Lesson Plan

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Lesson Plan
Grade: Date: 17/01/2026
Subject: Additional Mathematics
Lesson Topic: Use differentiation to find stationary points of functions
Learning Objective/s:
  • Describe what a stationary point is and how it relates to the derivative.
  • Apply the procedure to find and classify stationary points for polynomial and rational functions.
  • Use the second‑derivative test or a sign chart to determine whether a stationary point is a maximum, minimum or point of inflection.
  • Solve typical IGCSE Additional Mathematics problems involving differentiation and stationary points.
Materials Needed:
  • Projector or interactive whiteboard
  • Whiteboard and coloured markers
  • Graphing calculators (one per pair)
  • Worksheet with practice questions (including the three examples from the source)
  • Printed summary of differentiation formulas
  • Student notebooks
 Introduction:
Begin with a quick real‑world illustration of a hill and a valley to show a maximum and a minimum. Recall that the derivative gives the slope of a curve, so where the slope is zero we have a stationary point. Today students will locate and classify these points using differentiation and the second‑derivative test.
Lesson Structure:
  1. Do‑now (5'): Students complete a short worksheet identifying where the slope of given graphs is zero.
  2. Mini‑lecture (10'): Define stationary point, present the general four‑step procedure, and briefly recap power, product, quotient and chain rules.
  3. Guided Example 1 – Quadratic (10'): Work through the quadratic example on the board, checking each step with students.
  4. Guided Example 2 – Cubic (10'): Solve the cubic example, emphasising solving f′(x)=0 and using the second‑derivative test.
  5. Collaborative practice (15'): Pairs attempt the three practice questions from the source, using calculators; teacher circulates to support.
  6. Whole‑class discussion (5'): Groups share answers, highlight common pitfalls and correct misconceptions.
  7. Exit ticket (5'): Each student writes one stationary‑point problem (function and classification) to demonstrate mastery.
Conclusion:
Recap the checklist: write f(x), compute f′(x), solve f′(x)=0, find y‑coordinates, and apply the second‑derivative test or sign chart. Collect exit tickets and assign homework: complete a worksheet with two additional functions (one polynomial, one rational) and bring the solutions to the next lesson.