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S6 Maths: The Binomial Theorem: Paper 4 (Error clinic)
S6 Maths: The Binomial Theorem: Paper 4 (Error clinic)
Ten items on the usual slips: missing middle terms, confusing C(n, r) with permutations, and sign handling.
Direct answers Items 1-3: 5 terms, 36, 10. Items 4-6: 12, -3, 1. Items 7-9: 6, 16, 8. Item 10: 9 + 6x + x².
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S6 Maths: The Binomial Theorem |
| Level | Error clinic |
02 Questions (10 items)
- FoundationHow many terms are in the expansion of (a + b)^4?
- FoundationEvaluate C(9, 2).
- FoundationIn the expansion of (1 + x)^5, what number multiplies the x³ term?
- IntermediateIn the expansion of (1 + 2x)^3, what number multiplies the x² term?
- IntermediateIn the expansion of (x – 1)^3, what number multiplies the x² term?
- IntermediateEvaluate C(7, 0).
- ChallengeIn the expansion of (1 – x)^4, what number multiplies the x² term?
- ChallengeWhat is the constant term in the expansion of (2 + x)^4?
- ChallengeIn the expansion of (2 + x)^4, what number multiplies the x³ term?
- Error redoA student writes (3 + x)² = 9 + x². What is wrong and what is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 5 terms | The count is n + 1, so 4 + 1 = 5 terms. |
| 2 | 36 | C(9, 2) = (9 × 8) ÷ 2 = 36, not 72. |
| 3 | 10 | With r = 3, C(5, 3) = C(5, 2) = 10. |
| 4 | 12 | With r = 2, C(3, 2) × 2² = 3 × 4 = 12. |
| 5 | −3 | With r = 1, C(3, 1) x² (-1) = -3; the minus sign is easy to drop. |
| 6 | 1 | There is exactly one way to choose nothing, so C(n, 0) is always 1. |
| 7 | 6 | With r = 2, C(4, 2) × (-1)² = 6; an even power carries no minus sign. |
| 8 | 16 | The constant term is r = 0, giving C(4, 0) × 2^4 = 16. |
| 9 | 8 | With r = 3, C(4, 3) × 2 = 4 × 2 = 8. |
| 10 | The middle term 6x is missing; it is 9 + 6x + x² | The middle term is 2 × 3 × x = 6x, so squaring a binomial always gives three terms. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Write the general term C(n, r) a^(n-r) b^r first, then put in r.Tutor Registration →
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