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https://github.com/DeaDvey/mathgenerator.git
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Merge branch 'master' into prime_factorisation
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Luke Weiler
GitHub
48
README.md
48
README.md
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# mathgenerator
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A math problem generator, created for the purpose of giving self-studying students and teaching organizations the means to easily get access to random math problems to suit their needs.
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To try out generators, go to https://todarith.ml/generate/
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To try out generators, go to <https://todarith.ml/generate/>
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If you have an idea for a generator, please add it as an issue and tag it with the "New Generator" label.
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## Usage
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The project can be install via pip
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```
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```bash
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pip install mathgenerator
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```
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Here is an example of how you would generate an addition problem:
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```
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```python
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from mathgenerator import mathgen
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#generate an addition problem
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problem, solution = mathgen.addition()
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```
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## List of Generators
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| Id | Skill | Example problem | Example Solution | Function Name |
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|------|-----------------------------------|--------------------|-------------------|--------------------------|
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| 0 | Addition | 1+5= | 6 | addition |
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| 1 | Subtraction | 9-4= | 5 | subtraction |
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| 2 | Multiplication | 4*6= | 24 | multiplication |
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| 3 | Division | 4/3= | 1.33333333 | division |
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| 4 | Binary Complement 1s | 1010= | 0101 | binaryComplement1s |
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| 5 | Modulo Division | 10%3= | 1 | moduloDivision |
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| 6 | Square Root | sqrt(25)= | 5 | squareRootFunction |
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| 7 | Power Rule Differentiation | 4x^3 | 12x^2 | powerRuleDifferentiation |
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| 8 | Square | 4^2 | 16 | square |
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| 9 | LCM (Least Common Multiple) | LCM of 14 and 9 = | 126 | lcm |
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| 10 | GCD (Greatest Common Denominator) | GCD of 18 and 18 = | 18 | gcd |
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| 11 | Basic Algebra | 9x + 7 = 10 | 1/3 | basicAlgebra |
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| 12 | Logarithm | log3(3) | 1 | log |
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| 13 | Easy Division | 270/15 = | 18 | intDivision |
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| Id | Skill | Example problem | Example Solution | Function Name |
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|------|-----------------------------------|--------------------|-----------------------|--------------------------|
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| 0 | Addition | 1+5= | 6 | addition |
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| 1 | Subtraction | 9-4= | 5 | subtraction |
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| 2 | Multiplication | 4*6= | 24 | multiplication |
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| 3 | Division | 4/3= | 1.33333333 | division |
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| 4 | Binary Complement 1s | 1010= | 0101 | binaryComplement1s |
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| 5 | Modulo Division | 10%3= | 1 | moduloDivision |
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| 6 | Square Root | sqrt(25)= | 5 | squareRootFunction |
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| 7 | Power Rule Differentiation | 4x^3 | 12x^2 | powerRuleDifferentiation |
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| 8 | Square | 4^2 | 16 | square |
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| 9 | LCM (Least Common Multiple) | LCM of 14 and 9 = | 126 | lcm |
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| 10 | GCD (Greatest Common Denominator) | GCD of 18 and 18 = | 18 | gcd |
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| 11 | Basic Algebra | 9x + 7 = 10 | 1/3 | basicAlgebra |
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| 12 | Logarithm | log3(3) | 1 | log |
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| 13 | Easy Division | 270/15 = | 18 | intDivision |
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| 14 | Decimal to Binary | Binary of a= | b | decimalToBinary |
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| 15 | Binary to Decimal | Decimal of a= | b | binaryToDecimal |
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| 16 | Fraction Division | (a/b)/(c/d)= | x/y | fractionDivision |
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| 17 | Int 2x2 Matrix Multiplication | k * [[a,b],[c,d]]= | [[k*a,k*b],[k*c,k*d]] | intMatrix22Multiplication|
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@@ -15,8 +15,8 @@ class Generator:
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def __str__(self):
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return str(self.id) + " " + self.title + " " + self.generalProb + " " + self.generalSol
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def __call__(self):
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return self.func()
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def __call__(self, **kwargs):
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return self.func(**kwargs)
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# || Non-generator Functions
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def genById(id):
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@@ -216,6 +216,160 @@ def multiplyIntToMatrix22(maxMatrixVal = 10, maxRes = 100):
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solution = f"[[{a*constant},{b*constant}],[{c*constant},{d*constant}]]"
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return problem, solution
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def areaOfTriangleFunc(maxA=20, maxB=20, maxC=20):
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a = random.randint(1, maxA)
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b = random.randint(1, maxB)
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c = random.randint(1, maxC)
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s = (a+b+c)/2
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area = (s*(s-a)*(s-b)*(s-c)) ** 0.5
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problem = "Area of triangle with side lengths: "+ str(a) +" "+ str(b) +" "+ str(c) + " = "
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solution = area
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return problem, solution
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def isTriangleValidFunc(maxSideLength = 50):
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sideA = random.randint(1, maxSideLength)
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sideB = random.randint(1, maxSideLength)
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sideC = random.randint(1, maxSideLength)
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sideSums = [sideA + sideB, sideB + sideC, sideC + sideA]
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sides = [sideC, sideA, sideB]
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exists = True & (sides[0] < sideSums[0]) & (sides[1] < sideSums[1]) & (sides[2] < sideSums[2])
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problem = f"Does triangle with sides {sideA}, {sideB} and {sideC} exist?"
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if exists:
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solution = "Yes"
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return problem, solution
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solution = "No"
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return problem, solution
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def MidPointOfTwoPointFunc(maxValue=20):
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x1=random.randint(-20,maxValue)
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y1=random.randint(-20,maxValue)
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x2=random.randint(-20,maxValue)
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y2=random.randint(-20,maxValue)
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problem=f"({x1},{y1}),({x2},{y2})="
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solution=f"({(x1+x2)/2},{(y1+y2)/2})"
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return problem,solution
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def factoringFunc(range_x1 = 10, range_x2 = 10):
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x1 = random.randint(-range_x1, range_x1)
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x2 = random.randint(-range_x2, range_x2)
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def intParser(z):
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if (z == 0):
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return ""
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if (z > 0):
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return "+" + str(z)
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if (z < 0):
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return "-" + str(abs(z))
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b = intParser(x1 + x2)
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c = intParser(x1 * x2)
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if (b == "+1"):
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b = "+"
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if (b == ""):
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problem = f"x^2{c}"
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else:
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problem = f"x^2{b}x{c}"
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x1 = intParser(x1)
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x2 = intParser(x2)
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solution = f"(x{x1})(x{x2})"
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return problem, solution
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def thirdAngleOfTriangleFunc(maxAngle=89):
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angle1 = random.randint(1, maxAngle)
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angle2 = random.randint(1, maxAngle)
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angle3 = 180 - (angle1 + angle2)
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problem = f"Third angle of triangle with angles {angle1} and {angle2} = "
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solution = angle3
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return problem, solution
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def systemOfEquationsFunc(range_x = 10, range_y = 10, coeff_mult_range=10):
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# Generate solution point first
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x = random.randint(-range_x, range_x)
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y = random.randint(-range_y, range_y)
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# Start from reduced echelon form (coeffs 1)
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c1 = [1, 0, x]
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c2 = [0, 1, y]
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def randNonZero():
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return random.choice([i for i in range(-coeff_mult_range, coeff_mult_range)
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if i != 0])
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# Add random (non-zero) multiple of equations (rows) to each other
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c1_mult = randNonZero()
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c2_mult = randNonZero()
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new_c1 = [c1[i] + c1_mult * c2[i] for i in range(len(c1))]
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new_c2 = [c2[i] + c2_mult * c1[i] for i in range(len(c2))]
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# For extra randomness, now add random (non-zero) multiples of original rows
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# to themselves
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c1_mult = randNonZero()
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c2_mult = randNonZero()
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new_c1 = [new_c1[i] + c1_mult * c1[i] for i in range(len(c1))]
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new_c2 = [new_c2[i] + c2_mult * c2[i] for i in range(len(c2))]
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def coeffToFuncString(coeffs):
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# lots of edge cases for perfect formatting!
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x_sign = '-' if coeffs[0] < 0 else ''
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# No redundant 1s
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x_coeff = str(abs(coeffs[0])) if abs(coeffs[0]) != 1 else ''
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# If x coeff is 0, dont include x
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x_str = f'{x_sign}{x_coeff}x' if coeffs[0] != 0 else ''
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# if x isn't included and y is positive, dont include operator
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op = ' - ' if coeffs[1] < 0 else (' + ' if x_str != '' else '')
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# No redundant 1s
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y_coeff = abs(coeffs[1]) if abs(coeffs[1]) != 1 else ''
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# Don't include if 0, unless x is also 0 (probably never happens)
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y_str = f'{y_coeff}y' if coeffs[1] != 0 else ('' if x_str != '' else '0')
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return f'{x_str}{op}{y_str} = {coeffs[2]}'
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problem = f"{coeffToFuncString(new_c1)}, {coeffToFuncString(new_c2)}"
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solution = f"x = {x}, y = {y}"
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return problem, solution
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# Add random (non-zero) multiple of equations to each other
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def distanceTwoPointsFunc(maxValXY = 20, minValXY=-20):
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point1X = random.randint(minValXY, maxValXY+1)
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point1Y = random.randint(minValXY, maxValXY+1)
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point2X = random.randint(minValXY, maxValXY+1)
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point2Y = random.randint(minValXY, maxValXY+1)
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distanceSq = (point1X - point2X) ** 2 + (point1Y - point2Y) ** 2
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solution = f"sqrt({distanceSq})"
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problem = f"Find the distance between ({point1X}, {point1Y}) and ({point2X}, {point2Y})"
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return problem, solution
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def pythagoreanTheoremFunc(maxLength = 20):
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a = random.randint(1, maxLength)
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b = random.randint(1, maxLength)
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c = (a**2 + b**2)**0.5
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problem = f"The hypotenuse of a right triangle given the other two lengths {a} and {b} = "
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solution = f"{c:.0f}" if c.is_integer() else f"{c:.2f}"
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return problem, solution
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def linearEquationsFunc(n = 2, varRange = 20, coeffRange = 20):
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if n > 10:
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print("[!] n cannot be greater than 10")
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return None, None
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vars = ['x', 'y', 'z', 'a', 'b', 'c', 'd', 'e', 'f', 'g'][:n]
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soln = [ random.randint(-varRange, varRange) for i in range(n) ]
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problem = list()
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solution = ", ".join(["{} = {}".format(vars[i], soln[i]) for i in range(n)])
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for _ in range(n):
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coeff = [ random.randint(-coeffRange, coeffRange) for i in range(n) ]
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res = sum([ coeff[i] * soln[i] for i in range(n)])
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prob = ["{}{}".format(coeff[i], vars[i]) if coeff[i] != 0 else "" for i in range(n)]
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while "" in prob:
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prob.remove("")
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prob = " + ".join(prob) + " = " + str(res)
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problem.append(prob)
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problem = "\n".join(problem)
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return problem, solution
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def primeFactors(minVal=1, maxVal=200):
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a = random.randint(minVal, maxVal)
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n = a
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@@ -255,7 +409,14 @@ decimalToBinary = Generator("Decimal to Binary",14,"Binary of a=","b",DecimalToB
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binaryToDecimal = Generator("Binary to Decimal",15,"Decimal of a=","b",BinaryToDecimalFunc)
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fractionDivision = Generator("Fraction Division", 16, "(a/b)/(c/d)=", "x/y", divideFractionsFunc)
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intMatrix22Multiplication = Generator("Integer Multiplication with 2x2 Matrix", 17, "k * [[a,b],[c,d]]=", "[[k*a,k*b],[k*c,k*d]]", multiplyIntToMatrix22)
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primeFactors = Generator("Prime Factorisation", 18, "Prime Factors of a =", "[b, c, d, ...]", primeFactors)
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for i in range(0, 10):
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print(primeFactors())
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areaOfTriangle = Generator("Area of Triangle", 18, "Area of Triangle with side lengths a, b, c = ", "area", areaOfTriangleFunc)
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doesTriangleExist = Generator("Triangle exists check", 19, "Does triangle with sides a, b and c exist?","Yes/No", isTriangleValidFunc)
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midPointOfTwoPoint=Generator("Midpoint of the two point", 20,"((X1,Y1),(X2,Y2))=","((X1+X2)/2,(Y1+Y2)/2)",MidPointOfTwoPointFunc)
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factoring = Generator("Factoring Quadratic", 21, "x^2+(x1+x2)+x1*x2", "(x-x1)(x-x2)", factoringFunc)
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thirdAngleOfTriangle = Generator("Third Angle of Triangle", 22, "Third Angle of the triangle = ", "angle3", thirdAngleOfTriangleFunc)
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systemOfEquations = Generator("Solve a System of Equations in R^2", 23, "2x + 5y = 13, -3x - 3y = -6", "x = -1, y = 3",
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systemOfEquationsFunc)
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distance2Point = Generator("Distance between 2 points", 24, "Find the distance between (x1,y1) and (x2,y2)","sqrt(distanceSquared)", distanceTwoPointsFunc)
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pythagoreanTheorem = Generator("Pythagorean Theorem", 25, "The hypotenuse of a right triangle given the other two lengths a and b = ", "hypotenuse", pythagoreanTheoremFunc)
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linearEquations = Generator("Linear Equations", 26, "2x+5y=20 & 3x+6y=12", "x=-20 & y=12", linearEquationsFunc) #This has multiple variables whereas #23 has only x and y
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primeFactors = Generator("Prime Factorisation", 27, "Prime Factors of a =", "[b, c, d, ...]", primeFactors)
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