A-level Further Maths 2027: papers, options, exam dates and grade boundaries

What A-level Further Maths covers

Core pure is the same idea on every board. Edexcel's Further Maths specification lists it as proof, complex numbers, matrices, further algebra and functions, further calculus, further vectors, polar coordinates, hyperbolic functions and differential equations.

The options are where you shape the course: more pure maths, further statistics, further mechanics, or discrete and decision maths, which covers graphs, networks and algorithms. Your school usually decides which options it teaches.

A-level Further Maths papers by board

Edexcel's options pair a 3 paper with a 3 or 4 paper, for example Further Pure 1 with Further Statistics 1, and it limits which pairs you can take: there are ten allowed pairs in all. You can use a calculator in every Further Maths paper.

Formula booklet

AQA uses a larger Formulae and statistical tables booklet for Further Maths, with the statistical tables the options need. Edexcel's Mathematical Formulae and Statistical Tables booklet covers both Maths and Further Maths. The Maths formulae you had to memorise, such as the double angle formulae, still aren't given, so the A-level Maths guide list applies here too.

A-level Further Maths exam dates 2027

Every Further Maths paper is in the afternoon. Dates are from the timetables of AQA, Edexcel and OCR. A-level Maths falls on 26 May, 9 June and 16 June, so the two A-levels interleave. Results day is Thursday 12 August 2027 (JCQ).

A-level Further Maths grade boundaries

Boundaries are out of 300. AQA and Edexcel set different boundaries for each combination of options, while OCR set one overall boundary. These are from June 2026 (AQA, Edexcel and OCR).

Edexcel's boundaries depended on the option pair: an A* needed between 262 and 275 out of 300, and an A between 236 and 251. Boundaries differ between boards because the papers differ, so compare your marks with your own board's figures.

Worked examples from core pure

We wrote these questions for this guide.

Complex numbers in modulus-argument form

Question: write z = 1 + √3 i in modulus-argument form. Plot it first on an Argand diagram, with the real part across and the imaginary part up.

So z = 2(cos π/3 + i sin π/3). The diagram matters: for a point in another quadrant, tan⁻¹ alone gives the wrong angle, so always check where z lies. Explore it in the Complex Numbers Calculator.

Matrices and simultaneous equations

The matrix with rows (3, 2) and (5, 4) has determinant 3 × 4 − 2 × 5 = 2, which isn't zero, so it has an inverse: ½ times the matrix with rows (4, −2) and (−5, 3). Multiplying by that inverse solves the pair of equations 3x + 2y = a, 5x + 4y = b in one step. A zero determinant would mean no unique solution. Check with the Matrix Calculator, then solve a pair yourself from our Algebra course and press Mark.

Proof by induction

Question: prove that the sum of the first n odd numbers is n².

1. Basis: for n = 1 the sum is 1 and 1² = 1, so it is true.
2. Assumption: suppose the result holds when n = k, meaning 1 + 3 + ... + (2k − 1) = k².
3. Inductive step: add the next odd number, 2k + 1, to get k² + 2k + 1 = (k + 1)². That is the result with k + 1 in place of n.
4. Conclusion: the result holds for n = 1, and whenever it holds for one value it holds for the next, so it holds for every positive integer n.

The conclusion sentence earns a mark on its own, so write it in full every time.

Common A-level Further Maths mistakes

• Arguments in the wrong quadrant. Sketch the Argand diagram before using tan⁻¹.
• Matrix order. AB is not usually BA, and (AB)⁻¹ = B⁻¹A⁻¹.
• A thin induction conclusion. State the basis, the assumption, the step and the conclusion.
• Leaving out the constant in a differential equation, or applying the initial condition too early.
• Calculator answers to "show that" questions. Every step must be on the page.

Use a daily paper as a short timed mock

Year 13 mocks run through the winter. Between them, sit today's Further Maths paper, and keep your single maths sharp with the Calculus paper. For how to sit a full paper at home and grade it, see the A-level Maths mocks guide.

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