OCR A Level Further Mathematics B (MEI) Core
Pure(Y420/01) VERIFIED QP
AND MS
Oxford Cambridge and RSA
May – Afternoon
A Level Further Mathematics B (MEI)
Y420/01 Core Pure
Time allowed: 2 hours 40 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(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 144.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, OCR is an exempt Charity
Turn over
*1869096913*
,
, 2
Section A (33 marks)
1 The complex number z satisfies the equation z + 2iz* +1 - 4i = 0 .
You are given that z = x +iy, where x and y are real numbers.
Determine the values of x and y. [4]
2 In this question you must show detailed reasoning.
Find the acute angle between the planes 2x - y + 2z = 5 and x + 2y + z = 8. [4]
3 Using standard summation formulae, show that, for integers n H 1,
1
1 # 3 + 2 # 4 + ... + n # (n + 2) =6 n (n + 1)(an + b),
where a and b are integers to be determined. [5]
4 (a) You are given that M and N are non-singular 2 # 2 matrices.
Write down the product rule for the inverse matrices of M, N and MN. [1]
(b) Verify this rule for the matrices M and N, where
Ja 1N J0 -1N
= KK O K MO and N
O K O
= and a and b are non-zero constants. [6]
0 1 1 b
L P L P
5 The cubic equation 2x3 - 3x + 4 = 0 has roots a, b and c.
Determine a cubic equation with integer coefficients whose roots are 1 (a + 1), 1 (b + 1) and 1 (c + 1) .
2 2 2
[4]
Pure(Y420/01) VERIFIED QP
AND MS
Oxford Cambridge and RSA
May – Afternoon
A Level Further Mathematics B (MEI)
Y420/01 Core Pure
Time allowed: 2 hours 40 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
QP
(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 144.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, OCR is an exempt Charity
Turn over
*1869096913*
,
, 2
Section A (33 marks)
1 The complex number z satisfies the equation z + 2iz* +1 - 4i = 0 .
You are given that z = x +iy, where x and y are real numbers.
Determine the values of x and y. [4]
2 In this question you must show detailed reasoning.
Find the acute angle between the planes 2x - y + 2z = 5 and x + 2y + z = 8. [4]
3 Using standard summation formulae, show that, for integers n H 1,
1
1 # 3 + 2 # 4 + ... + n # (n + 2) =6 n (n + 1)(an + b),
where a and b are integers to be determined. [5]
4 (a) You are given that M and N are non-singular 2 # 2 matrices.
Write down the product rule for the inverse matrices of M, N and MN. [1]
(b) Verify this rule for the matrices M and N, where
Ja 1N J0 -1N
= KK O K MO and N
O K O
= and a and b are non-zero constants. [6]
0 1 1 b
L P L P
5 The cubic equation 2x3 - 3x + 4 = 0 has roots a, b and c.
Determine a cubic equation with integer coefficients whose roots are 1 (a + 1), 1 (b + 1) and 1 (c + 1) .
2 2 2
[4]
