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S6 Maths: Logarithms and Exponentials: Paper 1 (Basics)
S6 Maths: Logarithms and Exponentials: Paper 1 (Basics)
Ten items starting from switching between index and log form, then the basic log laws.
Direct answers Items 1-3: 5, 4, 4. Items 4-6: 7, 1, then 0 and 1. Items 7-9: 6, −3, 2. Item 10: 3.
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 | Basics |
02 Questions (10 items)
- FoundationFind log₂ 32.
- FoundationFind log₁₀ 10000.
- FoundationFind log₃ 81.
- IntermediateEvaluate log₂ 8 + log₂ 16.
- IntermediateEvaluate log₅ 125 − log₅ 25.
- IntermediateEvaluate log₂ 1 and log₇ 7.
- ChallengeSolve 2ˣ = 64.
- ChallengeSolve 10ˣ = 0.001.
- ChallengeEvaluate log₃ 27 + log₃ (1/3).
- Error redoA student writes log₂ (4 + 4) = log₂ 4 + log₂ 4 = 4. What is wrong and what is the correct value?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | log₂ 32 = 5 | Since 2⁵ = 32, the logarithm is 5. |
| 2 | log₁₀ 10000 = 4 | 10⁴ = 10000, so the value is 4. |
| 3 | log₃ 81 = 4 | 3⁴ = 81, so the value is 4. |
| 4 | 3 + 4 = 7 | The two parts are 3 and 4, so the sum is 7; log₂ 128 gives the same answer. |
| 5 | 3 − 2 = 1 | The values are 3 and 2, so the difference is 1, which is log₅ 5. |
| 6 | log₂ 1 = 0 and log₇ 7 = 1 | The log of 1 is always 0, and the log of the base itself is 1. |
| 7 | x = 6 | Write 64 as 2⁶ and compare the indices to get x = 6. |
| 8 | x = −3 | Since 0.001 = 10⁻³, the index is −3. |
| 9 | 3 + (−1) = 2 | The first term is 3 and the second is −1, giving 2. |
| 10 | The log law applies to products only; the correct value is 3 | log₂ 8 = 3. A sum inside a log cannot be split, so log(a + b) is not log a + log b. |
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 →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.