Differentiation | 30 Worked Examples | OCR B MEI A-Level Maths

30 fully worked questions on differentiation for OCR B (MEI) A-Level Mathematics (H640), built for Year 12 students (and Year 13 revision) who want to differentiate powers of x with confidence and then use the derivative to solve exam-style problems. Questions follow the H640/01 and H640/02 Section A and Section B style, with command words such as Find, Show that and Determine, and three questions carry the instruction to show detailed reasoning. The pack covers the gradient of a chord tending to the tangent gradient, differentiation from first principles for x squared, x cubed and quadratics, differentiating kx to the power n for rational n (including roots and reciprocals rewritten as powers), gradient at a point, second derivatives, stationary points and their nature, increasing and decreasing functions, tangents and normals, rates of change with units, optimisation (open box, fencing, cylinder tin) and sketching the gradient function from a curve. Six questions come with a clear TikZ diagram. Every solution is broken into single steps with a plain English reason, an arrow note on every line and OCR style M1, A1 and B1 marks placed exactly where a mark scheme rewards them, so students see how marks are earned and where they are lost. The total is 174 marks. Only powers of x are used, so no chain, product or quotient rule is needed. Ideal for homework, revision, tutoring or self study, and a complete answer for every question is included.

What’s inside:
Easy: 10 questions on chord gradients, differentiating powers and brackets, gradient at a point, a tangent, first principles for x squared, a simple increasing function and rate of change with units
Medium: 13 questions on first principles for quadratics and cubics, roots and reciprocals as powers, finding unknown constants, stationary points and their nature, increasing and decreasing functions, tangents and normals, no stationary points and sketching the gradient function
Hard: 7 questions on optimisation (box, fencing, cylinder), a tangent and area of a triangle with a normal meeting the curve again, sketching f’ for a quartic, constants from stationary points and a tangent that meets a cubic again