How AS & A Level Mathematics (9709) is really marked
9709 spans Papers 1, 2, 3, 4, 5 and 6, each in multiple variants, totalling 1,671 questions in our bank. Marking leans towards the points style overall (1,031 points-marked questions against 640 calculation), but the balance differs sharply by unit: the Pure Mathematics papers (1, 2, 3) are mostly points-marked, while the Mechanics and Probability & Statistics papers (4, 5, 6) are calculation-heavy — Paper 42, for instance, has 56 calculation questions against only 14 points-marked out of 70 questions.
Points-marked questions in 9709 still generally require working, since 'points' here means marks awarded for specific method or accuracy steps within a solution, rather than free-standing facts. The distinction from calculation-style questions is about how many discrete, separately creditable steps a question has versus how much the mark depends on reaching a specific numerical or algebraic result.
Because the syllabus is calculation-driven throughout, most marks in 9709 depend on showing a clear chain of working: the correct method applied in the correct order, with each step following from the last, rather than only on arriving at the correct final expression or value.
Where candidates actually lose marks
- When completing the square on an expression with a leading coefficient other than 1, candidates sometimes fail to factorise that coefficient out of the first two terms before completing the square, or forget to multiply the completing-the-square correction back by that factor when combining with the constant term, leading to an incorrect final value. (try the question)
- When solving a disguised quadratic using a result from an earlier part, many candidates do not use that earlier result at all, instead restarting with a fresh substitution and the quadratic formula; some also solve it entirely on a calculator without showing the substitution or factorisation step, which scores zero because the mark scheme requires supported working, and others give a decimal approximation rather than the required exact surd form or report only one of the two valid roots. (try the question)
Command words in AS & A Level Mathematics
| Command word | Times in our bank | What it demands |
|---|---|---|
| Find | 1017 | Work out the required value, expression or equation using an appropriate method, with method steps shown clearly enough to earn credit even if the final answer contains an error. |
| Show | 202 | Demonstrate, through full and logical working, that a given result or statement is true; stating the result without the supporting algebra does not satisfy this command word. |
| Solve | 100 | Find all values that satisfy a given equation or inequality, using an appropriate method and giving every valid solution, not just the first one found. |
| State | 63 | Give a value, term or result directly, without further working, where the answer follows immediately from given information. |
| Calculate | 57 | Substitute given values into the correct formula or model and work out a final numerical answer, with the method shown. |
| Express | 42 | Write an expression, equation or result in a specified alternative form, such as partial fractions or a single logarithm. |
| Draw | 38 | Produce an accurate graph or diagram, including key features such as intercepts, asymptotes or turning points where relevant. |
| Sketch | 36 | Produce a diagram showing the general shape and key features of a curve or graph without needing to be drawn to exact scale. |
How to revise with past papers
Because the calculation share of 9709 varies so much by unit — heavily calculation-based in Mechanics and Probability & Statistics, more points-based in Pure — past-paper practice should be spread across all the units you are sitting, rather than concentrated on the unit that feels most comfortable, since the working habits that earn marks differ slightly between them.
Where a question builds on an earlier part, get into the habit of checking whether the earlier result is meant to be reused before starting a fresh method; restarting from scratch with a different approach can still reach the right answer but risks missing marks tied specifically to using the given result, and using a calculator to skip the required working can score zero even with a correct final value.
For 'Show that' questions specifically, practise writing out every algebraic step in full rather than compressing steps mentally, since the command word requires the working itself to be shown as evidence, not just confirmation that the stated result is correct.
Practise real 9709 questions with AI marking →FAQs
Is 9709 more calculation-based or points-based?
It depends on the unit. Across the whole syllabus in our bank, 640 questions are calculation-style against 1,031 points-marked, but Mechanics and Probability & Statistics papers (like Paper 42, with 56 calculation questions against 14 points-marked) are far more calculation-heavy than the Pure papers.
Can I lose all the marks on a question if I use a calculator instead of showing working?
Yes, in specific cases. In our bank, solving a disguised quadratic entirely by calculator, without showing the substitution or factorisation, scores zero on that part because the mark scheme requires supported working.
What's the most common command word in 9709?
Find, appearing 1,017 times in our bank, far ahead of the next most common word, Show, at 202.
Does 'Show that' require different technique to 'Find'?
Yes. Show that requires you to demonstrate the stated result is true through full working; simply arriving at the correct final answer without showing the connecting steps does not satisfy this command word.