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S5 Maths: Indices and Logarithms: Paper 4 (error replay)
S5 Maths: Indices and Logarithms: Paper 4 (error replay)
Ten items on the usual slips: mixing up adding and multiplying indices, the direction of a negative index, and dividing logarithms instead of using change of base.
Direct answers Items 1-3: 9, 15625, 1/2. Items 4-6: 3, negative 2, 1. Items 7-9: x = 3, x = 2, x squared. Item 10: wrong; it is the base 2 logarithm of 6, about 2.585.
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: S5 Maths: Indices and Logarithms |
| Level | Error replay |
02 Questions (10 items)
- FoundationEvaluate 3 to the power 4 multiplied by 3 to the power negative 2.
- FoundationEvaluate 5 squared, all cubed, that is (5^2)^3.
- FoundationEvaluate 4 to the power negative one half.
- IntermediateFind the logarithm of 64 to base 4.
- IntermediateFind the base 10 logarithm of 0.01.
- IntermediateEvaluate the base 2 logarithm of 6 minus the base 2 logarithm of 3.
- ChallengeSolve 5 to the power x equals 125.
- ChallengeSolve 2 to the power of 3x minus 1 equals 32.
- ChallengeSimplify the square of 2x cubed, all divided by 4x to the fourth, where x is not zero.
- Error redoA student divides the base 10 logarithm of 6 by the base 10 logarithm of 2 and writes the answer as the base 10 logarithm of 3. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 9 | Adding the indices gives 3 squared, which is 9. |
| 2 | 15625 | Multiplying the indices gives 5 to the power 6, which is 15625. |
| 3 | 1/2 | The half power of 4 is 2, and the negative index makes it 1/2. |
| 4 | 3 | Since 4 cubed is 64, the logarithm to base 4 is 3. |
| 5 | Negative 2 | Since 0.01 is 10 to the power negative 2, the logarithm is negative 2. |
| 6 | 1 | Subtracting logarithms divides the numbers, and 6 over 3 is 2 whose base 2 logarithm is 1. |
| 7 | x = 3 | Since 125 is 5 cubed, x equals 3. |
| 8 | x = 2 | Since 32 is 2 to the power 5, 3x minus 1 is 5 and x equals 2. |
| 9 | x squared | The numerator is 4x to the sixth, and dividing by 4x to the fourth leaves x squared. |
| 10 | That is wrong; it is the base 2 logarithm of 6, about 2.585 | Dividing logarithms does not divide the numbers: it is the change of base formula, giving log 6 over log 2, about 2.585. |
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 one line for each slip, such as adding indices when the powers should be multiplied.Tutor Registration →
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