Is AQA A-Level Further Maths 2027 Predicted Practice Paper — Paper 1 an official exam paper?

No. It is an original StudyVector predicted-practice paper for revision. It is not official, leaked or guaranteed, and students should still revise the full specification.

How many marks and questions are in this predicted paper?

This paper has 100 marks across 11 questions and is designed for a 120-minute practice session.

What are the A-Level Further Mathematics Paper 1 predictions for 2027?

StudyVector's 2027 A-Level Further Mathematics Paper 1 predicted paper focuses on complex-numbers-de-moivre, matrices-and-transformations, hyperbolic-functions, proof-by-induction, polar-coordinates, differential-equations. This is an independent, AQA-style predicted-practice paper modelled on the published specification — it is not a leaked paper and is not official.

What is the A-Level Further Mathematics Paper 1 format (7367/1)?

A-Level Further Mathematics Paper 1 (7367/1) is 100 marks over 120 minutes. 7367/1 model: 100 marks, 120 minutes.

Published 8 March 2026Updated 22 April 2026By Lizzie D., founderPrivacy Policy

Source note: use official specifications as the source of truth. StudyVector is an independent revision platform. AQA, Pearson Edexcel and OCR

Direct answer

This page hosts StudyVector’s independent 2027 A-Level Further Mathematics Paper 1 predicted-practice paper modelled on 7367/1,100 marks over 120 minutes. Predicted focus topics: complex-numbers-de-moivre, matrices-and-transformations, hyperbolic-functions, proof-by-induction, polar-coordinates. It is not an official paper, not a leaked paper and not a guarantee — students should still revise the full specification and verify against official past papers from AQA.

Qualification: A-Level Further Mathematics
Exam board model: AQA
Paper code: 7367/1
Total marks: 100 marks
Time allowed: 120 minutes
Last reviewed: 16 May 2026

StudyVector is independent revision support, not affiliated with AQA, Edexcel, OCR, JCQ or any exam provider. Always verify topic coverage with your exam-board specification.

Predicted paper

AQA A-Level Further Maths 2027 Predicted Practice Paper — Paper 1

Q: Which topics are likely to come up in A-Level Further Mathematics Paper 1 2027?

Based on the AQA-style structure and recent paper patterns, StudyVector's prediction prioritises: complex-numbers-de-moivre; matrices-and-transformations; hyperbolic-functions; proof-by-induction; polar-coordinates; differential-equations. Students should still revise the full specification because exam boards rotate topics.

A-Level Further Mathematics · AQA-style · 120 minutes · 100 marks

Modelled component: 7367/1 · Calculator permitted

7367/1 model: 100 marks, 120 minutes.

Prediction type: predicted_paper · Evidence mode: historical · Full-length original StudyVector predicted-practice paper modelled on public exam-board structure. It is not official, leaked or guaranteed.

Evidence basis: public exam-board specification structure, historical topic weighting patterns, StudyVector practice-quality review.

AI-generated practice paper. Not an official AQA-style paper, not leaked exam content, and not an exam-board endorsement.

Predicted difficulty score (practice signal)

0–100 model (higher = more demanding)

Candidate focus topics (not guarantees)

complex-numbers-de-moivre
matrices-and-transformations
hyperbolic-functions
proof-by-induction
polar-coordinates
differential-equations

Preview mode

0/11 questions attempted · score 0/100 (0%)

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Answer ALL questions. Write your answers in the spaces provided. You must write down all the stages in your working.

Section A

Short and medium-length questions. Answer ALL questions.

Question SECTION-A1 (8 marks)
The complex number z = 2 + 2i. (a) Express z in modulus-argument (polar) form, giving the argument in radians in terms of pi. [3 marks] (b) Hence use de Moivre's theorem to find z^5, giving your answer in the form a + bi where a and b are integers. [5 marks]
(Total for Question SECTION-A1 is 8 marks)
Question SECTION-A2 (7 marks)
Prove by mathematical induction that for all positive integers n, sum from r=1 to n of r(r+2) = (n/6)(n+1)(2n+7).
(Total for Question SECTION-A2 is 7 marks)
Question SECTION-A3 (6 marks)
The 2x2 matrix M = [[3, 1], [2, 4]] represents a transformation of the plane. (a) Find the eigenvalues of M. [3 marks] (b) Find an eigenvector corresponding to the larger eigenvalue. [3 marks]
(Total for Question SECTION-A3 is 6 marks)
Question SECTION-A4 (7 marks)
(a) Given that cosh(x) = (e^x + e^-x)/2 and sinh(x) = (e^x - e^-x)/2, prove the identity cosh^2(x) - sinh^2(x) = 1. [3 marks] (b) Solve the equation 3cosh(x) - sinh(x) = 3, giving your answer(s) as exact logarithms or stating x = 0 where appropriate. [4 marks]
(Total for Question SECTION-A4 is 7 marks)
Question SECTION-A5 (6 marks)
The roots of the cubic equation 2x^3 - 5x^2 + 4x - 7 = 0 are alpha, beta and gamma. (a) Write down the values of alpha + beta + gamma, alpha*beta + beta*gamma + gamma*alpha, and alpha*beta*gamma. [3 marks] (b) Hence find the value of alpha^2 + beta^2 + gamma^2. [3 marks]
(Total for Question SECTION-A5 is 6 marks)
Question SECTION-A6 (8 marks)
A curve has polar equation r = 3(1 + cos(theta)) for 0 <= theta < 2pi (a cardioid). (a) State the maximum value of r and the value of theta at which it occurs. [2 marks] (b) Find the area of the region enclosed by the cardioid, using the formula A = (1/2) integral of r^2 dtheta. Give your answer as an exact multiple of pi. [6 marks]
(Total for Question SECTION-A6 is 8 marks)
Question SECTION-A7 (7 marks)
(a) Find the general solution of the differential equation dy/dx + 2y = 6, giving y in terms of x. [4 marks] (b) Given that y = 5 when x = 0, find the particular solution and state the limiting value of y as x tends to infinity. [3 marks]
(Total for Question SECTION-A7 is 7 marks)
Question SECTION-A8 (8 marks)
The points A, B and C have position vectors a = (1, 0, 2), b = (3, 1, -1) and c = (2, 4, 1) respectively. (a) Find the vector AB and the vector AC. [2 marks] (b) Find AB x AC (the vector/cross product). [3 marks] (c) Hence find the area of triangle ABC, giving your answer to 3 significant figures. [3 marks]
(Total for Question SECTION-A8 is 8 marks)

Section B

Extended multi-part questions. Answer ALL questions.

Question SECTION-B1 (14 marks)
This question concerns the matrix A = [[2, 0, 1], [0, 3, -1], [1, 0, 2]]. (a) Find the determinant of A. [3 marks] (b) Determine whether A is singular or non-singular, justifying your answer. [1 mark] (c) Find the inverse matrix A^-1. [7 marks] (d) Hence, or otherwise, solve the system of simultaneous equations: 2x + z = 5 3y - z = 1 x + 2z = 4. [3 marks]
(Total for Question SECTION-B1 is 14 marks)
Question SECTION-B2 (15 marks)
The complex number w satisfies w^4 = -8 + 8sqrt(3) i. (a) Express -8 + 8sqrt(3) i in modulus-argument form. [3 marks] (b) Find all four roots w of the equation w^4 = -8 + 8sqrt(3) i, giving each in the form r(cos(theta) + i sin(theta)) with -pi < theta <= pi. [8 marks] (c) Show that the four roots lie on a circle in the Argand diagram and state its radius. [2 marks] (d) State the geometric shape formed by joining the four roots in order, and explain briefly why. [2 marks]
(Total for Question SECTION-B2 is 15 marks)
Question SECTION-B3 (14 marks)
A particle moves so that its displacement x metres from the origin at time t seconds satisfies the differential equation d^2x/dt^2 + 4 dx/dt + 13x = 0. (a) Show that the auxiliary equation has complex roots and find them. [3 marks] (b) Find the general solution for x in terms of t. [3 marks] (c) Given that x = 2 and dx/dt = 0 when t = 0, find the particular solution. [6 marks] (d) State, with a reason, the long-term behaviour of x as t tends to infinity. [2 marks]
(Total for Question SECTION-B3 is 14 marks)

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Direct answer

Qualification

A-Level Further Mathematics

Exam board model

AQA

Paper code

7367/1

Total marks

100 marks

Time allowed

120 minutes

Last reviewed

16 May 2026

StudyVector is independent revision support, not affiliated with AQA, Edexcel, OCR, JCQ or any exam provider. Always verify topic coverage with your exam-board specification.

AQA A-Level Further Maths 2027 Predicted Practice Paper — Paper 1

A-Level Further Mathematics · AQA-style · 120 minutes · 100 marks

Modelled component: 7367/1 · Calculator permitted

7367/1 model: 100 marks, 120 minutes.

Evidence basis: public exam-board specification structure, historical topic weighting patterns, StudyVector practice-quality review.

Section A

Short and medium-length questions. Answer ALL questions.

Question SECTION-A1 (8 marks)

The complex number z = 2 + 2i. (a) Express z in modulus-argument (polar) form, giving the argument in radians in terms of pi. [3 marks] (b) Hence use de Moivre's theorem to find z^5, giving your answer in the form a + bi where a and b are integers. [5 marks]

(Total for Question SECTION-A1 is 8 marks)

Question SECTION-A2 (7 marks)

Prove by mathematical induction that for all positive integers n, sum from r=1 to n of r(r+2) = (n/6)(n+1)(2n+7).

(Total for Question SECTION-A2 is 7 marks)

Question SECTION-A3 (6 marks)

The 2x2 matrix M = [[3, 1], [2, 4]] represents a transformation of the plane. (a) Find the eigenvalues of M. [3 marks] (b) Find an eigenvector corresponding to the larger eigenvalue. [3 marks]

(Total for Question SECTION-A3 is 6 marks)

Question SECTION-A4 (7 marks)

(a) Given that cosh(x) = (e^x + e^-x)/2 and sinh(x) = (e^x - e^-x)/2, prove the identity cosh^2(x) - sinh^2(x) = 1. [3 marks] (b) Solve the equation 3cosh(x) - sinh(x) = 3, giving your answer(s) as exact logarithms or stating x = 0 where appropriate. [4 marks]

(Total for Question SECTION-A4 is 7 marks)

Question SECTION-A5 (6 marks)

The roots of the cubic equation 2x^3 - 5x^2 + 4x - 7 = 0 are alpha, beta and gamma. (a) Write down the values of alpha + beta + gamma, alpha*beta + beta*gamma + gamma*alpha, and alpha*beta*gamma. [3 marks] (b) Hence find the value of alpha^2 + beta^2 + gamma^2. [3 marks]

(Total for Question SECTION-A5 is 6 marks)

Question SECTION-A6 (8 marks)

A curve has polar equation r = 3(1 + cos(theta)) for 0 <= theta < 2pi (a cardioid). (a) State the maximum value of r and the value of theta at which it occurs. [2 marks] (b) Find the area of the region enclosed by the cardioid, using the formula A = (1/2) integral of r^2 dtheta. Give your answer as an exact multiple of pi. [6 marks]

(Total for Question SECTION-A6 is 8 marks)

Question SECTION-A7 (7 marks)

(a) Find the general solution of the differential equation dy/dx + 2y = 6, giving y in terms of x. [4 marks] (b) Given that y = 5 when x = 0, find the particular solution and state the limiting value of y as x tends to infinity. [3 marks]

(Total for Question SECTION-A7 is 7 marks)

Question SECTION-A8 (8 marks)

The points A, B and C have position vectors a = (1, 0, 2), b = (3, 1, -1) and c = (2, 4, 1) respectively. (a) Find the vector AB and the vector AC. [2 marks] (b) Find AB x AC (the vector/cross product). [3 marks] (c) Hence find the area of triangle ABC, giving your answer to 3 significant figures. [3 marks]

(Total for Question SECTION-A8 is 8 marks)

Section B

Extended multi-part questions. Answer ALL questions.

Question SECTION-B1 (14 marks)

This question concerns the matrix A = [[2, 0, 1], [0, 3, -1], [1, 0, 2]]. (a) Find the determinant of A. [3 marks] (b) Determine whether A is singular or non-singular, justifying your answer. [1 mark] (c) Find the inverse matrix A^-1. [7 marks] (d) Hence, or otherwise, solve the system of simultaneous equations: 2x + z = 5 3y - z = 1 x + 2z = 4. [3 marks]

(Total for Question SECTION-B1 is 14 marks)

Question SECTION-B2 (15 marks)

The complex number w satisfies w^4 = -8 + 8sqrt(3) i. (a) Express -8 + 8sqrt(3) i in modulus-argument form. [3 marks] (b) Find all four roots w of the equation w^4 = -8 + 8sqrt(3) i, giving each in the form r(cos(theta) + i sin(theta)) with -pi < theta <= pi. [8 marks] (c) Show that the four roots lie on a circle in the Argand diagram and state its radius. [2 marks] (d) State the geometric shape formed by joining the four roots in order, and explain briefly why. [2 marks]

(Total for Question SECTION-B2 is 15 marks)

Question SECTION-B3 (14 marks)

A particle moves so that its displacement x metres from the origin at time t seconds satisfies the differential equation d^2x/dt^2 + 4 dx/dt + 13x = 0. (a) Show that the auxiliary equation has complex roots and find them. [3 marks] (b) Find the general solution for x in terms of t. [3 marks] (c) Given that x = 2 and dx/dt = 0 when t = 0, find the particular solution. [6 marks] (d) State, with a reason, the long-term behaviour of x as t tends to infinity. [2 marks]

(Total for Question SECTION-B3 is 14 marks)