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S6 Maths: Definite Integrals – Error Replay (Paper 4)
S6 Maths: Definite Integrals – Error Replay (Paper 4)
Ten items targeting missing division, sign errors and area-versus-integral confusion.
Direct answers Answers in order: 3, 9, 7, 1/3, 1, 2/3, 36, 16/3, 2, 1/6.
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: Definite Integrals and Area |
| Level | Error replay |
02 Questions (10 items)
- FoundationEvaluate the integral of 6x from 0 to 1.
- FoundationEvaluate the integral of x squared from 0 to 3.
- FoundationEvaluate the integral of 3x squared from 1 to 2.
- IntermediateFind the area under y = x squared from x = 0 to x = 1.
- IntermediateEvaluate the integral of sine x from 0 to pi over 2.
- IntermediateEvaluate the integral of x squared from minus 1 to 1.
- ChallengeFind the area enclosed by y = 9 minus x squared and the x-axis.
- ChallengeEvaluate the integral of 4 minus x squared from 0 to 2.
- ChallengeGiven the integral of 3x squared from 0 to a equals 8 with a positive, find a.
- Error redoError replay: a student got minus 1/6 for the integral of x minus x squared from 0 to 1.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 3 | The antiderivative is 3x squared, which is 3 at x = 1. |
| 2 | 9 | The antiderivative is x cubed over 3, and 27 divided by 3 gives 9. |
| 3 | 7 | The antiderivative is x cubed, and 8 minus 1 gives 7. |
| 4 | 1/3 | The area is the integral of x squared, and x cubed over 3 gives 1/3. |
| 5 | 1 | The antiderivative is minus cosine, which gives 1 minus 0. |
| 6 | 2/3 | The antiderivative is x cubed over 3, so 1/3 minus minus 1/3 gives 2/3. |
| 7 | 36 | The curve cuts the axis at plus and minus 3, so twice the integral to 3 gives 36. |
| 8 | 16/3 | The antiderivative is 4x minus x cubed over 3, giving 8 minus 8/3. |
| 9 | 2 | The antiderivative is x cubed, so a cubed is 8 and a is 2. |
| 10 | 1/6 | The antiderivative gives 1/2 minus 1/3, which is positive 1/6; reversing the order gives the negative. |
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 per slip, such as forgetting to divide by the new index.Tutor Registration →
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