Is AQA A-Level Further Maths 2027 Predicted Practice Paper — Paper 2 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 is the A-Level Further Mathematics Paper 2 format (7367/2)?

A-Level Further Mathematics Paper 2 (7367/2) is 100 marks over 120 minutes. 7367/2 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 2 predicted-practice paper modelled on 7367/2,100 marks over 120 minutes. Predicted focus topics: complex-numbers-de-moivre, matrices-and-transformations, hyperbolic-functions, differential-equations, 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: 7367/2
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 2

Q: What are the A-Level Further Mathematics Paper 2 predictions for 2027?

StudyVector's 2027 A-Level Further Mathematics Paper 2 predicted paper focuses on complex-numbers-de-moivre, matrices-and-transformations, hyperbolic-functions, differential-equations, polar-coordinates, further-vectors. This is an independent, AQA-style predicted-practice paper modelled on the published specification — it is not a leaked paper and is not official.

Q: Which topics are likely to come up in A-Level Further Mathematics Paper 2 2027?

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

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

Modelled component: 7367/2 · Calculator permitted

7367/2 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
differential-equations
polar-coordinates
further-vectors

Preview mode

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

120:00Warm up with cards Play Daily

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 (7 marks)
The complex number z = 2 + 2*sqrt(3)*i. (a) Express z in modulus-argument form r(cos(theta) + i*sin(theta)), giving r exactly and theta in radians in terms of pi. [3 marks] (b) Hence use de Moivre's theorem to find z^4, giving your answer in the form a + b*i with a and b exact. [4 marks]
(Total for Question SECTION-A1 is 7 marks)
Question SECTION-A2 (7 marks)
The 2x2 matrix M = [[3, 1], [2, 4]] represents a linear transformation of the plane. (a) Find the eigenvalues of M. [3 marks] (b) Find an eigenvector corresponding to the larger eigenvalue. [2 marks] (c) State the geometrical significance of the eigenvectors of M under the transformation. [2 marks]
(Total for Question SECTION-A2 is 7 marks)
Question SECTION-A3 (7 marks)
(a) Show that d/dx (arcosh(x)) = 1/sqrt(x^2 - 1) for x > 1, by writing y = arcosh(x) and differentiating x = cosh(y). [4 marks] (b) Hence evaluate the integral of 1/sqrt(x^2 - 1) with respect to x from x = 1 to x = 2, giving your answer in the form ln(a + sqrt(b)). [3 marks]
(Total for Question SECTION-A3 is 7 marks)
Question SECTION-A4 (7 marks)
(a) Find the general solution of the differential equation d^2y/dx^2 - 4*dy/dx + 13*y = 0. Express your answer in real form. [4 marks] (b) Given that y = 0 when x = 0 and dy/dx = 6 when x = 0, find the particular solution. [3 marks]
(Total for Question SECTION-A4 is 7 marks)
Question SECTION-A5 (7 marks)
The curve C has polar equation r = 3 + 2*cos(theta) for 0 <= theta < 2*pi. (a) Find, in exact form, the area of the region enclosed by C. [You may use the result that the integral of cos^2(theta) over a full period 0 to 2*pi equals pi.] [5 marks] (b) State the maximum value of r and the value of theta at which it occurs. [2 marks]
(Total for Question SECTION-A5 is 7 marks)
Question SECTION-A6 (7 marks)
Use the method of differences to find a simplified expression for the sum from r = 1 to n of 1/(r(r+1)). (a) Show that 1/(r(r+1)) = 1/r - 1/(r+1). [2 marks] (b) Hence find the sum in terms of n and state its limit as n tends to infinity. [5 marks]
(Total for Question SECTION-A6 is 7 marks)
Question SECTION-A7 (8 marks)
The points A, B and C have position vectors a = i + 2j + k, b = 3i + j - k and c = 2i + 4j + 3k respectively. (a) Find the vectors AB and AC. [2 marks] (b) Find AB x AC (the vector product). [3 marks] (c) Hence find the exact area of triangle ABC. [3 marks]
(Total for Question SECTION-A7 is 8 marks)
Question SECTION-A8 (7 marks)
(a) Prove by induction that for all positive integers n, the sum from r = 1 to n of r*2^r = (n - 1)*2^(n+1) + 2. [6 marks] (b) Hence state the value of the sum from r = 1 to 5 of r*2^r. [1 mark]
(Total for Question SECTION-A8 is 7 marks)

Section B

Extended multi-part questions. Answer ALL questions.

Question SECTION-B1 (15 marks)
The cubic equation 2*x^3 - 5*x^2 + 4*x - 7 = 0 has roots 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) Find the value of alpha^2 + beta^2 + gamma^2. [3 marks] (c) Find the value of 1/alpha + 1/beta + 1/gamma. [2 marks] (d) Find a cubic equation, with integer coefficients, whose roots are 2*alpha, 2*beta and 2*gamma. [4 marks] (e) Hence, or otherwise, state the sum of the roots of the equation found in part (d). [3 marks]
(Total for Question SECTION-B1 is 15 marks)
Question SECTION-B2 (14 marks)
A curve is defined by the parametric equations x = 2*cosh(t), y = 3*sinh(t) for t >= 0. (a) Show that the curve satisfies the Cartesian equation x^2/4 - y^2/9 = 1. [3 marks] (b) Find dy/dx in terms of t. [3 marks] (c) Find the exact equation of the tangent to the curve at the point where t = ln(2), giving your answer in the form y = m*x + c with m and c exact. [5 marks] (d) The finite arc of the curve from t = 0 to t = 1 is rotated 2*pi radians about the x-axis. Write down (but do not evaluate) the definite integral, in terms of t, that gives the surface area generated. [3 marks]
(Total for Question SECTION-B2 is 14 marks)
Question SECTION-B3 (14 marks)
(a) Express the complex number w = -2 + 2*i in modulus-argument form. [3 marks] (b) Solve the equation z^3 = w, giving the three roots z_0, z_1, z_2 in modulus-argument form with arguments in the interval (-pi, pi]. [6 marks] (c) Show that the three roots lie on a circle in the Argand diagram, stating its radius, and find the sum z_0 + z_1 + z_2. [5 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

7367/2

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 2

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

Modelled component: 7367/2 · Calculator permitted

7367/2 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 (7 marks)

The complex number z = 2 + 2*sqrt(3)*i. (a) Express z in modulus-argument form r(cos(theta) + i*sin(theta)), giving r exactly and theta in radians in terms of pi. [3 marks] (b) Hence use de Moivre's theorem to find z^4, giving your answer in the form a + b*i with a and b exact. [4 marks]

(Total for Question SECTION-A1 is 7 marks)

Question SECTION-A2 (7 marks)

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

(Total for Question SECTION-A2 is 7 marks)

Question SECTION-A3 (7 marks)

(a) Show that d/dx (arcosh(x)) = 1/sqrt(x^2 - 1) for x > 1, by writing y = arcosh(x) and differentiating x = cosh(y). [4 marks] (b) Hence evaluate the integral of 1/sqrt(x^2 - 1) with respect to x from x = 1 to x = 2, giving your answer in the form ln(a + sqrt(b)). [3 marks]

(Total for Question SECTION-A3 is 7 marks)

Question SECTION-A4 (7 marks)

(a) Find the general solution of the differential equation d^2y/dx^2 - 4*dy/dx + 13*y = 0. Express your answer in real form. [4 marks] (b) Given that y = 0 when x = 0 and dy/dx = 6 when x = 0, find the particular solution. [3 marks]

(Total for Question SECTION-A4 is 7 marks)

Question SECTION-A5 (7 marks)

The curve C has polar equation r = 3 + 2*cos(theta) for 0 <= theta < 2*pi. (a) Find, in exact form, the area of the region enclosed by C. [You may use the result that the integral of cos^2(theta) over a full period 0 to 2*pi equals pi.] [5 marks] (b) State the maximum value of r and the value of theta at which it occurs. [2 marks]

(Total for Question SECTION-A5 is 7 marks)

Question SECTION-A6 (7 marks)

Use the method of differences to find a simplified expression for the sum from r = 1 to n of 1/(r(r+1)). (a) Show that 1/(r(r+1)) = 1/r - 1/(r+1). [2 marks] (b) Hence find the sum in terms of n and state its limit as n tends to infinity. [5 marks]

(Total for Question SECTION-A6 is 7 marks)

Question SECTION-A7 (8 marks)

The points A, B and C have position vectors a = i + 2j + k, b = 3i + j - k and c = 2i + 4j + 3k respectively. (a) Find the vectors AB and AC. [2 marks] (b) Find AB x AC (the vector product). [3 marks] (c) Hence find the exact area of triangle ABC. [3 marks]

(Total for Question SECTION-A7 is 8 marks)

Question SECTION-A8 (7 marks)

(a) Prove by induction that for all positive integers n, the sum from r = 1 to n of r*2^r = (n - 1)*2^(n+1) + 2. [6 marks] (b) Hence state the value of the sum from r = 1 to 5 of r*2^r. [1 mark]

(Total for Question SECTION-A8 is 7 marks)

Section B

Extended multi-part questions. Answer ALL questions.

Question SECTION-B1 (15 marks)

The cubic equation 2*x^3 - 5*x^2 + 4*x - 7 = 0 has roots 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) Find the value of alpha^2 + beta^2 + gamma^2. [3 marks] (c) Find the value of 1/alpha + 1/beta + 1/gamma. [2 marks] (d) Find a cubic equation, with integer coefficients, whose roots are 2*alpha, 2*beta and 2*gamma. [4 marks] (e) Hence, or otherwise, state the sum of the roots of the equation found in part (d). [3 marks]

(Total for Question SECTION-B1 is 15 marks)

Question SECTION-B2 (14 marks)

A curve is defined by the parametric equations x = 2*cosh(t), y = 3*sinh(t) for t >= 0. (a) Show that the curve satisfies the Cartesian equation x^2/4 - y^2/9 = 1. [3 marks] (b) Find dy/dx in terms of t. [3 marks] (c) Find the exact equation of the tangent to the curve at the point where t = ln(2), giving your answer in the form y = m*x + c with m and c exact. [5 marks] (d) The finite arc of the curve from t = 0 to t = 1 is rotated 2*pi radians about the x-axis. Write down (but do not evaluate) the definite integral, in terms of t, that gives the surface area generated. [3 marks]

(Total for Question SECTION-B2 is 14 marks)

Question SECTION-B3 (14 marks)

(a) Express the complex number w = -2 + 2*i in modulus-argument form. [3 marks] (b) Solve the equation z^3 = w, giving the three roots z_0, z_1, z_2 in modulus-argument form with arguments in the interval (-pi, pi]. [6 marks] (c) Show that the three roots lie on a circle in the Argand diagram, stating its radius, and find the sum z_0 + z_1 + z_2. [5 marks]

(Total for Question SECTION-B3 is 14 marks)