To get an A* in A Level Maths you need to be secure on every topic, not just most of them, and you need to stop losing marks to how you write as well as to what you know. In practice that means two things: practise each topic with exam-style questions until you can do the hard ones unaided, then sit full papers against the clock and mark them as strictly as an examiner would, fixing every type of mark you lose.
Most students aiming for an A* already understand the content. What separates them from the top grade is usually a handful of marks per paper, lost in places that are easy to fix once you can see them.
What an A* actually takes
For UK A Level Maths (Edexcel, AQA and OCR), the grade is set on your total across all three papers. There is no grade for one paper on its own. Boundaries are set after marking, every series, so there is no fixed percentage to aim for; a harder set of papers gets lower boundaries. Our grade boundaries page links each board's official tables.
International A Level works differently. Each unit is graded on uniform marks, and your final grade comes from the units you cash in. Check Pearson's specification for how your A* is decided.
Either way, the practical message is the same. An A* leaves very little room for marks lost carelessly, so the habits below matter as much as the hardest topics.
Where strong students still lose marks
From the Edexcel examiner reports we have read, summarised in our Edexcel Examiner Insights, these come up again and again:
- "Show that" working with steps missing, or worked backwards from the printed answer.
- Proofs with no concluding statement, or that rely on "squares are always positive".
- Inverse and composite functions with the domain left out, or $fg$ and $gf$ mixed up.
- Rounding too early, so that a later answer is wrong at the accuracy asked for.
- Sign errors in integration by parts.
- Modelling answers not in context, such as a limitation of a model that could apply to anything.
None of these are about not knowing the topic. They are about writing it down completely.
Worked example 1: a proof that gets full marks
Example 1 · Proof
Prove that $x^2 - 6x + 10 > 0$ for all real values of $x$.
Solution
Complete the square:
$$x^2 - 6x + 10 = (x - 3)^2 - 9 + 10 = (x - 3)^2 + 1$$
For all real $x$, $(x - 3)^2 \ge 0$.
So $(x - 3)^2 + 1 \ge 1 > 0$.
Therefore $x^2 - 6x + 10 > 0$ for all real values of $x$.
Two details carry the marks. First, a square is greater than or equal to zero, not always positive: $(x - 3)^2 = 0$ when $x = 3$. Writing "squares are always positive" is a false statement, and the examiner reports single it out. Second, the final line restates what you were asked to prove. Without it the argument is unfinished.
Worked example 2: integration by parts without the sign slip
Example 2 · Integration by parts
Find the exact value of $\displaystyle\int_0^1 x e^{2x}\,dx$.
Solution
Let $u = x$ and $\dfrac{dv}{dx} = e^{2x}$. Then $\dfrac{du}{dx} = 1$ and $v = \tfrac{1}{2}e^{2x}$.
$$\int_0^1 x e^{2x}\,dx = \left[\tfrac{1}{2}x e^{2x}\right]_0^1 - \int_0^1 \tfrac{1}{2}e^{2x}\,dx$$
$$= \tfrac{1}{2}e^2 - \left[\tfrac{1}{4}e^{2x}\right]_0^1 = \tfrac{1}{2}e^2 - \left(\tfrac{1}{4}e^2 - \tfrac{1}{4}\right)$$
$$= \tfrac{1}{4}e^2 + \tfrac{1}{4} = \frac{e^2 + 1}{4}$$
The slip happens in the last bracket. Subtracting $\left(\tfrac{1}{4}e^2 - \tfrac{1}{4}\right)$ gives $+\tfrac{1}{4}$, not $-\tfrac{1}{4}$. Keep the bracket on the page until you have expanded it. And "exact value" means leave $e^2$ in the answer; $2.097$ would lose the final mark.
A quick check on domains
If $f(x) = 3 + \sqrt{x - 2}$ for $x \ge 2$, then $f^{-1}(x) = (x - 3)^2 + 2$. That answer is incomplete. The range of $f$ is $f(x) \ge 3$, so the domain of $f^{-1}$ is $x \ge 3$, and it has to be stated. Without it, $f^{-1}$ would not be one-to-one, and the mark for the domain is lost.
A routine that gets you there
1. Topic by topic, to the hard end. For each topic, work through exam-style questions from easy to hard. You are not done with a topic until you can do the hardest questions on it without looking at a solution. The proof, integration and algebra and functions pages are good places to start, because they carry a lot of marks.
2. Mixed practice. In the exam, nobody tells you which topic a question is from. Once topics are secure, do mixed sets so that choosing the method becomes part of the practice.
3. Full papers, timed and marked strictly. Sit papers at the real length, then mark them against the official mark scheme line by line. Our Edexcel past papers page links each paper, mark scheme and examiner report.
4. A log of every lost mark. For each one, write the question, the topic, and the reason: did not know, slip, incomplete working, wrong form, ran out of time. After three or four papers, the reasons column tells you exactly what to practise.
5. The formulas that are not given. Learn the ones you have to know by heart, so you are not deriving them under time pressure. Our list of formulas not in the Edexcel booklet is the place to start.
Problem-solving questions
A* papers include questions that do not tell you which method to use. You get better at these by doing them, not by reading solutions. When you meet one, give yourself ten minutes before looking anything up, and write down what you tried. Then compare your attempt with the solution: which step did you not think of, and how could you have spotted it?
Free tools to keep track
A free account (no card) adds 5 more practice questions on every topic with instant feedback, answers and mark schemes on free questions, and your streak and progress on any device. Create a free account, then use the grade predictor to turn your practice marks into an estimate as the year goes on.
This week
Pick one full paper. Sit it timed, mark it strictly, and sort every lost mark by reason. That list is your revision plan for the next fortnight.
Practise this topic
FAQ
What percentage do you need for an A* in A Level Maths?
There is no fixed percentage. Each board sets its grade boundaries after marking, every series, and a harder set of papers gets lower boundaries. Look at your board's published boundaries for several recent series rather than one.
Is an A* in A Level Maths graded on each paper?
Not for UK A Level. Edexcel, AQA and OCR set the boundaries on your total across all three papers. International A Level is modular, and the final grade comes from the uniform marks of the units you cash in.
When should I start past papers for A Level Maths?
Once you have covered most of the course. Before that, use exam-style questions topic by topic. Full papers are most useful in the last few months, when you can sit them timed and mark them strictly.
The mistakes the Edexcel examiner reports keep naming, in our own words, each with a fix you can practise.
See where marks are lost →