Oxford Cambridge and RSA
May 2026 – Afternoon
A Level Further Mathematics A
Y540/01 Pure Core 1
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different degree
of accuracy is specified in the question.
• The acceleration due to gravity is denoted by gms–2. When a numerical value is needed
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR A Level Further Mathematics A Pure Core (Y540/01)
Question Paper And Mark Scheme
, 2
J5 0N
1 (a) A matrix M is given by M = K 0 5O.
L P
Describe the transformation represented by M. [2]
(b) Write down the 2 # 2 matrix that represents a rotation of 90° anticlockwise about the origin.
[1]
(c) Write down the 3 # 3 matrix that represents a reflection in the x–z plane. [1]
dy
2 (a) Given that y = cosh-1b1 xl, find in terms of x. [1]
3 dx
(b) Determine an equation of the normal to the curve y = cosh-13 b1 xl at the point where x = 5.
Give your answer in the form ax + by = c +ln d , where a, b, c and d are integers. [4]
, 3
80
3 The region R1 is bounded by the curve y = , the line x = k and the coordinate axes,
shown in Fig. 1.
Fig. 1
y
R1
O x
x=k
(a) In this question you must show detailed reasoning.
40
Given that the area of is r, determine the value of k. [3]
R1
3
80
The region R is bounded by the curve y = , the line y = 20 and the y-axis as shown in
2
Fig. 2.
Fig. 2
y
y = 20
R2
O x
(b) Find, in an exact form, the volume of the solid formed when R2 is rotated by 2r radians
Turn over
May 2026 – Afternoon
A Level Further Mathematics A
Y540/01 Pure Core 1
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a different degree
of accuracy is specified in the question.
• The acceleration due to gravity is denoted by gms–2. When a numerical value is needed
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 75.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer.
OCR A Level Further Mathematics A Pure Core (Y540/01)
Question Paper And Mark Scheme
, 2
J5 0N
1 (a) A matrix M is given by M = K 0 5O.
L P
Describe the transformation represented by M. [2]
(b) Write down the 2 # 2 matrix that represents a rotation of 90° anticlockwise about the origin.
[1]
(c) Write down the 3 # 3 matrix that represents a reflection in the x–z plane. [1]
dy
2 (a) Given that y = cosh-1b1 xl, find in terms of x. [1]
3 dx
(b) Determine an equation of the normal to the curve y = cosh-13 b1 xl at the point where x = 5.
Give your answer in the form ax + by = c +ln d , where a, b, c and d are integers. [4]
, 3
80
3 The region R1 is bounded by the curve y = , the line x = k and the coordinate axes,
shown in Fig. 1.
Fig. 1
y
R1
O x
x=k
(a) In this question you must show detailed reasoning.
40
Given that the area of is r, determine the value of k. [3]
R1
3
80
The region R is bounded by the curve y = , the line y = 20 and the y-axis as shown in
2
Fig. 2.
Fig. 2
y
y = 20
R2
O x
(b) Find, in an exact form, the volume of the solid formed when R2 is rotated by 2r radians
Turn over
