Exponential Models | OCR A-Level Maths | 40 Worked Examples (H240)

Forty fully worked exponential-models questions for OCR A-Level Mathematics A (H240), written to the exact style of the H240 papers and graded Easy to Challenging. Every solution is broken down one atomic step at a time, with a plain-English note on every line and OCR mark-scheme annotations (M/A/B marks) on the lines the real scheme rewards. Coverage spans the whole of spec points 1.06h and 1.06i: exponential growth and decay with y = Ae^(kt), continuous compound interest, radioactive decay, drug-concentration decay and population growth, finding the initial value and the growth or decay constant from data, half-life and doubling-time calculations, the rate of change of an exponential model by differentiation, and reduction to linear form, taking logarithms of y = ax^n and y = kb^x to read the parameters off the gradient and intercept of a straight-line log graph, including a log-linear graph-reading question and the classic ‘is the model appropriate’ argument. The Challenging section adds detailed-reasoning questions, a geometric-series sales total, Newton’s law of cooling, a logistic refinement of an exponential model, and a comment on the reliability of extrapolation. Answer conventions follow OCR exactly (exact form kept, money to the nearest penny, otherwise 3 s.f.), and the detailed-reasoning instruction is handled as OCR expects. Ideal for revision, homework or targeted 1-1 practice. Answers included.