Increasing and Decreasing Functions
Using the sign of the first derivative to identify the intervals where a function is increasing or decreasing - a core building block for curve sketching, optimisation, and stationary-point questions.
Start practising → Formula sheet (PDF) ↗Sample questions
- Easy Increasing interval of a quadratic No Calculator [3]
- Medium Increasing / decreasing No Calculator [4]
- Hard Increasing/decreasing No Calculator [4]
About this topic
These are original, exam-style questions written to match the IB Mathematics syllabus for Analysis & Approaches SL. Every question comes with a full step-by-step worked solution showing the method - finding f'(x), solving the inequality f'(x) > 0 or f'(x) < 0, and stating the correct interval notation - with mark allocations matching real IB marking schemes. 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.