A Level Further Mathematics B
(MEI)
Y420/01 Core Pure
Practice Paper – Set 1
Time allowed: 2 hours 40 minutes
INSTRUCTIONS
• Use black ink. HB
... [Show More] pencil may be used for graphs and diagrams
only.
• Complete the boxes provided on the Printed Answer
Booklet with your name, centrenumber and candidate
number.
• Answer all the questions.
• Write your answer to each question in the space
provided in the Printed AnswerBooklet. Additional
paper may be used if necessary but you must clearly
show your candidate number, centre number and
question number(s).
• Do not write in the barcodes.
• You are permitted to use a scientific or graphical calculator in
this paper.
• Final answers should be given to a degree of accuracy
appropriate to the context.
INFORMATION
• The total number of marks for this paper is 144.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks
unless you show sufficient detailof the working to indicate
that a correct method is used. You should communicate
your method with correct reasoning.
• The Printed Answer Booklet consists of 24 pages. The
Question Paper consists of
8 pages.
Turn over
2
3 + x
2
y =
1
3 +x
2
O
n
0 4 e
0
1+2x
1
Section A (33 marks)
Answer all the questions.
1 Using standard summation formulae, find / r^r + 2h, giving your answer in a fully factorised form. [5]
r=1
2 (i) Describe the transformation of the plane represented by the matrix M = c
1 k
m, where k is a non-zero
constant.
0 1
[2]
(ii) The image of the point (2, 3) under the transformation in part (i) lies on the y-axis. Find k. [3]
3 In this question you must show detailed reasoning.
Given that z = 2 is a root of the equation z
3
+ kz2
+ 7z- 6 = 0, find, in exact form, the other two roots. [6]
4 In this question you must show detailed reasoning.
Fig. 4 shows the region bounded by the curve y =
1
, the x-axis, the y-axis and the line x = 1.
y
x
Fig. 4
This region is rotated through 2r radians about the x-axis. Find, in an exact form, the volume of the solid of
revolution generated. [4]
5 In this question you must show detailed reasoning.
Show that y
1
sinh 2xdx =
1
ae -
1
k
2
. [3]
6 Verify that the lines x - 2
=
y + 3
=
z
and x + 6
=
y + 4
=
z- [Show Less]