| Lesson Plan |
| Grade: |
Date: 03/03/2026 |
| Subject: Additional Mathematics |
| Lesson Topic: Know and use the remainder and factor theorems |
Learning Objective/s:
- State the Remainder Theorem and the Factor Theorem.
- Apply synthetic (Horner’s) division to obtain remainders and quotients.
- Determine whether a linear expression $x‑a$ is a factor of a given polynomial.
- Factorise higher‑degree polynomials using the theorems.
- Identify and correct common errors when using these theorems.
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Materials Needed:
- Projector or interactive whiteboard
- Printed worksheets with practice questions
- Synthetic‑division template handout
- Graphing calculators (optional)
- Whiteboard markers and erasers
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Introduction:
Begin with a quick “mystery‑polynomial” challenge to spark curiosity about hidden factors. Review students’ prior experience with long division of polynomials and the concept of a remainder. Explain that by the end of the lesson they will be able to state the two theorems, use synthetic division, and factor polynomials confidently.
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Lesson Structure:
- Do‑now (5'): Quick mental recall – write the remainder when $f(x)$ is divided by $x‑a$.
- Mini‑lecture (10'): Introduce the Remainder Theorem and Factor Theorem with simple examples.
- Guided practice (12'): Demonstrate synthetic division step‑by‑step on $f(x)=2x^{3}-5x^{2}+3x-7$ divided by $x‑2$.
- Pair work (10'): Students complete practice questions 1 and 2 from the worksheet, using the template.
- Class discussion (5'): Review common mistakes listed in the source and correct them.
- Extension activity (8'): Factorise the cubic $h(x)=x^{3}-6x^{2}+11x-6$ using the Factor Theorem.
- Exit ticket (5'): Write one theorem statement and a brief example showing its use.
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Conclusion:
Summarise how the two theorems provide a fast route to remainders and factorisation. Collect exit tickets to gauge understanding and assign homework: complete the remaining practice questions (3‑4) and bring any difficulties to the next lesson.
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