Maths — Must-Know Formulas (Class 9–10)

Keep this sheet handy and revise it before every test. Understanding beats memorising — but these are the tools you reach for again and again. ALGEBRA • (a + b)² = a² + 2ab + b² • (a − b)² = a² − 2ab + b² • a² − b² = (a + b)(a − b) • (a + b)³ = a³ + 3a²b + 3ab² + b³ • Quadratic roots: x = [ −b ± √(b² − 4ac) ] / 2a TRIGONOMETRY (right triangle) • sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent • sin²θ + cos²θ = 1 • tanθ = sinθ / cosθ • Common values: sin30°=1/2, sin45°=1/√2, sin60°=√3/2 MENSURATION • Area of circle = πr² ; Circumference = 2πr • Area of triangle = ½ × base × height • Volume of cylinder = πr²h ; Sphere = (4/3)πr³ • Surface area of cube = 6a² COORDINATE GEOMETRY • Distance = √[(x₂−x₁)² + (y₂−y₁)²] • Midpoint = ( (x₁+x₂)/2 , (y₁+y₂)/2 ) • Slope = (y₂−y₁)/(x₂−x₁) Tip: don't just read formulas — solve two problems with each. That's how they stick.