official summer 2024 ocr gce further mathematics a
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Official summer 2024 OCR GCE A/AS LEVEL
Official summer 2024 OCR GCE A/AS LEVEL
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Official summer 2024
OCR
GCE
Further Mathematics A
Y541/01: Pure Core 2
A Level
Merged Question Paper + Mark Scheme + Answer
Booklet
Ace your Mocks!!!
, Oxford Cambridge and RSA
Monday 3 June 2024 – Afternoon
A Level Further Mathematics A
Y541/01 Pure Core 2
Time allowed: 1 hour 30 minutes
* 1 4 2 1 2 8 1 2 8 2 *
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 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 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.
, 3
JK1 NO 1
6 In polar coordinates, the equation of a curve, C, is r = 6 sin (2i) sinh KK3 iOO for 0 G i G 2 r .
L P
The pole of the polar coordinate system corresponds to the origin of the cartesian system and the
initial line corresponds to the positive x‑axis.
(a) Explain how you can tell that C comprises a single loop in the first quadrant, passing through
the pole. [3]
The incomplete table below shows values of r for various values of i.
1 1 1 1 5 1
0
i
12 r 6r 4r 3r 12 r 2r
r 0 0.262 1.851
(b) Use the copy of the table and the polar coordinate system diagram given in the Printed
Answer Booklet to complete the table and sketch C. [3]
The point on C which is furthest away from the pole is denoted by A and the value of i at A is
denoted by z.
(c) Show that z satisfies the equation z = 2 ln c m
3 6 - tan 2z
[4]
6 + tan 2z
(d) You are given that the relevant solution of the equation given in part (c) is z = 1.0207 correct
to 5 significant figures.
Find the distance from A to the pole. Give your answer correct to 3 significant figures. [1]
7 (a) Express 17 coshx - 15 sinhx in the form e -x (ae bx + c) where a, b and c are integers to be
determined. [3]
1
A function is defined by f (x) = . The region bounded by the curve y = f (x) ,
17 cosh x - 15 sinh x
the x‑axis, the y‑axis and the line x = ln 3 is rotated by 2r radians about the x‑axis to form a solid
of revolution S.
(b) In this question you must show detailed reasoning.
Use a suitable substitution, together with known results from the formula book, to show that
the volume of S is given by kr tan -1 q where k and q are rational numbers to be determined.
[7]
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