| Lesson Plan |
| Grade: |
Date: 25/02/2026 |
| Subject: Additional Mathematics |
| Lesson Topic: Understand integration as the reverse process of differentiation and include an arbitrary constant in indefinite integrals |
Learning Objective/s:
- Describe the concept of an antiderivative and its notation.
- Explain why an arbitrary constant must be added to indefinite integrals.
- Apply basic integration formulas to compute antiderivatives of common functions.
- Solve simple integration problems, including using initial conditions to determine the constant.
- Identify common errors when performing indefinite integration.
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Materials Needed:
- Projector or interactive whiteboard
- Printed worksheet with integration practice problems
- Formula cards for basic integration rules
- Graphing calculator or software (e.g., Desmos)
- Whiteboard markers and erasers
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Introduction:
Begin with a quick visual of a curve and its tangent, asking students how they could recover the original curve from its slope. Recall that differentiation finds the rate of change, so integration should reverse that process. Today we will explore antiderivatives, the integral sign, and why we always include a constant of integration. Success will be measured by correctly applying the basic formulas and justifying the constant.
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Lesson Structure:
- Do‑now (5') – Students complete a short exit ticket from the previous lesson on differentiation, focusing on slopes.
- Mini‑lecture (10') – Explain integration as reverse differentiation, introduce antiderivative notation and the constant C with examples.
- Guided practice (12') – Work through Example 1 and Example 2 together, emphasizing the power rule and logarithmic rule.
- Collaborative activity (10') – In pairs, students use formula cards to solve three mixed integration problems on the worksheet, checking each other’s work.
- Application with initial condition (8') – Demonstrate Example 4, then have students find the constant for a new problem using a given point.
- Check for understanding (5') – Quick quiz (Kahoot/hand‑raise) on selecting the correct formula and remembering the “+ C”.
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Conclusion:
Summarise that integration reverses differentiation and always yields a family of functions distinguished by the constant C. For the exit ticket, students write one real‑world scenario where the constant would be determined by extra information. Homework: complete the worksheet with five additional indefinite integrals and one problem requiring an initial condition.
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