Worked example · Maths · Year 9
DCF: Interacting and collaborating → Collaboration
One team's finished round, the comment thread that fixed an error in it, and the marked script of the team who sat it. Every answer and every mark below is correct, so you can use this sheet to settle any marking argument without doing the algebra yourself. Show it at the swap point (step 4) or at the end.
1. Expand and simplify 4(x − 3) − 2(x + 1). (3 marks)
2. Expand and simplify (2x − 3)(x + 5). (3 marks)
3. Solve 2x + 9 = 5x − 12. (3 marks)
4. Factorise fully 6x² + 15x. (3 marks)
5. The nth term of a sequence is 4n − 1. (a) Write down the 10th term. (b) Which term of the sequence is equal to 79? (3 marks)
Five different topics, no repeats, and the marks total exactly 15 as the task required.
| # | Answer | Marks, and what earns each one |
|---|---|---|
| 1 | 2x − 14 | M1 for 4x − 12 · M1 for −2x − 2 (both signs correct) · A1 for 2x − 14. A pupil who writes −2x + 1 loses the second M1 and the A1. |
| 2 | 2x² + 7x − 15 | M1 for four products attempted · M1 for 2x² + 10x − 3x − 15 · A1 for 2x² + 7x − 15. Accept the terms in any order. |
| 3 | x = 7 | M1 for collecting the x terms on one side (3x = 21 or 21 = 3x) · M1 for dividing both sides by 3 · A1 for x = 7. Full marks if x = 7 appears with correct working even if the sides are the other way round. |
| 4 | 3x(2x + 5) | M1 for any correct partial factorisation, for example 3(2x² + 5x) or x(6x + 15) · M1 for identifying the full common factor 3x · A1 for 3x(2x + 5). "Fully" means both the 3 and the x must come out. |
| 5 | (a) 39 (b) n = 20 | B1 for 39 (4 × 10 − 1) · M1 for forming 4n − 1 = 79 · A1 for n = 20. Award the A1 only if the answer is a term number, not the value 79. |
Check of the scheme: 4(x − 3) − 2(x + 1) = 4x − 12 − 2x − 2 = 2x − 14. (2x − 3)(x + 5) = 2x² + 10x − 3x − 15 = 2x² + 7x − 15. 2x + 9 = 5x − 12 gives 21 = 3x, x = 7, and both sides then equal 23. 3x(2x + 5) = 6x² + 15x. 4 × 10 − 1 = 39, and 4n − 1 = 79 gives 4n = 80, n = 20.
The scheme is written for a stranger: it says what a partial answer earns and where marks cannot be given — fourth success criterion.
Disagreements handled by comment and confirmation rather than by overwriting each other's work — third success criterion. The version history of the document shows three named contributors and this exchange sits inside it, which evidences the first two criteria.
| # | Team Tryfan's working | Marks awarded and comment | Mark |
|---|---|---|---|
| 1 | 4x − 12 − 2x + 1 = 2x − 11 | M1 for 4x − 12. The second bracket was multiplied by −2, so it must give −2x − 2, not −2x + 1 — the −2 has to hit both terms. Second M1 and the A1 not awarded. | 1 / 3 |
| 2 | 2x² + 10x − 3x − 15 = 2x² + 7x − 15 | M1, M1, A1. All four products correct and collected properly. Nothing to improve. | 3 / 3 |
| 3 | 2x + 9 = 5x − 12 → 9 + 12 = 5x − 2x → 21 = 3x → x = 7 | M1, M1, A1. Collecting onto the right-hand side is fine; the scheme allows it. Substituting back gives 23 = 23, so the check works too. | 3 / 3 |
| 4 | 3(2x² + 5x) | M1 for the correct partial factorisation. Not fully factorised, though: both terms inside still contain x, so x comes out as well and the answer is 3x(2x + 5). Second M1 and A1 not awarded. | 1 / 3 |
| 5 | (a) 4 × 10 − 1 = 39 (b) 4n − 1 = 79, 4n = 80, n = 20 | B1, M1, A1. Part (b) gives the term number rather than the value, which is exactly what the question asked for. | 3 / 3 |
| Total | 11 / 15 | ||
1 + 3 + 3 + 1 + 3 = 11.
Every question carries a written comment that names the error and the correction, not just a tick or a cross — fifth success criterion.
Tryfan told us question 5 was the only one that made them read it twice, because we had written "which term" and they were not sure whether we wanted 20 or 79. We would change the wording to "Which term number has a value of 79?" and add the answer type to the mark scheme. We would also swap question 1 for something less predictable — two of the three teams who saw it made the same sign error, so it was testing one small skill rather than the topic.
Acted on the feedback received, which completes the fifth criterion.