OCR
GCE
Further Mathematics A
Y540/01: Pure Core 1
A Level
Merged Question Paper + Mark Scheme + Answer
Booklet
Ace your Mocks!!!
, Oxford Cambridge and RSA
Wednesday 22 May 2024 – Afternoon
A Level Further Mathematics A
Y540/01 Pure Core 1
Time allowed: 1 hour 30 minutes
* 1 4 2 0 8 7 7 9 6 7 *
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.
The locus C1 is defined by C 1 = %z | 0 G arg (z + i) G r/ .
1
2
4
(a) Indicate by shading on the Argand diagram in the Printed Answer Booklet the region
representing C1. [2]
(b) Determine whether the complex number 1.2 + 0.8i is in C1. [2]
The locus C2 is the set of complex numbers represented by the interior of the circle with radius 2
and centre 3. The locus C2 is illustrated on the Argand diagram below.
Im
3
2
1 C2
Re
–2 –1 O 1 2 3 4 5
–1
–2
(c) Use set notation to define C2. [2]
(d) Determine whether the complex number 1.2 + 0.8i is in C 2 . [2]
6 In this question you must show detailed reasoning.
3
Determine the exact value of y9 x
18
2
x
dx . [4]
7 (a) By using the definitions of cosh u and sinh u in terms of e u and e -u , show that
sinh 2u / 2 sinh u cosh u . [2]
The equation of a curve, C, is y = 16 cosh x - sinh 2x .
d2y
(b) Show that there is only one solution to the equation =0 [4]
d x2
You are now given that C has exactly one point of inflection.
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