2O25 OCR A Level Further Mathematics B
(MEI) Y436/01 Further Pure with
Technology
Verified Question paper with Marking
Scheme combined
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
OCR A LEVEL given for using a correct method, even if your
answer is wrong.
FURTHER • Give your final answers to a degree of
accuracy that is appropriate to the context.
• Do not send this Question Paper for
MATHEMATICS B 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 [ ].
, Oxford Cambridge and RSA
Monday 23 June 2025 – Afternoon
A Level Further Mathematics B (MEI)
Y436/01 Further Pure with Technology
Time allowed: 1 hour 45 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI) QP
• a computer with appropriate software
• 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [K/508/5600] OCR is an exempt Charity
DC (PQ/FC) 352593/3 Turn over
, 2
1 A family of curves is given by the cartesian equation
x2 y2
+ mxy + =1
a2 b2
where a, b and m are real numbers with a and b non-zero.
(a) In this part of the question a = 2 and b = 1.
(i) On the axes in the Printed Answer Booklet, sketch the curve in each of these cases.
• m=0
• m=1
• m=2 [3]
(ii) State one feature of the curve for the case m = 0 that is not a feature of the curve in
the
cases m = 1 and m = 2. [1]
For the remainder of this question m = 0.
(b) Verify that the parametric equations of the curve
are x ( t) = a cos (t), y (t) = b sin (t),
where 0 G t 1 2r is a parameter. [1]
d y b [2]
(c) Show that d x =- a cot (t).
(d) Show that the equation of the normal to the curve at the point with parameter t is
a a2 - b2
y= tan (t) x - c msin (t). [5]
bb
(e) Show that the parametric equations of the envelope of the normal to the curve are
a2 - b2 3 b2 - a2 3
x (t) = c a mcos (t), y (t) = c b msin (t),
[6]
where 0 G t 1 2r is a parameter.
(f) In this part of the question a = 2 and b = 1.
[1]
On the axes in the Printed Answer Booklet, sketch the envelope of the normal to the
curve.
2 2 [2]
(g) By considering the expression (ax (t)) 3 + (by (t)) 3 or otherwise, determine a
cartesian equation of the envelope of the normal to the curve.
, © OCR 2025 Y436/01 Jun25
(MEI) Y436/01 Further Pure with
Technology
Verified Question paper with Marking
Scheme combined
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
OCR A LEVEL given for using a correct method, even if your
answer is wrong.
FURTHER • Give your final answers to a degree of
accuracy that is appropriate to the context.
• Do not send this Question Paper for
MATHEMATICS B 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 [ ].
, Oxford Cambridge and RSA
Monday 23 June 2025 – Afternoon
A Level Further Mathematics B (MEI)
Y436/01 Further Pure with Technology
Time allowed: 1 hour 45 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI) QP
• a computer with appropriate software
• 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [K/508/5600] OCR is an exempt Charity
DC (PQ/FC) 352593/3 Turn over
, 2
1 A family of curves is given by the cartesian equation
x2 y2
+ mxy + =1
a2 b2
where a, b and m are real numbers with a and b non-zero.
(a) In this part of the question a = 2 and b = 1.
(i) On the axes in the Printed Answer Booklet, sketch the curve in each of these cases.
• m=0
• m=1
• m=2 [3]
(ii) State one feature of the curve for the case m = 0 that is not a feature of the curve in
the
cases m = 1 and m = 2. [1]
For the remainder of this question m = 0.
(b) Verify that the parametric equations of the curve
are x ( t) = a cos (t), y (t) = b sin (t),
where 0 G t 1 2r is a parameter. [1]
d y b [2]
(c) Show that d x =- a cot (t).
(d) Show that the equation of the normal to the curve at the point with parameter t is
a a2 - b2
y= tan (t) x - c msin (t). [5]
bb
(e) Show that the parametric equations of the envelope of the normal to the curve are
a2 - b2 3 b2 - a2 3
x (t) = c a mcos (t), y (t) = c b msin (t),
[6]
where 0 G t 1 2r is a parameter.
(f) In this part of the question a = 2 and b = 1.
[1]
On the axes in the Printed Answer Booklet, sketch the envelope of the normal to the
curve.
2 2 [2]
(g) By considering the expression (ax (t)) 3 + (by (t)) 3 or otherwise, determine a
cartesian equation of the envelope of the normal to the curve.
, © OCR 2025 Y436/01 Jun25
