Matrix Transformations (all calculations restricted to 2x2 or 2x1 matrices) questions

Practice questions covering matrix transformations (all calculations restricted to 2x2 or 2x1 matrices) from this specification. Every question below is the real AQA question as it is printed on the paper, with its mark scheme.

Questions to attempt

6 questions on Matrix Transformations (all calculations restricted to 2x2 or 2x1 matrices), each with its mark scheme and worked method. Reveal the answer when you have had a go.

M1 · Multiplication of matrices (2x2 by 2x2 or by 2x1), and multiplication by a scalar
Q1
ORIGINAL
1
Work out $\begin{pmatrix}2&-1\\3&4\end{pmatrix}\begin{pmatrix}5\\-2\end{pmatrix}$ .
[2 marks]
M1 · Multiplication of matrices (2x2 by 2x2 or by 2x1), and multiplication by a scalar
Q2
ORIGINAL
2
Work out $3\begin{pmatrix}2&-1\\0&4\end{pmatrix}$ .
[1 mark]
M2 · The identity matrix I (2x2 only)
Q3
ORIGINAL
3
Let $A=\begin{pmatrix}2&-3\\5&1\end{pmatrix}$ . Work out both $AI$ and $IA$ .
[2 marks]
M2 · The identity matrix I (2x2 only)
Q4
ORIGINAL
4
Write down the $2\times2$ identity matrix $I$ .
[1 mark]
M3 · Transformations of the unit square in the x-y plane, represented by a 2x2 matrix (rotations of 90/180/270 about the origin, reflections in x=0, y=0, y=x, y=-x, enlargements centred on the origin)
Q5
ORIGINAL
5
Describe geometrically the single transformation represented by $\begin{pmatrix}-1&0\\0&1\end{pmatrix}$ and work out the image of $(4,-3)$ .
[3 marks]
M4 · Combination of transformations using matrix multiplication
Q6
ORIGINAL
6
Matrix $A$ rotates points $90^\circ$ anticlockwise about the origin. Matrix $B$ reflects points in the $x$ -axis. Transformation $A$ acts before transformation $B$ . Work out the combined matrix and describe its effect.
[3 marks]

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Printable question pack — M Matrix Transformations (all calculations restricted to 2x2 or 2x1 matrices)All 40 questions across 4 specification points — 34 more than the 6 above — with the full mark scheme. Guest accessible · browser print.

M Matrix Transformations (all calculations restricted to 2x2 or 2x1 matrices) revision notes

Real past-paper questions

9 questions shown as printed, 3 reference-only · newest series first

Question and mark-scheme extracts © AQA. Reproduced for educational use; the original paper is linked on every question. Contact hello@oscarsongtutoring.co.uk for removal.

AQA 8365 · June 2025 · Paper 1 · Q2 · 2 marks
2 marks
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Examiner report
This question was very well answered. Most errors were arithmetic with most students being able to correctly multiply matrices.
Text version
A matrix product is equal to a scalar multiple of a column vector: [[5, 0], [1, -6]] [12, 7]^T = 15[a, b]^T.
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AQA 8365 · June 2024 · Paper 1 · Q7 · 3 marks
3 marks
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Examiner report
Some students write the left-hand side correctly but don’t write the right-hand side. This could be recovered for M2 by writing the equations but didn’t qualify for M1 on its own. A number of students wrote the matrices in the wrong order which once again could be recovered but in most cases wasn’t. There were a number of special cases for this question. There was merit in multiplying the 2×2 matrix by (–8, 7) and if this was done correctly it gained SC1.
Text version
A point P(x, y) is transformed by the matrix [[4, 0], [-2, 3]]. Its image is (-8, 7).
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AQA 8365 · June 2024 · Paper 1 · Q15 · 3 marks
3 marks
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Examiner report
Parts a and b were marked together as some students drew diagrams that could overlap the space on the page. Part a was generally done well although some students put –1 instead of 0 and 0 instead of –1. Part b provided a range of answers. Many students just wrote down the correct answer whilst others preferred to find N2 first. A small number of students wrote down the transformation of N which was given the benefit of the doubt that this was the first part of their working rather than their final answer. Too many students lost the A mark for not stating the rotation or enlargement was about the origin or wrote it was round the centre.
Text version
This question concerns transformations represented by matrices.
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AQA 8365 · June 2023 · Paper 1 · Q3 · 3 marks
3 marks
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Examiner report
[3b] There are clearly some centres still not teaching the matrices topics judging by the number of non- attempts to this question. Those that did attempt the question usually made a good job of it. Some candidates lost the second mark due to not stating the identity matrix.
Text version
This question concerns transformation matrices and matrix multiplication.
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AQA 8365 · June 2023 · Paper 2 · Q3 · 2 marks
2 marks
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Examiner report
The vast majority of students managed to correctly multiply out the matrices and accurately solve for u. An incorrect method sometimes seen was working out t = 3 × 1 + 5 × 1 and 4u + 8 = 6.
Text version
[[3,5],[u,2]] [1,4]^T = [t,6]^T.
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AQA 8365 · June 2022 · Paper 1 · Q8 · 3 marks
3 marks
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Examiner report
Most of the answers that gained 2 marks came from SC2. The first mark was intentionally generous. A small number of students managed to show the transformations correctly using a unit square but there were also quite a few that tried to just use one point for the transformations. These students could still gain full marks by showing the matrix multiplication but in the majority of cases they only scored 1 mark.
Text version
In the x-y plane, a rotation of 90 degrees anticlockwise about the origin is followed by a reflection in y=x.
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AQA 8365 · November 2021 · Paper 1 · Q11 · 4 marks
4 marks
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Text version
The matrix product [[2,1],[0,3]][[a,b],[0,0.4]] equals [[k,0],[0,k]], where a, b and k are constants.
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AQA 8365 · November 2021 · Paper 2 · Q14 · 3 marks
3 marks
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Text version
Describe the transformations represented by the matrices.
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AQA 8365 · sample1 · Paper 2 · Q6 · 4 marks
4 marks
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Text version
A=[[4,-1],[-7,2]], B=[[s],[-5]], C=[[-1],[t]] and D=[[2,1],[7,u]], where s, t and u are constants.
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References open the specific AQA question paper when it is available. Missing, login-only or unverified question-paper sources are labelled on the affected row. Question content remains on the exam board's website.

June 20251 question

Paper 2 · Q124 marks · Calculator · calculate · standardView question in paper (p.12)Mark scheme (p.17)

June 20241 question

Paper 2: Q5 (p.5, 4 marks)

June 20221 question

Paper 2: Q3 (p.3, 6 marks)

Question extracts are shown for study alongside a link to the original AQA paper. Reference-only rows carry series, paper, question number and marks.

Matrix Transformations (all calculations restricted to 2x2 or 2x1 matrices) questions

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