mult_range=10` |
| 24 | [Distance between 2 points](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/distance_two_points.py) | Find the distance between (-6, -4) and (13, -13) | sqrt(442) | distance_two_points | `maxValXY=20` `minValXY=-20` |
| 26 | [Linear Equations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/linear_equations.py) | 4x + 17y = -187, 20x + -9y = 99 | x = 0, y = -11 | linear_equations | `n=2` `varRange=20` `coeffRange=20` |
| 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 = -3x + 8 and y = -5x + 7 | (-1/2, 19/2) | intersection_of_two_lines | `minM=-10` `maxM=10` `minB=-10` `maxB=10` `minDenominator=1` `maxDenominator=6` |
| 43 | [Cross Product of 2 Vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/vector_cross.py) | [-17, 5, -14] X [-7, 10, 12] = | [200, 302, -135] | vector_cross | `minVal=-20` `maxVal=20` |
| 45 | [Simple Interest](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/simple_interest.py) | Simple interest for a principle amount of 7064 dollars, 8% rate of interest and for a time period of 4 years is = | 2260.48 | simple_interest | `maxPrinciple=10000` `maxRate=10` `maxTime=10` |
| 46 | [Multiplication of two matrices](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/matrix_multiplication.py) | Multiply<table><tr><td>-9</td><td>6</td><td>-3</td></tr><tr><td>-3</td><td>0</td><td>10</td></tr></table>and<table><tr><td>-3</td><td>-4</td></tr><tr><td>-7</td><td>2</td></tr><tr><td>10</td><td>-3</td></tr></table> | <table><tr><td>-45</td><td>57</td></tr><tr><td>109</td><td>-18</td></tr></table> | matrix_multiplication | `maxVal=100` `max_dim=10` |
| 50 | [Quadratic Equation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/quadratic_equation.py) | Zeros of the Quadratic Equation 34x^2+110x+49=0 | [-0.53, -2.7] | quadratic_equation | `maxVal=100` |
| 65 | [Multiplication of 2 complex numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/multiply_complex_numbers.py) | (-13-14j) * (-18-15j) = | (24+447j) | multiply_complex_numbers | `minRealImaginaryNum=-20` `maxRealImaginaryNum=20` |
| 72 | [Dot Product of 2 Vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/vector_dot.py) | [11, 15, 2] . [-12, 6, 16] = | -10 | vector_dot | `minVal=-20` `maxVal=20` |
| 74 | [Inverse of a Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/invert_matrix.py) | Inverse of Matrix Matrix([[48, 56, 11], [2, 79, 45], [81, 43, 55]]) is: | Matrix([[2410/244197, -869/81399, 1651/244197], [3535/244197, 583/81399, -2138/244197], [-6313/244197, 824/81399, 3680/244197]]) | invert_matrix | `SquareMatrixDimension=3` `MaxMatrixElement=99` `OnlyIntegerElementsInInvertedMatrix=False` |
| 77 | [Determinant to 2x2 Matrix](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/int_matrix_22_determinant.py) | Det([[48, 42], [83, 76]]) = | 162 | int_matrix_22_determinant | `maxMatrixVal=100` |
| 78 | [Compound Interest](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/compound_interest.py) | Compound interest for a principle amount of 5893 dollars, 3% rate of interest and for a time period of 7 year is = | 7247.65 | compound_interest | `maxPrinciple=10000` `maxRate=10` `maxTime=10` |
| 100 | [complex Quadratic Equation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/complex_quadratic.py) | Find the roots of given Quadratic Equation x^2 + 8x + 5 = 0 | simplified solution : ((-0.683, -7.317)), generalized solution : ((-8 + sqrt(44))/2*1, (-8 - sqrt(44))/2*1) | complex_quadratic | `prob_type=0` `max_range=10` |
| 105 | [Combine Like terms](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/combine_like_terms.py) | 8x^2 + 5x^4 + 1x^1 + 4x^7 + 7x^1 + 2x^6 + 3x^5 + 1x^1 + 4x^5 | 9x^1 + 8x^2 + 5x^4 + 7x^5 + 2x^6 + 4x^7 | combine_like_terms | `maxCoef=10` `maxExp=20` `maxTerms=10` |
| 111 | [Expanding Factored Binomial](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/algebra/expanding.py) | (-6x+6)(-1x+2) | 6*x^2-18*x+12 | expanding | `range_x1=10` `range_x2=10` `range_a=10` `range_b=10` |
## basic_math ## basic_math
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------| |------|-------|-----------------|------------------|---------------|--------|
| 0 | [Addition](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/addition.py) | 21+45= | 66 | addition | `maxSum=99` `maxAddend=50` |
| 1 | [Subtraction](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/subtraction.py) | 52-9= | 43 | subtraction | `maxMinuend=99` `maxDiff=99` |
| 2 | [Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/multiplication.py) | 1*4= | 4 | multiplication | `maxMulti=12` |
| 3 | [Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/division.py) | 144/9= | 16 | division | `maxA=25` `maxB=25` |
| 6 | [Square Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square_root.py) | sqrt(81)= | 9 | square_root | `minNo=1` `maxNo=12` |
| 8 | [Square](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/square.py) | 10^2= | 100 | square | `maxSquareNum=20` |
| 13 | [Complex Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/complex_division.py) | 91/92= | 0.99 | complex_division | `maxRes=99` `maxDivid=99` |
| 16 | [Fraction Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/divide_fractions.py) | (8/2)/(2/8) | 16 | divide_fractions | `maxVal=10` |
| 28 | [Fraction Multiplication](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/fraction_multiplication.py) | (2/4)*(10/3) | 5/3 | fraction_multiplication | `maxVal=10` |
| 31 | [Factorial](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/factorial.py) | 4! = | 24 | factorial | `maxInput=6` |
| 44 | [Compare Fractions](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/compare_fractions.py) | Which symbol represents the comparison between 2/1 and 8/9? | > | compare_fractions | `maxVal=10` |
| 47 | [Cube Root](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/cube_root.py) | What is the cube root of 87 up to 2 decimal places? | 4.43 | cube_root | `minNo=1` `maxNo=1000` |
| 53 | [Exponentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/exponentiation.py) | 1^1 = | 1 | exponentiation | `maxBase=20` `maxExpo=10` |
| 71 | [Absolute difference between two numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/absolute_difference.py) | |-66--25|= | 41 | absolute_difference | `maxA=100` `maxB=100` |
| 80 | [Percentage of a number](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/percentage.py) | What is 85% of 55? | 46.75 | percentage | `maxValue=99` `maxpercentage=99` |
| 90 | [isprime](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/is_prime.py) | Is 59 prime? | Yes | is_prime | `max_num=100` |
| 97 | [Power of Powers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/basic_math/power_of_powers.py) | Simplify 42^3^5= | 42^15 | power_of_powers | `maxBase=50` `maxPower=10` |
## calculus ## calculus
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------| |------|-------|-----------------|------------------|---------------|--------|
| 7 | [Power Rule Differentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/power_rule_differentiation.py) | 5x^3 | 15x^2 | power_rule_differentiation | `maxCoef=10` `maxExp=10` `maxTerms=5` |
| 48 | [Power Rule Integration](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/power_rule_integration.py) | 1x^3 + 10x^7 + 10x^1 + 2x^7 + 6x^10 | (1/3)x^4 + (10/7)x^8 + (10/1)x^2 + (2/7)x^8 + (6/10)x^11 + c | power_rule_integration | `maxCoef=10` `maxExp=10` `maxTerms=5` |
| 88 | [Differentiation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/differentiation.py) | differentiate w.r.t x : d(cos(x)+7*x^(-2))/dx | -sin(x) - 14/x^3 | differentiation | `diff_lvl=2` |
| 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 63x^2 + 1x + 68 is = | 89.5 | definite_integral | `max_coeff=100` |
| 110 | [Stationary Points](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/calculus/stationary_points.py) | f(x)=5*x^3 + x^2 + 5*x + 1 | | stationary_points | `maxExp=3` `maxCoef=10` |
## computer_science ## computer_science
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------| |------|-------|-----------------|------------------|---------------|--------|
| 4 | [Binary Complement 1s](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_complement_1s.py) | 01100001= | 10011110 | binary_complement_1s | `maxDigits=10` |
| 5 | [Modulo Division](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/modulo_division.py) | 94%96= | 94 | modulo_division | `maxRes=99` `maxModulo=99` |
| 14 | [Decimal to Binary](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_binary.py) | Binary of 65= | 1000001 | decimal_to_binary | `max_dec=99` |
| 15 | [Binary to Decimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_decimal.py) | 1100 | 12 | binary_to_decimal | `max_dig=10` |
| 56 | [Fibonacci Series](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/fibonacci_series.py) | 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 | `minNo=1` |
| 62 | [nth Fibonacci number](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/nth_fibonacci_number.py) | What is the 85th Fibonacci number? | 259695496911123328 | nth_fibonacci_number | `maxN=100` |
| 64 | [Binary to Hexidecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_to_hex.py) | 0 | 0x0 | binary_to_hex | `max_dig=10` |
| 73 | [Binary 2's Complement](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/binary_2s_complement.py) | 2's complement of 111011 = | 101 | binary_2s_complement | `maxDigits=10` |
| 79 | [Decimal to Hexadecimal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_hexadeci.py) | Binary of 398= | 0x18e | decimal_to_hexadeci | `max_dec=1000` |
| 84 | [Converts decimal to octal](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/computer_science/decimal_to_octal.py) | The decimal number 3316 in Octal is: | 0o6364 | decimal_to_octal | `maxDecimal=4096` |
| 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 1 is = | 5768 | bcd_to_decimal | `maxNumber=10000` |
| 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 8538 is = | 21510 | decimal_to_bcd | `maxNumber=10000` |
## geometry ## geometry
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------| |------|-------|-----------------|------------------|---------------|--------|
| 18 | [Area of Triangle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_triangle.py) | Area of triangle with side lengths: 15 19 6 = | 37.416573867739416 | area_of_triangle | `maxA=20` `maxB=20` `maxC=20` |
| 19 | [Triangle exists check](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/valid_triangle.py) | Does triangle with sides 17, 30 and 50 exist? | No | valid_triangle | `maxSideLength=50` |
| 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 86 and 40 = | 54 | third_angle_of_triangle | `maxAngle=89` |
| 25 | [Pythagorean Theorem](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/pythagorean_theorem.py) | The hypotenuse of a right triangle given the other two lengths 7 and 13 = | 14.76 | pythagorean_theorem | `maxLength=20` |
| 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 5 sides | 108.0 | angle_regular_polygon | `minVal=3` `maxVal=20` |
| 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 = 14m is | 1176 m^2 | surface_area_cube | `maxSide=20` `unit='m'` |
| 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 = 8m, 20m, 7m is | 712 m^2 | surface_area_cuboid | `maxSide=20` `unit='m'` |
| 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 = 45m and radius = 10m is | 3455 m^2 | surface_area_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'` |
| 35 | [Volum of Cube](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cube.py) | Volume of cube with side = 19m is | 6859 m^3 | volume_cube | `maxSide=20` `unit='m'` |
| 36 | [Volume of Cuboid](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cuboid.py) | Volume of cuboid with sides = 6m, 18m, 6m is | 648 m^3 | volume_cuboid | `maxSide=20` `unit='m'` |
| 37 | [Volume of cylinder](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cylinder.py) | Volume of cylinder with height = 6m and radius = 19m is | 6804 m^3 | volume_cylinder | `maxRadius=20` `maxHeight=50` `unit='m'` |
| 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 = 23m and radius = 6m is | 561 m^2 | surface_area_cone | `maxRadius=20` `maxHeight=50` `unit='m'` |
| 39 | [Volume of cone](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_cone.py) | Volume of cone with height = 28m and radius = 1m is | 29 m^3 | volume_cone | `maxRadius=20` `maxHeight=50` `unit='m'` |
| 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 34 , 28, 124 = | 174 | fourth_angle_of_quadrilateral | `maxAngle=180` |
| 57 | [Trigonometric Values](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/basic_trigonometry.py) | What is tan(30)? | 1/√3 | basic_trigonometry | `angles=[0, 30, 45, 60, 90]` `functions=['sin', 'cos', 'tan']` |
| 58 | [Sum of Angles of Polygon](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/sum_of_polygon_angles.py) | Sum of angles of polygon with 4 sides = | 360 | sum_of_polygon_angles | `maxSides=12` |
| 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 = 10m is | 1256.6370614359173 m^2 | surface_area_sphere | `maxSide=20` `unit='m'` |
| 61 | [Volume of Sphere](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/volume_sphere.py) | Volume of sphere with radius 88 m = | 2854543.2384361913 m^3 | volume_sphere | `maxRadius=100` |
| 70 | [Angle between 2 vectors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/angle_btw_vectors.py) | angle between the vectors [445.87, 643.14, 725.82, 487.36, 253.17, 866.17, 410.55, 67.88, 225.36, 525.53, 635.68, 918.19, 52.39] and [203.15, 873.75, 556.81, 879.48, 909.96, 767.26, 845.65, 785.81, 745.86, 876.93, 877.72, 619.64, 905.23] is: | 0.61 radians | angle_btw_vectors | `maxEltAmt=20` |
| 75 | [Area of a Sector](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/sector_area.py) | Given radius, 30 and angle, 283. Find the area of the sector. | Area of sector = 2222.67680 | sector_area | `maxRadius=49` `maxAngle=359` |
| 86 | [Degrees to Radians](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/degree_to_rad.py) | Angle 110 in radians is = | 1.92 | degree_to_rad | `max_deg=360` |
| 87 | [Radians to Degrees](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/radian_to_deg.py) | Angle 3 in degrees is = | 171.89 | radian_to_deg | `max_rad=3` |
| 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, 36 and height, 86? | CSA of cylinder = 19452.74 | curved_surface_area_cylinder | `maxRadius=49` `maxHeight=99` |
| 96 | [Perimeter of Polygons](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/perimeter_of_polygons.py) | The perimeter of a 9 sided polygon with lengths of [49, 15, 63, 56, 87, 59, 13, 35, 84]cm is: | 461 | perimeter_of_polygons | `maxSides=12` `maxLength=120` |
| 104 | [Circumference](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/circumference.py) | Circumference of circle with radius 39 | 245.04422698000386 | circumference | `maxRadius=100` |
| 108 | [Arc length of Angle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/arc_length.py) | Given radius, 24 and angle, 323. Find the arc length of the angle. | Arc length of the angle = 135.29792 | arc_length | `maxRadius=49` `maxAngle=359` |
| 112 | [Area of Circle](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/geometry/area_of_circle.py) | Area of circle with radius 79 | 19614.571428571428 | area_of_circle | `maxRadius=100` |
## misc ## misc
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | Id | Skill | Example problem | Example Solution | Function Name | Kwargs |
|------|-------|-----------------|------------------|---------------|--------| |------|-------|-----------------|------------------|---------------|--------|
| 9 | [LCM (Least Common Multiple)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/lcm.py) | LCM of 3 and 12 = | 12 | lcm | `maxVal=20` |
| 10 | [GCD (Greatest Common Denominator)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/gcd.py) | GCD of 12 and 6 = | 6 | gcd | `maxVal=20` |
| 27 | [Prime Factorisation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/prime_factors.py) | Find prime factors of 55 | [5, 11] | prime_factors | `minVal=1` `maxVal=200` |
| 40 | [Common Factors](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/common_factors.py) | Common Factors of 42 and 55 = | [1] | common_factors | `maxVal=100` |
| 51 | [HCF (Highest Common Factor)](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/hcf.py) | HCF of 18 and 15 = | 3 | hcf | `maxVal=20` |
| 55 | [Comparing surds](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/surds_comparison.py) | Fill in the blanks 94^(1/2) _ 76^(1/8) | > | surds_comparison | `maxValue=100` `maxRoot=10` |
| 63 | [Profit or Loss Percent](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/profit_loss_percent.py) | Loss percent when CP = 568 and SP = 428 is: | 24.647887323943664 | profit_loss_percent | `maxCP=1000` `maxSP=1000` |
| 66 | [Geometric Progression](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/geometric_progression.py) | For the given GP [5, 40, 320, 2560, 20480, 163840] ,Find the value of a,common ratio,6th term value, sum upto 6th term | The value of a is 5, common ratio is 8 , 6th term is 163840 , sum upto 6th term is 187245.0 | geometric_progression | `number_values=6` `min_value=2` `max_value=12` `n_term=7` `sum_term=5` |
| 67 | [Geometric Mean of N Numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/geometric_mean.py) | Geometric mean of 3 numbers 17 , 96 and 65 = | (17*96*65)^(1/3) = 47.33813788872301 | geometric_mean | `maxValue=100` `maxNum=4` |
| 68 | [Harmonic Mean of N Numbers](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/harmonic_mean.py) | Harmonic mean of 3 numbers 18 , 16 and 15 = | 3/((1/18) + (1/16) + (1/15)) = 16.240601503759397 | harmonic_mean | `maxValue=100` `maxNum=4` |
| 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[5.635634088805297, 25.010440136540968, 396.32418220000267, 107.53011787670164, 545.6874361227574, 184.6826627723569, 174.06643859373185, 464.3440136677789, 7.224673708081664, 8.876015680626349, 492.79488489985056, 829.9627437839996, 114.95586474177044, 158.35106542211696, 957.6000447259205, 232.33194190040297, 458.35579555527363, 362.21539076262013, 811.1637217594521, 912.2055239005433] is: | 2125.927366092163 | euclidian_norm | `maxEltAmt=20` |
| 81 | [Celsius To Fahrenheit](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/celsius_to_fahrenheit.py) | Convert 68 degrees Celsius to degrees Fahrenheit = | 154.4 | celsius_to_fahrenheit | `maxTemp=100` |
| 82 | [AP Term Calculation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/arithmetic_progression_term.py) | Find the term number 10 of the AP series: -71, -56, -41 ... | 64 | arithmetic_progression_term | `maxd=100` `maxa=100` `maxn=100` |
| 83 | [AP Sum Calculation](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/arithmetic_progression_sum.py) | Find the sum of first 23 terms of the AP series: -37, 30, 97 ... | 16100.0 | arithmetic_progression_sum | `maxd=100` `maxa=100` `maxn=100` |
| 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: | MCDX | decimal_to_roman_numerals | `maxDecimal=4000` |
| 92 | [Complex To Polar Form](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/complex_to_polar.py) | 14.87(-10.0theta + i11.0theta) | 2.31 | complex_to_polar | `minRealImaginaryNum=-20, maxRealImaginaryNum=20` |
| 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={8, 6, 7} ,b={3, 6, 7, 8, 10}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {3, 6, 7, 8, 10},Intersection is {8, 6, 7}, a-b is set(),b-a is {10, 3}, Symmetric difference is {3, 10} | set_operation | `minval=3` `maxval=7` `n_a=4` `n_b=5` |
| 94 | [Base Conversion](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/base_conversion.py) | Convert 17284 from base 12 to base 6. | 413444 | base_conversion | `maxNum=60000` `maxBase=16` |
| 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 30^9 and 30^8 = 30^(9-8) = 30^1 | 30 | quotient_of_power_same_base | `maxBase=50` `maxPower=10` |
| 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 1^6 and 18^6 = (1/18)^6 = 0.05555555555555555^6 | 2.9401194111858127e-08 | quotient_of_power_same_power | `maxBase=50` `maxPower=10` |
| 101 | [Leap Year or Not](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/is_leap_year.py) | Year 2024 | is a leap year | is_leap_year | `minNumber=1900` `maxNumber=2099` |
| 102 | [Minute to Hour conversion](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/minutes_to_hours.py) | Convert 357 minutes to Hours & Minutes | 5 hours and 57 minutes | minutes_to_hours | `maxMinutes=999` |
| 106 | [signum function](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/misc/signum_function.py) | signum of 608 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, 40.25% 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 8 rejected pistons? | 93.94 | binomial_distribution | `` |
## statistics ## statistics
| Id | Skill | Example problem | Example Solution | Function Name | Kwargs | | 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) | Number of combinations from 20 objects picked 1 at a time | 20 | combinations | `maxlength=20` |
| 42 | [Permutations](https://github.com/lukew3/mathgenerator/blob/main/mathgenerator/funcs/statistics/permutation.py) | Number of Permutations from 17 objects picked 0 at a time = | 1 | 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 8 = | 21/216 | 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 [216, 210, 293, 229, 272, 227, 262, 252, 281, 284, 258, 275, 285, 261, 283, 289, 288, 212, 282, 254, 221, 278, 271, 297, 225, 251, 222, 238, 246, 213, 215, 280, 263, 236] with 95% confidence is | (264.22307058301857, 245.7181058875697) | confidence_interval | `` |
| 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[13, 8, 13, 48, 10, 27, 46, 21, 16, 46, 26, 41, 8, 27, 39] | The Mean is 25.933333333333334 , Standard Deviation is 203.12888888888887, Variance is 14.252329244333673 | 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 [10, 22, 36, 42, 45, 62, 72, 78, 86, 93]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 54.6 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 1.55% of population have. Test sensitivity (true positive) is equal to SN= 97.42% whereas test specificity (true negative) SP= 91.78%. What is the probability that this guy really has that disease? | 15.73% | conditional_probability | `` |

1
mathgenerator/funcs/geometry/__init__.py
View File

@@ -9,6 +9,7 @@ from .basic_trigonometry import *
from .circumference import * from .circumference import *
from .curved_surface_area_cylinder import * from .curved_surface_area_cylinder import *
from .degree_to_rad import * from .degree_to_rad import *
from .equation_of_line_from_two_points import *
from .fourth_angle_of_quadrilateral import * from .fourth_angle_of_quadrilateral import *
from .perimeter_of_polygons import * from .perimeter_of_polygons import *
from .pythagorean_theorem import * from .pythagorean_theorem import *

50
mathgenerator/funcs/geometry/equation_of_line_from_two_points.py Normal file
View File

@@ -0,0 +1,50 @@
from .__init__ import *
def gen_func(maxCoordinate=20, minCoordinate=-20, format='string'):
def greatest_common_divisor(num1,num2):
if num2==0:
return num1
else:
return greatest_common_divisor(num2 , num1%num2)
x1 = random.randint(minCoordinate, maxCoordinate)
x2 = random.randint(minCoordinate, maxCoordinate)
y1 = random.randint(minCoordinate, maxCoordinate)
y2 = random.randint(minCoordinate, maxCoordinate)
coeff_y = (x2-x1)
coeff_x = (y2-y1)
constant = y2*coeff_y - x2*coeff_x
gcd = greatest_common_divisor(abs(coeff_x), abs(coeff_y))
if gcd !=1:
if coeff_y > 0: coeff_y //= gcd
if coeff_x > 0: coeff_x //= gcd
if constant > 0: constant //= gcd
if coeff_y < 0: coeff_y = -(-coeff_y//gcd)
if coeff_x < 0: coeff_x = -(-coeff_x//gcd)
if constant < 0: constant = -(-constant//gcd)
if coeff_y < 0 :
coeff_y = -(coeff_y)
coeff_x = -(coeff_x)
constant = -(constant)
if format == 'string':
problem = f"What is the equation of the line between points ({x1},{y1}) and ({x2},{y2}) in slope-intercept form?"
if constant > 0:
solution = str(coeff_y)+"y = " + str(coeff_x)+ "x + " + str(constant)
else:
solution = str(coeff_y)+"y = " + str(coeff_x)+ "x - " + str(-constant)
return problem, solution
elif format == 'latex':
return 'Latex unavailable'
else:
return x1, x2, y1, y2, coeff_x, coeff_y, constant
equation_of_line_from_two_points = Generator(
"Equation of line from two points", <id>, gen_func,
["maxCoordinate=20", "minCoordinate=-20"])