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S5 Maths: Indices and Logarithms: Paper 1 (basics)
S5 Maths: Indices and Logarithms: Paper 1 (basics)
Ten items to build the base: multiplying and dividing powers, a power of a power, negative and fractional indices, and the definition of a logarithm.
Direct answers Items 1-3: a to the power 8, 64, 1/8. Items 4-6: 3, 8, 5. Items 7-9: 3, negative 2, x to the power 3. Item 10: 2 to the power 6 is wrong; the answer is 2 to the power 5, that is 32.
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 | Basic |
02 Questions (10 items)
- FoundationSimplify a to the power 3 multiplied by a to the power 5.
- FoundationEvaluate 2 cubed, all squared, that is (2^3)^2.
- FoundationEvaluate 2 to the power negative 3.
- IntermediateEvaluate 9 to the power one half.
- IntermediateEvaluate 16 to the power three quarters.
- IntermediateFind the logarithm of 32 to base 2.
- ChallengeFind the logarithm of 1000 to base 10.
- ChallengeFind the logarithm of one ninth to base 3.
- ChallengeSimplify x to the power 5 divided by x to the power 2, where x is not zero.
- Error redoA student writes 2 cubed times 2 squared as 2 to the power 6. What is wrong, and what is the correct value?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | a to the power 8 | For the same base we add the indices, since 3 + 5 = 8. |
| 2 | 64 | A power of a power multiplies the indices, so 2 to the power 6 equals 64. |
| 3 | 1/8 | A negative index means a reciprocal, so it is 1 divided by 8. |
| 4 | 3 | A power of one half is a square root, and the square root of 9 is 3. |
| 5 | 8 | Take the fourth root first to get 2, then cube it to get 8. |
| 6 | 5 | Since 2 to the power 5 is 32, the logarithm is 5. |
| 7 | 3 | Since 10 cubed is 1000, the logarithm to base 10 is 3. |
| 8 | Negative 2 | One ninth is 3 to the power negative 2, so the logarithm is negative 2. |
| 9 | x to the power 3 | For the same base we subtract the indices, since 5 – 2 = 3. |
| 10 | 2 to the power 6 is wrong; it should be 2 to the power 5, that is 32 | When multiplying we add the indices instead of multiplying them, so 3 + 2 = 5 and the value is 32. |
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.
Name the index law or logarithm definition you use before you calculate.Tutor Registration →
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