Math Formula Sheet
Presented to Azka Abdulrauf
For achieving the highest marks in Mathematics
Algebra
- (a + b)² = a² + 2ab + b²
- (a - b)² = a² - 2ab + b²
- a² - b² = (a + b)(a - b)
- Quadratic Formula: x = (-b ± √(b² - 4ac)) / 2a
- (x + a)(x + b) = x² + (a + b)x + ab
- x² + y² = (x + y)² - 2xy
- Sum of n natural numbers: S = n(n + 1)/2
- Arithmetic Series: Sn = n/2 [2a + (n - 1)d]
- Factor Theorem & Remainder Theorem basics
Geometry
- Area of Triangle: A = ½ × b × h
- Area of Circle: A = πr²
- Perimeter of Circle: C = 2πr
- Area of Rectangle: A = l × w
- Pythagoras Theorem: a² + b² = c²
Trigonometry
- sin²θ + cos²θ = 1
- tanθ = sinθ / cosθ
- sin A = opposite / hypotenuse
- cos A = adjacent / hypotenuse
- Sine Rule: a/sin A = b/sin B
Statistics
- Mean = Sum of values / Total number
- Median = Middle value of ordered set
- Mode = Most frequent value
- Percentage = (Part / Whole) × 100
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