AQA AS Further Mathematics 7366/1
Paper 1 Mark Scheme June 2026,
Document Information
| Detail | Information |
|:|:|
| Exam Board | AQA |
| Qualification | AS Further Mathematics |
| Paper Code | 7366/1 |
| Paper Title | Paper 1 |
| Date | June 2026 |
| Total Pages | 28 (including question paper) |
| Question Types | Short answer, proof, problem-solving |
Assessment Overview
Paper 1 covers core AS Further Mathematics content across both compulsory topics:
| Topic Area | Approx. Weighting | Key Skills Tested |
|:|:|:|
| Complex Numbers | 20% | Operations, Argand diagram, roots of unity |
| Matrices | 20% | Multiplication, determinants, inverses, transformations |
| Further Algebra | 15% | Roots of polynomials, partial fractions |
| Further Calculus | 20% | Integration techniques, differential equations |
| Vectors | 15% | 3D vectors, dot/cross product |
| Proof | 10% | Induction, contradiction |
Section A – Short Answer Questions (40 marks)
Question 1 – Complex Numbers (4 marks)
The complex numbers \( z = 2 + 3i \) and \( w = 1 - i \) are given.
(a) Find \( z + \bar{w} \) in the form \( a + bi \). [2 marks]
Answer: \( z + \bar{w} = (2 + 3i) + (1 + i) = 3 + 4i \)
, (b) Find \( |z \times w| \). [2 marks]
Answer: \( |z \times w| = |z| \times |w| = \sqrt{2^2 + 3^2} \times \sqrt{1^2 + (-1)^2} = \sqrt{13}
\times \sqrt{2} = \sqrt{26} \)
Question 2 – Matrices (4 marks)
Given the matrix \( M = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \).
(a) Find the determinant of \( M \). [1 mark]
Answer: \( \det(M) = (2 \times 4) - (1 \times 3) = 8 - 3 = 5 \)
(b) Find the inverse matrix \( M^{-1} \). [3 marks]
Answer: \( M^{-1} = \frac{1}{5} \begin{pmatrix} 4 & -1 \\ -3 & 2 \end{pmatrix} = \begin{pmatrix}
\frac{4}{5} & -\frac{1}{5} \\ -\frac{3}{5} & \frac{2}{5} \end{pmatrix} \)
Question 3 – Roots of Polynomials (5 marks)
The cubic equation \( 2x^{3} + 5x^{2} - 4x + 3 = 0 \) has roots \( \alpha, \beta, \gamma \).
(a) Find \( \alpha + \beta + \gamma \). [1 mark]
Answer: \( \alpha + \beta + \gamma = -\frac{5}{2} \)
(b) Find \( \alpha\beta + \beta\gamma + \gamma\alpha \). [1 mark]
Answer: \( \alpha\beta + \beta\gamma + \gamma\alpha = \frac{-4}{2} = -2 \)
(c) Find \( \alpha\beta\gamma \). [1 mark]
Answer: \( \alpha\beta\gamma = -\frac{3}{2} \)
(d) Find \( \alpha^{2} + \beta^{2} + \gamma^{2} \). [2 marks]
Answer: \( \alpha^{2} + \beta^{2} + \gamma^{2} = (\alpha + \beta + \gamma)^{2} - 2(\alpha\beta
+ \beta\gamma + \gamma\alpha) = \left(-\frac{5}{2}\right)^{2} - 2(-2) = \frac{25}{4} + 4 =
\frac{25}{4} + \frac{16}{4} = \frac{41}{4} \)
Paper 1 Mark Scheme June 2026,
Document Information
| Detail | Information |
|:|:|
| Exam Board | AQA |
| Qualification | AS Further Mathematics |
| Paper Code | 7366/1 |
| Paper Title | Paper 1 |
| Date | June 2026 |
| Total Pages | 28 (including question paper) |
| Question Types | Short answer, proof, problem-solving |
Assessment Overview
Paper 1 covers core AS Further Mathematics content across both compulsory topics:
| Topic Area | Approx. Weighting | Key Skills Tested |
|:|:|:|
| Complex Numbers | 20% | Operations, Argand diagram, roots of unity |
| Matrices | 20% | Multiplication, determinants, inverses, transformations |
| Further Algebra | 15% | Roots of polynomials, partial fractions |
| Further Calculus | 20% | Integration techniques, differential equations |
| Vectors | 15% | 3D vectors, dot/cross product |
| Proof | 10% | Induction, contradiction |
Section A – Short Answer Questions (40 marks)
Question 1 – Complex Numbers (4 marks)
The complex numbers \( z = 2 + 3i \) and \( w = 1 - i \) are given.
(a) Find \( z + \bar{w} \) in the form \( a + bi \). [2 marks]
Answer: \( z + \bar{w} = (2 + 3i) + (1 + i) = 3 + 4i \)
, (b) Find \( |z \times w| \). [2 marks]
Answer: \( |z \times w| = |z| \times |w| = \sqrt{2^2 + 3^2} \times \sqrt{1^2 + (-1)^2} = \sqrt{13}
\times \sqrt{2} = \sqrt{26} \)
Question 2 – Matrices (4 marks)
Given the matrix \( M = \begin{pmatrix} 2 & 1 \\ 3 & 4 \end{pmatrix} \).
(a) Find the determinant of \( M \). [1 mark]
Answer: \( \det(M) = (2 \times 4) - (1 \times 3) = 8 - 3 = 5 \)
(b) Find the inverse matrix \( M^{-1} \). [3 marks]
Answer: \( M^{-1} = \frac{1}{5} \begin{pmatrix} 4 & -1 \\ -3 & 2 \end{pmatrix} = \begin{pmatrix}
\frac{4}{5} & -\frac{1}{5} \\ -\frac{3}{5} & \frac{2}{5} \end{pmatrix} \)
Question 3 – Roots of Polynomials (5 marks)
The cubic equation \( 2x^{3} + 5x^{2} - 4x + 3 = 0 \) has roots \( \alpha, \beta, \gamma \).
(a) Find \( \alpha + \beta + \gamma \). [1 mark]
Answer: \( \alpha + \beta + \gamma = -\frac{5}{2} \)
(b) Find \( \alpha\beta + \beta\gamma + \gamma\alpha \). [1 mark]
Answer: \( \alpha\beta + \beta\gamma + \gamma\alpha = \frac{-4}{2} = -2 \)
(c) Find \( \alpha\beta\gamma \). [1 mark]
Answer: \( \alpha\beta\gamma = -\frac{3}{2} \)
(d) Find \( \alpha^{2} + \beta^{2} + \gamma^{2} \). [2 marks]
Answer: \( \alpha^{2} + \beta^{2} + \gamma^{2} = (\alpha + \beta + \gamma)^{2} - 2(\alpha\beta
+ \beta\gamma + \gamma\alpha) = \left(-\frac{5}{2}\right)^{2} - 2(-2) = \frac{25}{4} + 4 =
\frac{25}{4} + \frac{16}{4} = \frac{41}{4} \)
