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OXFORD CAMBRIDGE AND RSA 2024 GCE Mathematics B MEI H640/03: Pure Mathematics and Comprehension A Level ACTUAL QUESTION PAPER AND MARKING SCHEME (MERGED)$7.39
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OXFORD CAMBRIDGE AND RSA 2024 GCE Mathematics B MEI H640/03: Pure Mathematics and Comprehension A Level ACTUAL QUESTION PAPER AND MARKING SCHEME (MERGED)
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OXFORD CAMBRIDGE AND RSA 2024 GCE Mathematics B MEI H640/03: Pure Mathematics and Comprehension A Level ACTUAL QUESTION PAPER AND MARKING SCHEME (MERGED)
OCR 2024
GCE Mathematics B
MEIH640/03: Pure Mathematics
and Comprehension A Level
, Oxford Cambridge and RSA
Thursday 20 June 2024 – Afternoon
A Level Mathematics B (MEI)
H640/03 Pure Mathematics and Comprehension
Time allowed: 2 hours
• the Printed Answer Booklet
• the Insert
QP
• 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 75.
• The marks for each question are shown in brackets [ ].
• This document has 12 pages.
ADVICE
• Read each question carefully before you start your answer.
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Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
Sn = 12n^a + lh = 21 n"2a +^n - 1hd,
Geometric series
a^1 - rnh
Sn =
1-r
a
S3 = for r 1 1
1-r
Binomial series
^a + bhn = a n + n C 1 a n-1 b + n C 2 a n-2 b 2 + f + n C r a n-r b r + f + b n neN ,
JnN n!
n
where Cr = n Cr = Kr O = ^
r! n - rh!
L P
n ^n - 1h 2 n ^n - 1h f ^n - r + 1h r x 1 1, n e R
^1 + xhn = 1 + nx + x +f+ x +f
2! r!
Differentiation
fx fl x
tan kx k sec2kx
sec x sec x tan x
cot x -cosec 2 x
cosec x -cosec x cot x
v du - u dv
u dy
Quotient Rule y = v , = dx v2 dx
dx
Differentiation from first principles
f^x + hh - f^xh
f l^xh = lim
h "0 h
Integration
c f l^xh
d dx = ln f^xh + c
e f^ x h
n 1 af^xhkn +1 + c
; f l^xhaf^xhk dx =
n+1
dv du
Integration by parts ; u dx = uv - ; v dx
dx dx
Small angle approximations
sin i . i , cos i . 1 - 12 i 2 , tan i . i where i is measured in radians
, 3
Trigonometric identities
sin A ! B = sin A cos B ! cos A sin B
cos A ! B = cos A cos B " sin A sin B
^ htan A ! tan A ! tan B aA ! B ! ^k + 12h rk
1 " tan A tan B
B=
Numerical methods
b-a
Trapezium rule: ; b y dx . 1 h"^y + y h + 2^y + y + f + y h,, where h =
a
2 0 n 1 2 n -1 n
f^xnh
The Newton‑Raphson iteration for solving f^xh = 0: x n +1 = xn -
f l^xnh
Probability
P A j B = P A +P B - P A k B P^A k Bh
^ h
P AkB = P A P B A = P B P A B or PA B = P^Bh
Sample variance
2 1 2 ^/ xih2 2
s = n - S xx where S xx = /^xi - -xh = / x2i - = / x 2i -
- nx
1 n
Standard deviation, s = variance
The binomial distribution
If X + B n, p then P ^X = rh = n C r p r q n-r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J v2N X-n
2
If X + N n, v then X + NKn, O and + N^0, 1h
L nP v n
Percentage points of the Normal distribution
p 10 5 2 1
1 p% 1 p%
z 1.645 1.960 2.326 2.576 2 2
z
Kinematics
Motion in a straight line Motion in two dimensions
v = u + at v = u + at
s = ut + 21 at2 s = ut + 12 at2
s = 12^u + vht s = 12^u + vht
v2 = u2 + 2as
s = vt - 12 at2 s = vt - 12 at2
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