Laws of indices, simplifying surds, rationalising denominators
Graphs of aˣ and eˣ, exponential growth/decay, modelling
Logarithm laws, simplifying log expressions, solving log equations
Solving equations involving exponentials using logs, reducing to linear form, exponential growth/decay modelling
nth term, common difference, sum of n terms, sigma notation
nth term, common ratio, sum of n terms, sum to infinity
Differentiation from first principles, limit definition, proving derivatives
Finding gradients, tangents, normals, stationary points, increasing/decreasing functions, optimisation using basic differentiation (power rule)
Indefinite integration, finding antiderivatives, definite integrals, evaluating integrals
Areas between two curves, area enclosed by intersecting curves
Area under curves using integration, area between curve and axes, area between two curves, numerical integration (trapezium rule)
Volumes of revolution about x-axis and y-axis, parametric volumes
Introduction to vectors, position vectors, 2D vector problems
3D vectors, vector equations of lines and planes, scalar product
Constant acceleration equations (SUVAT) in 1D, distance-time and velocity-time graphs, kinematics definitions
Constant acceleration in 2D, motion under gravity (vertical), multi-stage problems
Non-constant acceleration using calculus in 1D and 2D, v = ds/dt and a = dv/dt, integrating to find displacement.
Newton's laws (N1, N2, N3), weight and normal reaction, connected particles, resolving forces, and equilibrium conditions.
Pulley systems with connected particles, tensions, and applying Newton's second law to each particle.
Motion on inclined planes, resolving forces parallel and perpendicular to slope, and acceleration down slopes.
Frictional contact force F ≤ μR, limiting friction F = μR, rough surfaces, limiting equilibrium, and angle of friction.
Linear momentum mv, impulse as change in momentum, conservation of momentum in collisions.
Moment of a force about a point (Fd), equilibrium of rigid bodies, and taking moments about different points.
Parametric equations x=f(t), y=g(t) for curves, parametric differentiation dy/dx, parametric integration, and volumes of revolution.
Projectile motion as a particle under constant acceleration, resolving horizontally and vertically, time of flight, range, and maximum height.