Power Rule — Differentiation

Product Rule

Quotient Rule

Chain Rule

Key Derivatives

Power Rule — Integration

Key Integrals

Definite Integral — Area Under Curve

For area between two curves: \(\displaystyle\int_a^b \bigl[f(x) - g(x)\bigr]\, dx\) where \(f(x) \geq g(x)\).

Pythagorean Identity

Derived Identities

Sine Rule

Cosine Rule

Area of Triangle

Double Angle Formulas

Radian Conversion

where \(\theta\) is in radians.

SUVAT Equations — Constant Acceleration

\(s\) = displacement (m), \(u\) = initial velocity (ms⁻¹), \(v\) = final velocity (ms⁻¹), \(a\) = acceleration (ms⁻²), \(t\) = time (s).

Newton's Second Law

Net force \(F\) (N) = mass \(m\) (kg) × acceleration \(a\) (ms⁻²).

Projectile Motion

Horizontal (\(x\)) and vertical (\(y\)) components. Take \(g = 9.8\,\text{ms}^{-2}\) unless stated otherwise.

Variable Acceleration (Calculus)

Friction Force

At limiting equilibrium: \(F = \mu R\), where \(\mu\) is the coefficient of friction and \(R\) is the normal reaction force.