OCR AS Level Further Mathematics A
Y531/01 Combined Question paper &
Marking Scheme A+ May 2025
Oxford Cambridge and RSA
Monday 12 May 2025 – Afternoon
AS Level Further Mathematics A
Y531/01 Pure Core
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for AS Level Further
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 page 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 g m s–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 60.
• The marks for each question are shown in brackets [ ].
• This document has 4 pages.
ADVICE
• Read each question carefully before you start your answer.
Turn over
, 2
1 (a) The complex number z is such that z = 7 and arg (z) = 2.2 radians.
Express z in cartesian form. [3]
(b) Use an algebraic method to determine the exact square roots of 1 +^4 3hi. [5]
J 2N J N
K O K -4 O
2 Two vectors, a and b, are given by a = K O d b = K O here p is a constant.
-K3 Oan 6 w
13 K pO
L P L P
(a) Find expressions in terms of p for each of the following.
• a.b
• a# b
[3]
(b) Hence or otherwise find the value of p in each of the following cases.
• a and b are perpendicular
• a and b are parallel
[2]
3 The roots of the equation 2x2 + 3x + 5 = 0 are denoted by a and b.
(a) Write down the value of a + b and the value of ab. [2]
(b) Using the answers to part (a) determine the value of each of the following.
• a2 + b2
• a1 + 1b
[4]
© OCR 2025 Y531/01 Jun25
, 3
4 Two transformations, TA and TB, are represented by matrices A and B respectively.
J0 1N
The matrix A is given by A = K .
1 0O
L P
(a) (i) Describe the transformation TA. [1]
(ii) Explain geometrically why A-1 = A. [1]
1 J 1 - 3N
The matrix B is given by B = K O.
2L 3 1 P
(b) Describe the transformation TB. [2]
The transformation TC is equivalent to TA followed by TB.
(c) Determine the single matrix which represents TC. [2]
5 The locus L is defined by L = "z | z e C, z - (20 + 15i) ≤ 7,.
(a) On the Argand diagram in the Printed Answer Booklet, sketch and label L. [2]
(b) Determine the value of z e L for which the value of z is smallest. Give your answer in
cartesian form. [3]
(c) Determine the largest value of arg(z) for z e L. [3]
J 16N J 2N J 3N J 1N
6 The equations of two lines, l and l , are l r
| K O K O K O+ n K O.
= -1 + m K -27 and l2 | r = 10
K 10OO
1 2 1
K O K O K O
3 -19
L P L P L-10P L10P
(a) Show that l1 and l2 intersect at a single point, P, giving the coordinates of P. [5]
O is the origin of the coordinate system. The point Q lies on the line segment OP.
(b) Comment on the claim that the distance OQ is less than 100. [2]
© OCR 2025 Y531/01 Jun25 Turn over
Y531/01 Combined Question paper &
Marking Scheme A+ May 2025
Oxford Cambridge and RSA
Monday 12 May 2025 – Afternoon
AS Level Further Mathematics A
Y531/01 Pure Core
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for AS Level Further
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 page 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 g m s–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 60.
• The marks for each question are shown in brackets [ ].
• This document has 4 pages.
ADVICE
• Read each question carefully before you start your answer.
Turn over
, 2
1 (a) The complex number z is such that z = 7 and arg (z) = 2.2 radians.
Express z in cartesian form. [3]
(b) Use an algebraic method to determine the exact square roots of 1 +^4 3hi. [5]
J 2N J N
K O K -4 O
2 Two vectors, a and b, are given by a = K O d b = K O here p is a constant.
-K3 Oan 6 w
13 K pO
L P L P
(a) Find expressions in terms of p for each of the following.
• a.b
• a# b
[3]
(b) Hence or otherwise find the value of p in each of the following cases.
• a and b are perpendicular
• a and b are parallel
[2]
3 The roots of the equation 2x2 + 3x + 5 = 0 are denoted by a and b.
(a) Write down the value of a + b and the value of ab. [2]
(b) Using the answers to part (a) determine the value of each of the following.
• a2 + b2
• a1 + 1b
[4]
© OCR 2025 Y531/01 Jun25
, 3
4 Two transformations, TA and TB, are represented by matrices A and B respectively.
J0 1N
The matrix A is given by A = K .
1 0O
L P
(a) (i) Describe the transformation TA. [1]
(ii) Explain geometrically why A-1 = A. [1]
1 J 1 - 3N
The matrix B is given by B = K O.
2L 3 1 P
(b) Describe the transformation TB. [2]
The transformation TC is equivalent to TA followed by TB.
(c) Determine the single matrix which represents TC. [2]
5 The locus L is defined by L = "z | z e C, z - (20 + 15i) ≤ 7,.
(a) On the Argand diagram in the Printed Answer Booklet, sketch and label L. [2]
(b) Determine the value of z e L for which the value of z is smallest. Give your answer in
cartesian form. [3]
(c) Determine the largest value of arg(z) for z e L. [3]
J 16N J 2N J 3N J 1N
6 The equations of two lines, l and l , are l r
| K O K O K O+ n K O.
= -1 + m K -27 and l2 | r = 10
K 10OO
1 2 1
K O K O K O
3 -19
L P L P L-10P L10P
(a) Show that l1 and l2 intersect at a single point, P, giving the coordinates of P. [5]
O is the origin of the coordinate system. The point Q lies on the line segment OP.
(b) Comment on the claim that the distance OQ is less than 100. [2]
© OCR 2025 Y531/01 Jun25 Turn over
