Mathematics — Differentiation

Exam board: AQA  |  Back to subjects

Board-Specific Note

Spec taught as Pure, Mechanics, and Statistics papers.

Learning Objectives

• Differentiate polynomials
• Find gradients and stationary points
• Apply the second derivative test

Key Points

• Power rule d/dx(xⁿ)=nxⁿ⁻¹
• Stationary point where f′(x)=0
• Second derivative classifies max/min

Lesson Plan (50 minutes)

1. Starter (5 min): Recall prior knowledge of differentiation with quick questions.
2. Teaching (15 min): Work through each of the learning objectives, explaining principles step by step.
3. Key points review (5 min): Revisit the key points together, confirming understanding.
4. Worked example (10 min): Model the example question: Differentiate y = 3x⁴ - 2x³ + x. Solution: dy/dx = 12x³ - 6x² + 1
5. Practice (10 min): Students attempt the practice questions independently; circulate and support.
6. Plenary (5 min): Review answers and address misconceptions.

Homework

• Differentiate x⁵ - 4x³
• Find stationary points of y = x³ - 3x
• Classify with the second derivative

Assessment

Check practice answers against the model answer; use the built-in practice questions as formative assessment.