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ocr A Level Further Mathematics B (MEI) (Y435-01) Question Paper June2024.
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ocr A Level Further Mathematics B (MEI) (Y435-01) Question Paper June2024.
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ocrFriday 21 June 2024 – Afternoon
A Level Further Mathematics B (MEI)
Y435/01 Extra Pure
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI)
• 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.
Turn over
, 2
1 A surface, S, is defined in 3-D by z = f(x, y) where f(x, y) = 12x - 30y + 6xy .
(a) Determine the coordinates of any stationary points on the surface. [5]
(b) The equation z = f(x, a), where a is a constant, defines a section of S.
Given that this equation is z = 24x + b, find the value of a and the value of b. [3]
The diagram shows the contour z = 12 and its associated asymptotes.
y
O x
(c) Find the equations of the asymptotes. [3]
(d) By forming grad g, where g(x, y, z) = f(x, y) - z , find the equation of the tangent plane
to S at the point where x = 3 and y = 2. Give your answer in vector form. [3]
The point (0, 4, -120), which lies on S, is denoted by A.
J
TheK plane with equation 3N
K 3OO = 52 is denoted by P.
r.
K O
L -2P
(e) Show that the normal to S at A intersects P at the point (-360, 304, -110). [3]
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