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OCR A Level Further Maths

Topic questions Pure mathematics Matrix arithmetic

Matrix arithmetic

5 questions · 30 marks · about 35 minutes

Matrix arithmetic questions

TopicMatrix arithmetic

OCR H245 Matrix arithmetic 5 questions

Pure Core 1 June 2024, Question 3 8 marks

Question 3, shown as an image
(a)

Find N2 in terms of a.

[3]
Reveal mark scheme Mark scheme for question 3(a)
(b)

Find det N in terms of a.

[2]
Reveal mark scheme Mark scheme for question 3(b)
(c)
Figure for question 3
[3]
Reveal mark scheme Mark scheme for question 3(c)

Pure Core 2 June 2023, Question 1 8 marks

(a)
1 Question 1, shown as an image
(a)(i)
Figure for question 1
[1]
Reveal mark scheme Mark scheme for question 1(a)(i)
(a)(ii)

Write down the transpose of P.

[1]
Reveal mark scheme Mark scheme for question 1(a)(ii)
(b)
Figure for question 1
[1]
Reveal mark scheme Mark scheme for question 1(b)
(c)

The dimensions of matrix A are 4 by 5. The matrices A and B are conformable for multiplication so that the matrix C = BA can be formed. The matrix C has 6 rows.

(c)(i)

Write down the number of columns that C has.

[1]
Reveal mark scheme Mark scheme for question 1(c)(i)
(c)(ii)

Write down the dimensions of B.

[1]
Reveal mark scheme Mark scheme for question 1(c)(ii)
(c)(iii)

Explain whether the matrix AB can be formed.

[1]
Reveal mark scheme Mark scheme for question 1(c)(iii)
(d)
Figure for question 1
[2]
Reveal mark scheme Mark scheme for question 1(d)

Pure Core 2 November 2021, Question 9 6 marks

Figure for question 9
(a)

By considering A, A2, A3 and A4 make a conjecture about the form of the matrix An in terms

of n for n ⩾ 1.

[2]
Reveal mark scheme Mark scheme for question 9(a)
(b)

Use induction to prove the conjecture made in part (a).

[4]
Reveal mark scheme Mark scheme for question 9(b)

Pure Core 1 November 2020, Question 3 5 marks

Figure for question 3
(a)

Find A4.

[1]
Reveal mark scheme Mark scheme for question 3(a)
(b)

Describe the transformation that A represents.

[2]
Reveal mark scheme Mark scheme for question 3(b)
(c)

The matrix B represents a reflection in the plane x = 0.

Write down the matrix B.

[1]
Reveal mark scheme Mark scheme for question 3(c)
(d)

The point P has coordinates (2, 3, 4). The point P ′ is the image of P under the transformation represented by B.

Find the coordinates of P ′.

[1]
Reveal mark scheme Mark scheme for question 3(d)

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Prove it by induction
Write ‘clearly’ and move on
Me on the final ‘show that’
Using the formula booklet
Proving it by induction
Writing ‘by symmetry’ to skip half the work
Writing ‘trivially’ and daring the examiner
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