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S6 Maths: Definite Integrals – Core Evaluation (Paper 1: Basics)
S6 Maths: Definite Integrals – Core Evaluation (Paper 1: Basics)
Ten core definite-integral items from polynomials to exponential and trigonometric functions.
Direct answers Answers in order: 8, 8, 3, 4, 10, 2, 1, 1.718, 9, 8/3.
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: Definite Integrals and Area |
| Level | S6 |
02 Questions (10 items)
- FoundationEvaluate the integral of 3x squared from 0 to 2.
- FoundationEvaluate the integral of 2x from 1 to 3.
- FoundationEvaluate the integral of 4x plus 1 from 0 to 1.
- IntermediateEvaluate the integral of x cubed from 0 to 2.
- IntermediateEvaluate the integral of the constant 2 from 0 to 5.
- IntermediateEvaluate the integral of sine x from 0 to pi.
- ChallengeEvaluate the integral of 1 over x from 1 to e.
- ChallengeEvaluate the integral of e to the x from 0 to 1, to 3 decimal places.
- ChallengeFind the area under y = 2x above the x-axis from x = 0 to x = 3.
- Error redoError replay: a student got 8 for the integral of x squared from 0 to 2. What is correct?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 8 | The antiderivative is x cubed; at 2 it is 8 and at 0 it is 0, so the value is 8. |
| 2 | 8 | The antiderivative is x squared, and 9 minus 1 gives 8. |
| 3 | 3 | The antiderivative is 2x squared plus x, which is 3 at x = 1 and 0 at x = 0. |
| 4 | 4 | The antiderivative is x to the fourth over 4; 16 divided by 4 gives 4. |
| 5 | 10 | A constant integrates to the constant times the interval length, so 2 times 5 gives 10. |
| 6 | 2 | The antiderivative minus cosine gives 1 at pi and minus 1 at 0, so the difference is 2. |
| 7 | 1 | The antiderivative is the natural log, which is 1 at e and 0 at 1. |
| 8 | 1.718 | e is about 2.718, and subtracting 1 gives 1.718. |
| 9 | 9 | The area is the integral of 2x, and the antiderivative x squared gives 9. |
| 10 | 8/3 (about 2.67) | The antiderivative is x cubed over 3, giving 8/3; forgetting to divide by 3 produces 8. |
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 the antiderivative first, substitute the limits second, and use the calculator last.Tutor Registration →
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