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S4 Mathematics: Indices and Logarithms (Paper 1)
S4 Mathematics: Indices and Logarithms (Paper 1)
Ten original questions begin with the index laws: adding indices for the same base, multiplying for a power of a power, zero and negative indices giving six fifths, division, raising a coefficient and a letter separately to get 16x to the twelfth, and converting between 0.00042 and 3.2 times ten to the fifth. Later items solve 2 to the x equals 32 and evaluate eight to the two thirds, ending with the error of writing x to the fifth for (x squared) cubed.
Direct answer Add indices when multiplying and subtract when dividing the same base, multiply for a power of a power, and treat the coefficient separately.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 25 |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S4 Mathematics: Indices and Logarithms |
| Level | Four basic, three advanced, two challenge and one error-repair item |
02 Questions (10 items)
- FoundationSimplify 2 to the power 3 times 2 to the power 4.
- FoundationSimplify (3 squared) to the power 4.
- FoundationFind the value of 5 to the power 0 plus 5 to the power minus 1 as a fraction.
- FoundationSimplify a to the seventh divided by a cubed, where a is not zero.
- IntermediateSimplify (2x cubed) to the power 4.
- IntermediateWrite 0.00042 in scientific notation.
- IntermediateWrite 3.2 times 10 to the power 5 as an integer.
- ChallengeSolve 2 to the power x equals 32.
- ChallengeFind the value of 8 to the power two thirds.
- Error redoError repair: a student writes x to the fifth for (x squared) cubed. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 2 to the power 7, which is 128 | For the same base the indices add, giving seven, and two to the seventh is 128. |
| 2 | 3 to the power 8, which is 6561 | A power of a power multiplies the indices, so two times four gives eight. |
| 3 | 6/5, that is 1.2 | Any non-zero number to the power zero is one, and five to the minus one is one fifth. |
| 4 | a to the power 4 | For the same base in a division the indices subtract, seven minus three. |
| 5 | 16 x to the power 12 | Raise the coefficient and the letter separately, giving sixteen and x to the twelfth. |
| 6 | 4.2 times 10 to the power minus 4 | The point moves four places to the right, so the index of ten is minus four. |
| 7 | 320 000 | Ten to the fifth is one hundred thousand, and 3.2 times that is 320 000. |
| 8 | x equals 5 | Thirty-two is two to the fifth, so the indices must be equal. |
| 9 | 4 | Take the cube root to get two, then square it to get four. |
| 10 | x to the power 6 | A power of a power multiplies the indices instead of adding them. |
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.
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.
