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## algebra ## algebra
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 11 | Basic Algebra | 10x + 5 = 5 | 0 | basic_algebra | | 11 | Basic Algebra | 5x + 10 = 10 | 0 | basic_algebra |
| 12 | Logarithm | log3(3) | 1 | log | | 12 | Logarithm | log2(4) | 2 | log |
| 17 | Integer Multiplication with 2x2 Matrix | 8 * [[10, 5], [3, 9]] = | [[80,40],[24,72]] | multiply_int_to_22_matrix | | 17 | Integer Multiplication with 2x2 Matrix | 12 * [[8, 7], [2, 0]] = | [[96,84],[24,0]] | multiply_int_to_22_matrix |
| 20 | Midpoint of the two point | (-14,1),(-2,2)= | (-8.0,1.5) | midpoint_of_two_points | | 20 | Midpoint of the two point | (10,9),(1,13)= | (5.5,11.0) | midpoint_of_two_points |
| 21 | Factoring Quadratic | x^2-2x-15 | (x-5)(x+3) | factoring | | 21 | Factoring Quadratic | x^2+3x-4 | (x+4)(x-1) | factoring |
| 23 | Solve a System of Equations in R^2 | -8x - 3y = -31, 4x - 6y = 38 | x = 5, y = -3 | system_of_equations | | 23 | Solve a System of Equations in R^2 | 5x - 5y = 20, -4x - 7y = -38 | x = 6, y = 2 | system_of_equations |
| 24 | Distance between 2 points | Find the distance between (-4, -6) and (-4, 15) | sqrt(441) | distance_two_points | | 24 | Distance between 2 points | Find the distance between (12, 2) and (16, 13) | sqrt(137) | distance_two_points |
| 26 | Linear Equations | 8x + 9y = -202, 5x + -7y = 0 | x = -14, y = -10 | linear_equations | | 26 | Linear Equations | 19x + -19y = -494, -12x + -2y = 200 | x = -18, y = 8 | linear_equations |
| 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 7/2x + 3 and y = 2/5x + 10 | (70/31, 338/31) | intersection_of_two_lines | | 41 | Intersection of Two Lines | Find the point of intersection of the two lines: y = 4x + 5 and y = -5/6x - 4 | (-54/29, -71/29) | intersection_of_two_lines |
| 43 | Cross Product of 2 Vectors | [-18, 12, 1] X [-12, -19, 1] = | [31, 6, 486] | vector_cross | | 43 | Cross Product of 2 Vectors | [7, 11, 10] X [12, 2, -15] = | [-185, 225, -118] | vector_cross |
| 45 | Simple Interest | Simple interest for a principle amount of 4200 dollars, 5% rate of interest and for a time period of 8 years is = | 1680.0 | simple_interest | | 45 | Simple Interest | Simple interest for a principle amount of 5927 dollars, 2% rate of interest and for a time period of 5 years is = | 592.7 | simple_interest |
| 46 | Multiplication of two matrices | Multiply<table><tr><td>-8</td><td>7</td></tr><tr><td>0</td><td>-5</td></tr><tr><td>-3</td><td>0</td></tr><tr><td>7</td><td>2</td></tr></table>and<table><tr><td>-7</td><td>-4</td></tr><tr><td>6</td><td>-4</td></tr></table> | <table><tr><td>98</td><td>4</td></tr><tr><td>-30</td><td>20</td></tr><tr><td>21</td><td>12</td></tr><tr><td>-37</td><td>-36</td></tr></table> | matrix_multiplication | | 46 | Multiplication of two matrices | Multiply<table><tr><td>4</td><td>-5</td><td>6</td><td>2</td></tr><tr><td>0</td><td>10</td><td>7</td><td>-3</td></tr><tr><td>-6</td><td>-7</td><td>-4</td><td>-1</td></tr></table>and<table><tr><td>6</td><td>-7</td><td>8</td><td>-9</td></tr><tr><td>-7</td><td>-6</td><td>7</td><td>-3</td></tr><tr><td>10</td><td>0</td><td>6</td><td>2</td></tr><tr><td>-6</td><td>-4</td><td>-5</td><td>-1</td></tr></table> | <table><tr><td>107</td><td>-6</td><td>23</td><td>-11</td></tr><tr><td>18</td><td>-48</td><td>127</td><td>-13</td></tr><tr><td>-21</td><td>88</td><td>-116</td><td>68</td></tr></table> | matrix_multiplication |
| 50 | Quadratic Equation | Zeros of the Quadratic Equation 33x^2+199x+22=0 | [-0.11, -5.92] | quadratic_equation | | 50 | Quadratic Equation | Zeros of the Quadratic Equation 89x^2+190x+87=0 | [-0.67, -1.47] | quadratic_equation |
| 65 | Multiplication of 2 complex numbers | (-4-10j) * (4-18j) = | (-196+32j) | multiply_complex_numbers | | 65 | Multiplication of 2 complex numbers | (-15+15j) * 20j = | (-300-300j) | multiply_complex_numbers |
| 72 | Dot Product of 2 Vectors | [7, -2, 14] . [14, -17, -16] = | -92 | vector_dot | | 72 | Dot Product of 2 Vectors | [-2, 10, -10] . [16, -20, 3] = | -262 | vector_dot |
| 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[81, 23, 19], [73, 75, 49], [7, 71, 93]]) is: | Matrix([[874/55855, -79/22342, -149/111710], [-3223/111710, 370/11171, -1291/111710], [2329/111710, -559/22342, 1099/55855]]) | invert_matrix | | 74 | Inverse of a Matrix | Inverse of Matrix Matrix([[55, 61, 1], [28, 67, 9], [53, 91, 33]]) is: | Matrix([[696/24145, -961/24145, 241/24145], [-447/48290, 881/24145, -467/48290], [-1003/48290, -886/24145, 1977/48290]]) | invert_matrix |
| 77 | Determinant to 2x2 Matrix | Det([[9, 31], [5, 30]]) = | 115 | int_matrix_22_determinant | | 77 | Determinant to 2x2 Matrix | Det([[18, 97], [57, 84]]) = | -4017 | int_matrix_22_determinant |
| 78 | Compound Interest | Compound interest for a principle amount of 8699 dollars, 9% rate of interest and for a time period of 9 year is = | 18893.3 | compound_interest | | 78 | Compound Interest | Compound interest for a principle amount of 9310 dollars, 5% rate of interest and for a time period of 9 year is = | 14442.87 | compound_interest |
| 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 8x^2 + 8x + 1 = 0 | simplified solution : ((-0.146, -0.854)), generalized solution : ((-8 + sqrt(32))/2*8, (-8 - sqrt(32))/2*8) | complex_quadratic | | 100 | complex Quadratic Equation | Find the roots of given Quadratic Equation 9x^2 + 6x + 1 = 0 | simplified solution : ((-0.333, -0.333)), generalized solution : ((-6 + 0)/2*9, (-6 - 0)/2*9) | complex_quadratic |
| 105 | Combine Like terms | 6x^1 + 5x^1 + 2x^2 | 11x^1 + 2x^2 | combine_like_terms | | 105 | Combine Like terms | 6x^1 + 3x^1 + 9x^1 | 18x^1 | combine_like_terms |
| 111 | Expanding Factored Binomial | (3x-1)(+4x-7) | 12*x^2-25*x+7 | expanding | | 111 | Expanding Factored Binomial | (4x+8)(+10x-7) | 40*x^2+52*x-56 | expanding |
## basic_math ## basic_math
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 0 | Addition | 46+24= | 70 | addition | | 0 | Addition | 48+14= | 62 | addition |
| 1 | Subtraction | 17-10= | 7 | subtraction | | 1 | Subtraction | 88-49= | 39 | subtraction |
| 2 | Multiplication | 28*0= | 0 | multiplication | | 2 | Multiplication | 17*0= | 0 | multiplication |
| 3 | Division | 150/6= | 25 | division | | 3 | Division | 320/16= | 20.0 | division |
| 6 | Square Root | sqrt(144)= | 12 | square_root | | 6 | Square Root | sqrt(100)= | 10 | square_root |
| 8 | Square | 9^2= | 81 | square | | 8 | Square | 10^2= | 100 | square |
| 13 | Complex Division | 3/39= | 0.08 | complex_division | | 13 | Complex Division | 32/47= | 0.68 | complex_division |
| 16 | Fraction Division | (4/1)/(10/1) | 2/5 | divide_fractions | | 16 | Fraction Division | (9/7)/(6/5) | 15/14 | divide_fractions |
| 28 | Fraction Multiplication | (9/7)*(9/6) | 27/14 | fraction_multiplication | | 28 | Fraction Multiplication | (1/6)*(3/10) | 1/20 | fraction_multiplication |
| 31 | Factorial | 0! = | 1 | factorial | | 31 | Factorial | 2! = | 2 | factorial |
| 44 | Compare Fractions | Which symbol represents the comparison between 4/10 and 8/9? | < | compare_fractions | | 44 | Compare Fractions | Which symbol represents the comparison between 3/1 and 9/1? | < | compare_fractions |
| 47 | Cube Root | cuberoot of 685 upto 2 decimal places is: | 8.82 | cube_root | | 47 | Cube Root | cuberoot of 576 upto 2 decimal places is: | 8.32 | cube_root |
| 53 | Exponentiation | 2^7 = | 128 | exponentiation | | 53 | Exponentiation | 1^8 = | 1 | exponentiation |
| 71 | Absolute difference between two numbers | Absolute difference between numbers -43 and 99 = | 142 | absolute_difference | | 71 | Absolute difference between two numbers | Absolute difference between numbers -97 and 92 = | 189 | absolute_difference |
| 80 | Percentage of a number | What is 58% of 84? | Required percentage = 48.72% | percentage | | 80 | Percentage of a number | What is 74% of 3? | Required percentage = 2.22% | percentage |
| 90 | isprime | 32 | False | is_prime | | 90 | isprime | 31 | True | is_prime |
| 97 | Power of Powers | The 34^2^9 = | 34^18 | power_of_powers | | 97 | Power of Powers | The 20^9^7 = | 20^63 | power_of_powers |
## calculus ## calculus
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 7 | Power Rule Differentiation | 6x^10 + 4x^7 + 6x^4 + 2x^2 + 7x^8 | 60x^9 + 28x^6 + 24x^3 + 4x^1 + 56x^7 | power_rule_differentiation | | 7 | Power Rule Differentiation | 1x^1 + 1x^6 | 1x^0 + 6x^5 | power_rule_differentiation |
| 48 | Power Rule Integration | 1x^2 + 8x^8 | (1/2)x^3 + (8/8)x^9 + c | power_rule_integration | | 48 | Power Rule Integration | 8x^5 + 8x^9 + 4x^1 + 1x^8 + 8x^1 | (8/5)x^6 + (8/9)x^10 + (4/1)x^2 + (1/8)x^9 + (8/1)x^2 + c | power_rule_integration |
| 88 | Differentiation | differentiate w.r.t x : d(exp(x)+9*x^(-2))/dx | exp(x) - 18/x^3 | differentiation | | 88 | Differentiation | differentiate w.r.t x : d(sec(x)+2*x^(-2))/dx | tan(x)*sec(x) - 4/x^3 | differentiation |
| 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 16x^2 + 29x + 67 is = | 86.8333 | definite_integral | | 89 | Definite Integral of Quadratic Equation | The definite integral within limits 0 to 1 of the equation 51x^2 + 66x + 69 is = | 119.0 | definite_integral |
| 110 | Stationary Points | f(x)=6*x^3 + 8*x^2 + 3*x + 2 | (-4/9 - sqrt(10)/18,6*(-4/9 - sqrt(10)/18)**3 - sqrt(10)/6 + 2/3 + 8*(-4/9 - sqrt(10)/18)**2),(-4/9 + sqrt(10)/18,6*(-4/9 + sqrt(10)/18)**3 + sqrt(10)/6 + 8*(-4/9 + sqrt(10)/18)**2 + 2/3) | stationary_points | | 110 | Stationary Points | f(x)=3*x^3 + 6*x^2 + 4*x + 3 | (-2/3,19/9) | stationary_points |
## computer_science ## computer_science
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 4 | Binary Complement 1s | 000= | 111 | binary_complement_1s | | 4 | Binary Complement 1s | 01000= | 10111 | binary_complement_1s |
| 5 | Modulo Division | 3%97= | 3 | modulo_division | | 5 | Modulo Division | 99%30= | 9 | modulo_division |
| 14 | Decimal to Binary | Binary of 35= | 100011 | decimal_to_binary | | 14 | Decimal to Binary | Binary of 98= | 1100010 | decimal_to_binary |
| 15 | Binary to Decimal | 0001100 | 12 | binary_to_decimal | | 15 | Binary to Decimal | 0000 | 0 | binary_to_decimal |
| 56 | Fibonacci Series | The Fibonacci Series of the first 3 numbers is ? | [0, 1, 1] | fibonacci_series | | 56 | Fibonacci Series | The Fibonacci Series of the first 16 numbers is ? | [0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610] | fibonacci_series |
| 62 | nth Fibonacci number | What is the 28th Fibonacci number? | 317811 | nth_fibonacci_number | | 62 | nth Fibonacci number | What is the 46th Fibonacci number? | 1836311903 | nth_fibonacci_number |
| 64 | Binary to Hexidecimal | 110101 | 0x35 | binary_to_hex | | 64 | Binary to Hexidecimal | 1000 | 0x8 | binary_to_hex |
| 73 | Binary 2's Complement | 2's complement of 11101010 = | 10110 | binary_2s_complement | | 73 | Binary 2's Complement | 2's complement of 1111101010 = | 10110 | binary_2s_complement |
| 79 | Decimal to Hexadecimal | Binary of 858= | 0x35a | decimal_to_hexadeci | | 79 | Decimal to Hexadecimal | Binary of 450= | 0x1c2 | decimal_to_hexadeci |
| 84 | Converts decimal to octal | The decimal number 1377 in Octal is: | 0o2541 | decimal_to_octal | | 84 | Converts decimal to octal | The decimal number 2724 in Octal is: | 0o5244 | decimal_to_octal |
| 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 3 is = | 12386 | bcd_to_decimal | | 91 | Binary Coded Decimal to Integer | Integer of Binary Coded Decimal 3 is = | 14161 | bcd_to_decimal |
| 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 4841 is = | 12149 | decimal_to_bcd | | 103 | Decimal to Binary Coded Decimal | BCD of Decimal Number 4899 is = | 1323 | decimal_to_bcd |
## geometry ## geometry
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 18 | Area of Triangle | Area of triangle with side lengths: 20 16 14 = | 111.24297730643494 | area_of_triangle | | 18 | Area of Triangle | Area of triangle with side lengths: 4 12 16 = | 0.0 | area_of_triangle |
| 19 | Triangle exists check | Does triangle with sides 44, 29 and 14 exist? | No | valid_triangle | | 19 | Triangle exists check | Does triangle with sides 37, 10 and 11 exist? | No | valid_triangle |
| 22 | Third Angle of Triangle | Third angle of triangle with angles 26 and 79 = | 75 | third_angle_of_triangle | | 22 | Third Angle of Triangle | Third angle of triangle with angles 73 and 50 = | 57 | third_angle_of_triangle |
| 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 9 and 20 = | 21.93 | pythagorean_theorem | | 25 | Pythagorean Theorem | The hypotenuse of a right triangle given the other two lengths 4 and 13 = | 13.60 | pythagorean_theorem |
| 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 15 sides | 156.0 | angle_regular_polygon | | 29 | Angle of a Regular Polygon | Find the angle of a regular polygon with 11 sides | 147.27 | angle_regular_polygon |
| 32 | Surface Area of Cube | Surface area of cube with side = 6m is | 216 m^2 | surface_area_cube | | 32 | Surface Area of Cube | Surface area of cube with side = 20m is | 2400 m^2 | surface_area_cube |
| 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 9m, 13m, 1m is | 278 m^2 | surface_area_cuboid | | 33 | Surface Area of Cuboid | Surface area of cuboid with sides = 16m, 20m, 14m is | 1648 m^2 | surface_area_cuboid |
| 34 | Surface Area of Cylinder | Surface area of cylinder with height = 44m and radius = 2m is | 578 m^2 | surface_area_cylinder | | 34 | Surface Area of Cylinder | Surface area of cylinder with height = 26m and radius = 15m is | 3864 m^2 | surface_area_cylinder |
| 35 | Volum of Cube | Volume of cube with side = 6m is | 216 m^3 | volume_cube | | 35 | Volum of Cube | Volume of cube with side = 7m is | 343 m^3 | volume_cube |
| 36 | Volume of Cuboid | Volume of cuboid with sides = 9m, 10m, 17m is | 1530 m^3 | volume_cuboid | | 36 | Volume of Cuboid | Volume of cuboid with sides = 16m, 7m, 16m is | 1792 m^3 | volume_cuboid |
| 37 | Volume of cylinder | Volume of cylinder with height = 46m and radius = 3m is | 1300 m^3 | volume_cylinder | | 37 | Volume of cylinder | Volume of cylinder with height = 46m and radius = 12m is | 20809 m^3 | volume_cylinder |
| 38 | Surface Area of cone | Surface area of cone with height = 15m and radius = 6m is | 417 m^2 | surface_area_cone | | 38 | Surface Area of cone | Surface area of cone with height = 45m and radius = 10m is | 1762 m^2 | surface_area_cone |
| 39 | Volume of cone | Volume of cone with height = 2m and radius = 4m is | 33 m^3 | volume_cone | | 39 | Volume of cone | Volume of cone with height = 19m and radius = 10m is | 1989 m^3 | volume_cone |
| 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 16 , 182, 51 = | 111 | fourth_angle_of_quadrilateral | | 49 | Fourth Angle of Quadrilateral | Fourth angle of quadrilateral with angles 86 , 102, 52 = | 120 | fourth_angle_of_quadrilateral |
| 57 | Trigonometric Values | What is cos(0)? | 1 | basic_trigonometry | | 57 | Trigonometric Values | What is sin(30)? | 1/2 | basic_trigonometry |
| 58 | Sum of Angles of Polygon | Sum of angles of polygon with 7 sides = | 900 | sum_of_polygon_angles | | 58 | Sum of Angles of Polygon | Sum of angles of polygon with 10 sides = | 1440 | sum_of_polygon_angles |
| 60 | Surface Area of Sphere | Surface area of Sphere with radius = 4m is | 201.06192982974676 m^2 | surface_area_sphere | | 60 | Surface Area of Sphere | Surface area of Sphere with radius = 12m is | 1809.5573684677208 m^2 | surface_area_sphere |
| 61 | Volume of Sphere | Volume of sphere with radius 95 m = | 3591364.0018287315 m^3 | volume_sphere | | 61 | Volume of Sphere | Volume of sphere with radius 62 m = | 998305.9919263308 m^3 | volume_sphere |
| 70 | Angle between 2 vectors | angle between the vectors [971.6, 661.5, 319.66, 602.97, 423.53, 190.72, 120.07, 795.33] and [448.68, 587.18, 139.74, 198.63, 570.02, 430.49, 735.04, 51.89] is: | 0.82 radians | angle_btw_vectors | | 70 | Angle between 2 vectors | angle between the vectors [355.55, 510.69, 466.34, 362.76, 361.29, 361.07, 460.5, 967.62, 124.59, 627.19, 696.33, 269.54, 766.51, 903.59, 246.94, 158.86] and [928.29, 464.69, 667.73, 869.08, 547.6, 899.66, 562.23, 961.55, 952.5, 111.01, 259.45, 322.58, 893.48, 592.59, 865.67, 790.67] is: | 0.65 radians | angle_btw_vectors |
| 75 | Area of a Sector | Given radius, 12 and angle, 292. Find the area of the sector. | Area of sector = 366.93802 | sector_area | | 75 | Area of a Sector | Given radius, 21 and angle, 120. Find the area of the sector. | Area of sector = 461.81412 | sector_area |
| 86 | Degrees to Radians | Angle 182 in radians is = | 3.18 | degree_to_rad | | 86 | Degrees to Radians | Angle 56 in radians is = | 0.98 | degree_to_rad |
| 87 | Radians to Degrees | Angle 3 in degrees is = | 171.89 | radian_to_deg | | 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, 2 and height, 30? | CSA of cylinder = 376.99 | curved_surface_area_cylinder | | 95 | Curved surface area of a cylinder | What is the curved surface area of a cylinder of radius, 17 and height, 35? | CSA of cylinder = 3738.5 | curved_surface_area_cylinder |
| 96 | Perimeter of Polygons | The perimeter of a 10 sided polygon with lengths of [64, 97, 94, 42, 33, 71, 98, 104, 50, 47]cm is: | 700 | perimeter_of_polygons | | 96 | Perimeter of Polygons | The perimeter of a 8 sided polygon with lengths of [100, 106, 97, 63, 31, 97, 21, 24]cm is: | 539 | perimeter_of_polygons |
| 104 | Circumference | Circumference of circle with radius 24 | 150.79644737231007 | circumference | | 104 | Circumference | Circumference of circle with radius 24 | 150.79644737231007 | circumference |
| 108 | Arc length of Angle | Given radius, 39 and angle, 318. Find the arc length of the angle. | Arc length of the angle = 216.45573 | arc_length | | 108 | Arc length of Angle | Given radius, 23 and angle, 40. Find the arc length of the angle. | Arc length of the angle = 16.05703 | arc_length |
| 112 | Area of Circle | Area of circle with radius 11 | 380.2857142857143 | area_of_circle | | 112 | Area of Circle | Area of circle with radius 70 | 15400.0 | area_of_circle |
## misc ## misc
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 9 | LCM (Least Common Multiple) | LCM of 1 and 5 = | 5 | lcm | | 9 | LCM (Least Common Multiple) | LCM of 17 and 4 = | 68 | lcm |
| 10 | GCD (Greatest Common Denominator) | GCD of 3 and 18 = | 3 | gcd | | 10 | GCD (Greatest Common Denominator) | GCD of 1 and 4 = | 1 | gcd |
| 27 | Prime Factorisation | Find prime factors of 52 | [2, 2, 13] | prime_factors | | 27 | Prime Factorisation | Find prime factors of 173 | [173] | prime_factors |
| 40 | Common Factors | Common Factors of 13 and 11 = | [1] | common_factors | | 40 | Common Factors | Common Factors of 79 and 64 = | [1] | common_factors |
| 51 | HCF (Highest Common Factor) | HCF of 4 and 14 = | 2 | hcf | | 51 | HCF (Highest Common Factor) | HCF of 18 and 1 = | 1 | hcf |
| 55 | Comparing surds | Fill in the blanks 27^(1/5) _ 4^(1/3) | > | surds_comparison | | 55 | Comparing surds | Fill in the blanks 29^(1/4) _ 91^(1/2) | < | surds_comparison |
| 63 | Profit or Loss Percent | Profit percent when CP = 198 and SP = 209 is: | 5.555555555555555 | profit_loss_percent | | 63 | Profit or Loss Percent | Profit percent when CP = 781 and SP = 878 is: | 12.419974391805377 | profit_loss_percent |
| 66 | Geometric Progression | For the given GP [6, 66, 726, 7986, 87846, 966306] ,Find the value of a,common ratio,8th term value, sum upto 9th term | The value of a is 6, common ratio is 11 , 8th term is 116923026 , sum upto 9th term is 1414768614.0 | geometric_progression | | 66 | Geometric Progression | For the given GP [12, 84, 588, 4116, 28812, 201684] ,Find the value of a,common ratio,11th term value, sum upto 11th term | The value of a is 12, common ratio is 7 , 11th term is 3389702988 , sum upto 11th term is 3954653484.0 | geometric_progression |
| 67 | Geometric Mean of N Numbers | Geometric mean of 2 numbers 79 and 94 = | (79*94)^(1/2) = 86.17424209124209 | geometric_mean | | 67 | Geometric Mean of N Numbers | Geometric mean of 2 numbers 55 and 48 = | (55*48)^(1/2) = 51.38093031466052 | geometric_mean |
| 68 | Harmonic Mean of N Numbers | Harmonic mean of 3 numbers 40 , 14 and 88 = | 3/((1/40) + (1/14) + (1/88)) = 27.83132530120482 | harmonic_mean | | 68 | Harmonic Mean of N Numbers | Harmonic mean of 4 numbers 18 , 24 , 1 , 31 = | 4/((1/18) + (1/24) + (1/1) + (1/31)) = 3.5414518048393493 | harmonic_mean |
| 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[261.42719124755655, 829.8065702712056, 82.49007842320133, 333.03044204454835, 102.77960652154705, 201.9111176608831, 309.0507046659713, 610.4565223359361, 41.43497441732025, 690.4630475041106, 925.7944414219104, 349.37781230105634, 204.28488944053746, 377.3045460430586, 370.27260172442533, 215.3422861061215, 881.7450792783372, 736.7449607302535, 186.25288081152647, 512.2187637065] is: | 2199.237457798086 | euclidian_norm | | 69 | Euclidian norm or L2 norm of a vector | Euclidian norm or L2 norm of the vector[943.6989301957527, 942.687709334459, 415.08527238528325, 794.7248710456973] is: | 1607.206020456812 | euclidian_norm |
| 81 | Celsius To Fahrenheit | Convert 55 degrees Celsius to degrees Fahrenheit = | 131.0 | celsius_to_fahrenheit | | 81 | Celsius To Fahrenheit | Convert 18 degrees Celsius to degrees Fahrenheit = | 64.4 | celsius_to_fahrenheit |
| 82 | AP Term Calculation | Find the term number 94 of the AP series: -72, -115, -158 ... | -4071 | arithmetic_progression_term | | 82 | AP Term Calculation | Find the term number 55 of the AP series: 63, 7, -49 ... | -2961 | arithmetic_progression_term |
| 83 | AP Sum Calculation | Find the sum of first 48 terms of the AP series: 57, -36, -129 ... | -102168.0 | arithmetic_progression_sum | | 83 | AP Sum Calculation | Find the sum of first 68 terms of the AP series: -58, 37, 132 ... | 212466.0 | arithmetic_progression_sum |
| 85 | Converts decimal to Roman Numerals | The number 3762 in Roman Numerals is: | MMMDCCLXII | decimal_to_roman_numerals | | 85 | Converts decimal to Roman Numerals | The number 2089 in Roman Numerals is: | MMLXXXIX | decimal_to_roman_numerals |
| 92 | Complex To Polar Form | rexp(itheta) = | 17.46exp(i1.98) | complex_to_polar | | 92 | Complex To Polar Form | rexp(itheta) = | 7.28exp(i-1.85) | complex_to_polar |
| 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={1, 2, 5, 6, 7} ,b={1, 2, 5, 7, 8}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {1, 2, 5, 6, 7, 8},Intersection is {1, 2, 5, 7}, a-b is {6},b-a is {8}, Symmetric difference is {6, 8} | set_operation | | 93 | Union,Intersection,Difference of Two Sets | Given the two sets a={2, 3, 4, 5, 8, 9} ,b={9, 5, 6, 7}.Find the Union,intersection,a-b,b-a and symmetric difference | Union is {2, 3, 4, 5, 6, 7, 8, 9},Intersection is {9, 5}, a-b is {8, 2, 3, 4},b-a is {6, 7}, Symmetric difference is {2, 3, 4, 6, 7, 8} | set_operation |
| 94 | Base Conversion | Convert 1011000110100000 from base 2 to base 10. | 45472 | base_conversion | | 94 | Base Conversion | Convert DD5D from base 15 to base 10. | 46888 | base_conversion |
| 98 | Quotient of Powers with Same Base | The Quotient of 7^6 and 7^10 = 7^(6-10) = 7^-4 | 0.00041649312786339027 | quotient_of_power_same_base | | 98 | Quotient of Powers with Same Base | The Quotient of 49^2 and 49^2 = 49^(2-2) = 49^0 | 1 | quotient_of_power_same_base |
| 99 | Quotient of Powers with Same Power | The Quotient of 49^7 and 10^7 = (49/10)^7 = 4.9^7 | 67822.30728490003 | quotient_of_power_same_power | | 99 | Quotient of Powers with Same Power | The Quotient of 40^4 and 39^4 = (40/39)^4 = 1.0256410256410255^4 | 1.1065767400162785 | quotient_of_power_same_power |
| 101 | Leap Year or Not | Year 2051 | is not a leap year | is_leap_year | | 101 | Leap Year or Not | Year 2037 | is not a leap year | is_leap_year |
| 102 | Minute to Hour conversion | Convert 86 minutes to Hours & Minutes | 1 hours and 26 minutes | minutes_to_hours | | 102 | Minute to Hour conversion | Convert 897 minutes to Hours & Minutes | 14 hours and 57 minutes | minutes_to_hours |
| 106 | signum function | signum of -742 is = | -1 | signum_function | | 106 | signum function | signum of 650 is = | 1 | signum_function |
| 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 39.96% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 16 pistons will contain no more than 3 rejected pistons? | 6.56 | binomial_distribution | | 109 | Binomial distribution | A manufacturer of metal pistons finds that, on average, 30.15% of the pistons they manufacture are rejected because they are incorrectly sized. What is the probability that a batch of 17 pistons will contain no more than 5 rejected pistons? | 59.15 | binomial_distribution |
## statistics ## statistics
| Id | Skill | Example problem | Example Solution | Function Name | | Id | Skill | Example problem | Example Solution | Function Name |
|------|-------|-----------------|------------------|---------------| |------|-------|-----------------|------------------|---------------|
| 30 | Combinations of Objects | Number of combinations from 12 objects picked 7 at a time | 792 | combinations | | 30 | Combinations of Objects | Number of combinations from 14 objects picked 7 at a time | 3432 | combinations |
| 42 | Permutations | Number of Permutations from 11 objects picked 6 at a time = | 332640 | permutation | | 42 | Permutations | Number of Permutations from 15 objects picked 4 at a time = | 32760 | 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 6 = | 1/6 | dice_sum_probability | | 52 | Probability of a certain sum appearing on faces of dice | If 3 dice are rolled at the same time, the probability of getting a sum of 8 = | 21/216 | dice_sum_probability |
| 54 | Confidence interval For sample S | The confidence interval for sample [270, 268, 245, 251, 295, 291, 257, 276, 284, 283, 282, 279, 211, 258, 277, 290, 265, 271, 208, 219, 247, 260, 259, 273, 244, 207, 281, 294, 293, 216, 212, 248, 231, 254, 233, 289, 263, 249, 298, 201] with 95% confidence is | (266.9073350347248, 249.69266496527527) | confidence_interval | | 54 | Confidence interval For sample S | The confidence interval for sample [272, 295, 283, 209, 260, 200, 276, 247, 223, 249, 221, 271, 231, 213, 284, 211, 281, 210, 212, 207, 239, 245, 229, 253] with 80% confidence is | (250.11440157643338, 234.96893175689993) | confidence_interval |
| 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[13, 42, 48, 42, 44, 10, 37, 26, 33, 20, 50, 9, 43, 24, 41] | The Mean is 32.13333333333333 , Standard Deviation is 184.64888888888893, Variance is 13.588557277683638 | data_summary | | 59 | Mean,Standard Deviation,Variance | Find the mean,standard deviation and variance for the data[29, 8, 22, 18, 9, 33, 36, 31, 32, 5, 45, 42, 41, 23, 15] | The Mean is 25.933333333333334 , Standard Deviation is 154.99555555555557, Variance is 12.449721103524993 | data_summary |
| 76 | Mean and Median | Given the series of numbers [26, 66, 31, 85, 23, 25, 42, 19, 46, 92]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 45.5 and Arithmetic median of this series is 36.5 | mean_median | | 76 | Mean and Median | Given the series of numbers [63, 37, 98, 21, 76, 85, 23, 47, 2, 44]. find the arithmatic mean and mdian of the series | Arithmetic mean of the series is 49.6 and Arithmetic median of this series is 45.5 | mean_median |
| 107 | Conditional Probability | Someone tested positive for a nasty disease which only 0.05% of population have. Test sensitivity (true positive) is equal to SN= 95.33% whereas test specificity (true negative) SP= 95.03%. What is the probability that this guy really has that disease? | 0.95% | conditional_probability | | 107 | Conditional Probability | Someone tested positive for a nasty disease which only 0.59% of population have. Test sensitivity (true positive) is equal to SN= 94.30% whereas test specificity (true negative) SP= 90.17%. What is the probability that this guy really has that disease? | 5.39% | conditional_probability |

9
mathgenerator/funcs/basic_math/fraction_multiplication.py
View File

@@ -1,7 +1,7 @@
from .__init__ import * from .__init__ import *
def multiplyFractionsFunc(maxVal=10): def multiplyFractionsFunc(maxVal=10, style='raw'):
a = random.randint(1, maxVal) a = random.randint(1, maxVal)
b = random.randint(1, maxVal) b = random.randint(1, maxVal)
c = random.randint(1, maxVal) c = random.randint(1, maxVal)
@@ -27,6 +27,13 @@ def multiplyFractionsFunc(maxVal=10):
if (tmp_d == 1 or tmp_d == gcd): if (tmp_d == 1 or tmp_d == gcd):
x = f"{tmp_n//gcd}" x = f"{tmp_n//gcd}"
if style == 'latex':
problem = f"\\(\\frac{{{a}}}{{{b}}}\\cdot\\frac{{{c}}}{{{d}}}=\\)"
if (tmp_d == 1 or tmp_d == gcd):
solution = f"\\(\\frac{{{tmp_n}}}{{{gcd}}}\\)"
else:
solution = f"\\(\\frac{{{tmp_n//gcd}}}{{{tmp_d//gcd}}}\\)"
else:
problem = f"({a}/{b})*({c}/{d})" problem = f"({a}/{b})*({c}/{d})"
solution = x solution = x
return problem, solution return problem, solution

4
test.py
View File

@@ -1,4 +1,4 @@
from mathgenerator import mathgen from mathgenerator import mathgen
for _ in range(1000): for _ in range(100):
print(mathgen.genById(111)) print(mathgen.genById(28, style='latex'))