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S6 Maths: Logarithms and Exponentials: Paper 4 (Error clinic)
S6 Maths: Logarithms and Exponentials: Paper 4 (Error clinic)
Ten items on the usual slips: splitting a sum, dividing logs, mixing up added and multiplied indices, and dropping a coefficient.
Direct answers Items 1-3: undefined, 0, then 6 and 9. Items 4-6: 1/2, 128, 64. Items 7-9: 6 and 9, 3/2, 1. Item 10: 1/2.
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: Logarithms and Exponentials |
| Level | Error clinic |
02 Questions (10 items)
- FoundationWhat is the value of log 0?
- FoundationEvaluate log₂ 1.
- FoundationFind log (1000²) and (log 1000)², and say how they differ.
- IntermediateEvaluate log₁₆ 4.
- IntermediateCompute 2³ × 2⁴ and explain why it is not 2^(3×4).
- IntermediateCompute (2³)² and compare it with 2^(3²).
- ChallengeFind log₂ 8 + log₂ 8 and (log₂ 8)².
- ChallengeSolve 5^(2x) = 125.
- ChallengeEvaluate log₇ 7 and state the general result for log_a a.
- Error redoEvaluate log₄ 2.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Undefined | The number inside a log must be positive, so 0 has no logarithm. |
| 2 | 0 | Since 2⁰ = 1, the value is 0. |
| 3 | 6 and 9 | The first gives 2 log 1000 = 6; the second squares the answer 3 to get 9. |
| 4 | 1/2 | Since 16^(1/2) = 4 the value is 1/2, not 2. |
| 5 | 128; the indices add, not multiply | Multiplying powers of the same base adds the indices: 2⁷ = 128, while 2¹² = 4096. |
| 6 | 64; different from 512 | A power of a power multiplies the indices: 2⁶ = 64, whereas 2⁹ = 512. |
| 7 | 6 and 9 | The sum is log₂ 64 = 6; squaring the answer 3 gives 9. |
| 8 | x = 3/2 | 125 = 5³ so 2x = 3 and x = 3/2; answering 3 forgets the factor of 2. |
| 9 | 1; log_a a = 1 | For any a > 0 with a ≠ 1, a¹ = a, so the log of the base is 1. |
| 10 | 1/2 | Since 4^(1/2) = 2 the value is 1/2; writing 2 swaps the base and the number. |
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.
Switch between index and log form first, then apply the log laws.Tutor Registration →
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