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ocr AS Level Further Mathematics B (MEI):Core Pure(Y410/01) -may 2024 Question Paper
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ocr AS Level Further Mathematics B (MEI):Core Pure(Y410/01) -may 2024 Question Paper
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ocrMonday 13 May 2024 – Afternoon
AS Level Further Mathematics B (MEI)
Y410/01 Core 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 4 pages.
ADVICE
• Read each question carefully before you start your answer.
Turn over
, 2
1 The quadratic equation x2 + ax + b = 0, where a and b are real constants, has a root 2 - 3i.
(a) Write down the other root. [1]
(b) Hence or otherwise determine the values of a and b. [3]
J 1 aN J2 0N N
J-1
0
2 The matrices A, B and C are given by A = K O, B = O and C = K O, where a is
K
a constant. -1 1 - L 2 1
L L P
2 1
P P
(a) By multiplying out the matrices on both sides of the equation, verify that A^BCh =
^ABhC.
[4]
(b) State the property of matrix multiplication illustrated by this result. [1]
2n
3 (a) Using standard summation formulae, write down an expression in terms of n for /r . 3
[1]
2n r=1
(b) Hence show that /r
r=n+
3
= 14 n2 (an + b)(cn + d ) , where a, b, c and d are integers to be
1
determined. [5]
4 In this question you must show detailed reasoning.
The roots of the cubic equation x3 - 3x2 + 19x - 17 = 0 are a, b and c.
(a) Find a cubic equation with integer coefficients whose roots are 1
(a - 1), 1
(b - 1) and
1
(c - 2 2
[4]
1).
2
(b) Hence or otherwise solve the equation x3 - 3x2 + 19x - 17 = 0. [3]
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