The derivative measures how fast something changes. Once you can find one, you can find gradients, tangents, maxima, minima and rates of change — which is most of the applied content in the paper.
Syllabus points covered
- Differentiate xⁿ, eˣ, ln x, sin x, cos x and tan x
- Use the chain, product and quotient rules
- Find the equations of tangents and normals to a curve
- Find and classify stationary points using the first or second derivative
- Apply differentiation to connected rates of change and small increments
Common mistakes
- Using the product rule where the chain rule is needed, or applying both at once without brackets.
- Finding stationary points but not classifying them, when the question asks for a maximum or minimum specifically.
- Using the gradient of the tangent for the normal. The normal's gradient is the negative reciprocal.
- In rates-of-change problems, setting up the chain of derivatives in the wrong order.
Worksheets
Use these as soon as you've learned the topic and need to practise it. Start with the worksheet, check yourself against the answers, and only then look at the step-by-step solutions.
- Practice worksheetComing soon
- Worksheet answersComing soon
- Step-by-step solutionsComing soon
Topical past papers
Move on to these once you've worked through the worksheets and are ready for harder, exam-style questions. Real past-paper questions on this topic, with the official mark scheme and full worked solutions.
- Topical questionsComing soon
- Mark schemeComing soon
- Step-by-step worked solutionsComing soon
Looking for whole papers by session? All Additional Mathematics past papers