Lesson Plan

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Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Integrate functions of the form (ax + b)^n, sin(ax + b), cos(ax + b), sec²(ax + b) and e^(ax + b), including the case n = –1
Learning Objective/s:
  • Apply the substitution u = ax + b to integrate each standard form.
  • Derive and use the integration formulas for power, trigonometric, sec², and exponential functions, including the logarithmic case when n = –1.
  • Identify and correct common errors such as missing the 1/a factor or sign mistakes.
  • Solve integration problems involving these forms with accurate working.
  • Explain when the integral results in a natural logarithm for n = –1.
Materials Needed:
  • Projector and screen
  • Whiteboard and markers
  • Printed worksheet with mixed integration problems
  • Formula summary handout
  • Graphing calculators (one per pair)
  • Index cards with integrand examples for quick practice
 Introduction:
Begin with a brief recall of the chain rule and its role in integration. Ask students to list the basic antiderivatives they already know. Explain that today they will learn a systematic method to integrate functions of the form (ax+b)^n, sin(ax+b), cos(ax+b), sec²(ax+b) and e^(ax+b), and that success will be shown by correctly applying the substitution and recognising the special case n = –1.
Lesson Structure:
  1. Do‑now (5') – Students complete a short task identifying a, b, and n in given expressions.
  2. Mini‑lecture (10') – Derive the general u‑substitution method and present the five integration formulas.
  3. Guided practice (15') – Work through the example ∫(3x‑2)^4 dx together, prompting each step.
  4. Collaborative activity (15') – Pairs solve a set of mixed problems, checking each other’s use of the 1/a factor and sign.
  5. Error‑analysis (10') – Present common mistakes; students correct flawed solutions.
  6. Quick quiz (5') – Exit ticket with three integrals to be answered individually.
Conclusion:
Summarise that the key to these integrals is the u‑substitution and remembering the 1/a factor, with the logarithmic form for n = –1. Collect a one‑sentence takeaway from each student as an exit ticket. Assign homework: a worksheet containing five integrals of each type to reinforce the method.