| Lesson Plan |
| Grade: |
Date: 25/02/2026 |
| Subject: Additional Mathematics |
| Lesson Topic: Solve graphically cubic inequalities of the form f(x) ≥ d, f(x) > d, f(x) ≤ d or f(x) < d where f(x) is a product of three linear factors |
Learning Objective/s:
- Describe the process of converting a cubic inequality into a zero‑based form.
- Sketch the graph of a cubic function using its roots, leading coefficient and end behaviour.
- Use a sign chart or graph to determine intervals that satisfy f(x) ≥ d, > d, ≤ d or < d.
- Express the solution set correctly in interval notation, including or excluding endpoints as required.
- Identify common errors such as mishandling double roots or sign reversal when the leading coefficient is negative.
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Materials Needed:
- Projector or interactive whiteboard
- Graph paper and rulers
- Scientific calculators or graphing software
- Worksheet with practice cubic inequalities
- Set of pre‑printed cubic function cards (optional)
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Introduction:
Begin with a quick real‑world example where cubic relationships appear, such as profit curves, to capture interest. Review how students factor cubic expressions and locate x‑intercepts. Explain that by the end of the lesson they will be able to solve any cubic inequality graphically and write the solution in interval notation.
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Lesson Structure:
- Do‑now (5'): Students solve a simple quadratic inequality on the board to activate prior knowledge.
- Mini‑lecture (10'): Explain rewriting f(x) ≥ d as g(x)=f(x)−d and introduce the sign‑chart method.
- Guided practice (15'): Work through the example 2(x‑1)(x+2)(x‑3) ≥ 5 step‑by‑step; students sketch the graph.
- Pair activity (15'): Students receive a new cubic inequality, find its roots (using calculators), sketch the graph, and determine solution intervals.
- Whole‑class check (10'): Discuss answers and highlight common pitfalls (double roots, negative leading coefficient).
- Exit ticket (5'): Each student writes one interval solution for a given inequality on a sticky note.
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Conclusion:
Summarise the five‑step procedure and emphasise checking endpoint inclusion. Collect the exit tickets to gauge understanding, then assign homework: complete the worksheet with three additional cubic inequalities to solve graphically.
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