Calculus
The mathematics of change, and the most important new idea in the qualification. Differentiation and integration are restricted to kxⁿ with n a positive integer or zero, and sums of such terms.
- An Overview — the two rules that do everything, the notation, and the common mistakes
The specification statements
- CA1–CA3 · Differentiation — the gradient function, the rule for kxⁿ, and what the answer means
- CA4 · Tangents and Normals — finding the equation of a tangent or normal at any point
- CA5–CA7 · Stationary Points — locating them, determining their nature, and sketching the curve
- Applications · Maximum and Minimum Problems — using calculus to find the best design or the largest volume
- CA8–CA11 · Integration — indefinite and definite integrals, and finding a curve from its gradient
- CA12–CA13 · Areas Under and Between Curves — areas bounded by a curve and the axis, and between two curves
- CA14–CA15 · Application to Kinematics — displacement, velocity and acceleration, with variable acceleration
Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.