Oxford Cambridge and RSA
A Level Further Mathematics B (MEI)
Y420/01 Core Pure
Practice Paper – Set 1
Time allowed: 2 hours 40 minutes
You must have:
• Printed Answer Booklet
• Formulae Further Mathematics B (MEI)
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre
number and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. 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 detail
of 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.
© OCR 2018 Practice paper OCR is an exempt Charity
DC
This study source (LEG/TP)
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, 2
Section A (33 marks)
Answer all the questions.
/ r^r + 2h, giving your answer in a fully factorised form.
n
1 Using standard summation formulae, find [5]
r =1
Describe the transformation of the plane represented by the matrix M = c m , where k is a non-zero
1 k
2 (i)
0 1
constant. [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 + kz 2 + 7z - 6 = 0, find, in exact form, the other two roots. [6]
4 In this question you must show detailed reasoning.
1
Fig. 4 shows the region bounded by the curve y = , the x-axis, the y-axis and the line x = 1.
3 + x2
y
1
y=
3 + x2
x
O
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.
y01 sinh 2x dx = 14 ae - 1ek .
2
Show that [3]
x-2 y+3 z x+6 y+4 z-6
6 Verify that the lines = = and = = intersect, stating clearly the coordinates of
2 3 2 -3 1 4
the point of intersection. [6]
7 In this question you must show detailed reasoning.
3
Evaluate y0
1
^1 + 2xh2
dx. [4]
This study
© OCRsource was downloaded
2018 Practice paper by 100000850629869 from CourseHero.comY420/01
on 04-23-2023 15:12:31 GMT -05:00
https://www.coursehero.com/file/90841389/Further-Pure-Y420-01-paper-Mar-18pdf/
A Level Further Mathematics B (MEI)
Y420/01 Core Pure
Practice Paper – Set 1
Time allowed: 2 hours 40 minutes
You must have:
• Printed Answer Booklet
• Formulae Further Mathematics B (MEI)
You may use:
• a scientific or graphical calculator
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre
number and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer
Booklet. 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 detail
of 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.
© OCR 2018 Practice paper OCR is an exempt Charity
DC
This study source (LEG/TP)
was 163822/2
downloaded by 100000850629869 from CourseHero.com on 04-23-2023 15:12:31 GMT -05:00 Turn over
https://www.coursehero.com/file/90841389/Further-Pure-Y420-01-paper-Mar-18pdf/
, 2
Section A (33 marks)
Answer all the questions.
/ r^r + 2h, giving your answer in a fully factorised form.
n
1 Using standard summation formulae, find [5]
r =1
Describe the transformation of the plane represented by the matrix M = c m , where k is a non-zero
1 k
2 (i)
0 1
constant. [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 + kz 2 + 7z - 6 = 0, find, in exact form, the other two roots. [6]
4 In this question you must show detailed reasoning.
1
Fig. 4 shows the region bounded by the curve y = , the x-axis, the y-axis and the line x = 1.
3 + x2
y
1
y=
3 + x2
x
O
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.
y01 sinh 2x dx = 14 ae - 1ek .
2
Show that [3]
x-2 y+3 z x+6 y+4 z-6
6 Verify that the lines = = and = = intersect, stating clearly the coordinates of
2 3 2 -3 1 4
the point of intersection. [6]
7 In this question you must show detailed reasoning.
3
Evaluate y0
1
^1 + 2xh2
dx. [4]
This study
© OCRsource was downloaded
2018 Practice paper by 100000850629869 from CourseHero.comY420/01
on 04-23-2023 15:12:31 GMT -05:00
https://www.coursehero.com/file/90841389/Further-Pure-Y420-01-paper-Mar-18pdf/
