A-LEVEL OCR FURTHER MATHEMATICS A
(Y541/01) PURE CORE 2 JUNE SUMMER EXAM
QUESTION PAPER
(AUTHENTIC MARKING SCHEME ATTACHED)
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.
–2
• The acceleration due to gravity is denoted by g m s . 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
4 In this question you must show detailed reasoning.
2 2 2
1 + 2 +... +n
Determine the smallest value of n for which 2 341. [4]
1 + 2 +... +n
5 (a) By using the exponential definitions of sinh x and cosh x, prove the identity
2 2
cosh 2x / cosh x +sinh x. [2]
(b) Hence find an expression for cosh 2x in terms of cosh x. [1]
(c) Determine the solutions of the equation 5cosh 2x = 16cosh x + 21, giving your answers in
exact logarithmic form. [4]
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