Lesson Plan

Resources → Subject Notes → Additional Mathematics → Notes
Lesson Plan
Grade: Date: 25/02/2026
Subject: Additional Mathematics
Lesson Topic: Integrate sums of terms in powers of x, including x⁻¹ and 1/(ax + b), including an arbitrary constant
Learning Objective/s:
  • Apply the power rule to integrate $x^{n}$ when $n\neq-1$.
  • Use the logarithmic rule for $\displaystyle\int\frac{1}{x}\,dx$ and $\displaystyle\int\frac{1}{ax+b}\,dx$.
  • Decompose a sum of terms and integrate each component correctly.
  • Combine the integrated results and attach a single constant $C$.
  • Verify solutions by differentiating the antiderivative.
Materials Needed:
  • Whiteboard and markers
  • Projector or interactive display
  • Printed worksheet with practice problems
  • Calculator (optional)
  • Prepared example slides
 Introduction:
Begin with a 2‑minute recall of the basic integration rules, asking students to state the power rule and the logarithmic rule. Connect this to today’s goal: integrating sums of powers, including the special cases $x^{-1}$ and $\frac{1}{ax+b}$, and producing a single constant $C$. Explain that success will be measured by correctly applying each rule and checking work by differentiation.
Lesson Structure:
  1. Do‑Now (5'): Quick worksheet on identifying the correct rule for given single terms.
  2. Direct Instruction (10'): Present the three key integration formulas and the principle “integral of a sum = sum of integrals”.
  3. Worked Example 1 (8'): Integrate $\int(3x^{2}+5x-7)\,dx$ step‑by‑step, highlighting the constant addition.
  4. Worked Example 2 (8'): Integrate $\int\left(\frac{1}{x}+ \frac{4}{2x+3}\right)dx$ showing the logarithmic rule.
  5. Guided Practice (12'): Students work in pairs on Example 3 (mixed powers) while teacher circulates, providing prompts.
  6. Independent Practice (10'): Complete the five practice problems on the worksheet.
  7. Exit Ticket (5'): Write the integrated form of one chosen problem and state which rule was used for each term.
Conclusion:
Summarise the steps: separate terms, select the appropriate rule, integrate each, then combine and add $C$. Collect exit tickets to gauge understanding. Assign homework: complete a set of three additional integrals, including one with a linear denominator, and verify each answer by differentiation.