Differentiation
Introduction to differentiation — the gradient of a curve, derivatives of polynomials, tangents and normals, increasing and decreasing functions, stationary points, and optimisation in real-world contexts.
Start practising → Formula sheet (PDF) ↗Sample questions
- Easy Gradient of a curve at a point No Calculator [3]
- Medium Equation of a tangent No Calculator [5]
- Hard Optimisation — maximum area Calculator [6]
About this topic
These are original, exam-style questions written to match the IB Mathematics syllabus for Applications & Interpretation SL (Topic 5: Calculus). Every question comes with a full step-by-step worked solution showing the method, with mark allocations matching real IB marking schemes, and graphics-calculator key sequences where a GDC is used. Questions are labelled Paper 1 (no calculator) or Paper 2 (calculator allowed) so you practise under realistic exam conditions.
How to practise
- Open the question bank using the button above.
- Attempt the question, writing out your working.
- Reveal the full worked solution and compare your method step by step.
- Use the difficulty and calculator filters to focus on what you need most.