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OXFORD CAMBRIDGE AND RSA 2024 A Level Mathematics A H240/03 Pure Mathematics and Mechanics ACTUAL QUESTION PAPER WITH MERGED MARKING SCHEME $7.69
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OXFORD CAMBRIDGE AND
RSA 2024
A Level Mathematics AH240/03 Pure Mathematics and Mechanics
A Level Mathematics AH240/03 Pure Mathematics and Mechanics
, Oxford Cambridge and RSA
Thursday 20 June 2024 – Afternoon
A Level Mathematics A
H240/03 Pure Mathematics and Mechanics
Time allowed: 2 hours
You must have:
• the Printed Answer Booklet
• a scientific or graphical calculator
QP
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 AnswerBooklet. 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 begiven
for using a correct method, even if your answer is wrong.
• Give non-exact numerical answers correct to 3 significant figures unless a differentdegree
of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value isneeded
use g = 9.8 unless a different value is specified in the question.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 100.
• 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
, 3
Formulae
A Level Mathematics A (H240)
Arithmetic series
S n = 1 2n^a + lh = 1 n2 "2a +^n - 1hd,
Geometric series
a^1 - rn1h
Sn =
-r
a
S3= fo r 1 1
1-r
r
Binomial series
^a + bhn = a n + n C1 a n-1 b + n C2 a n -2 b 2 + f + n Cr a n-r b r + f + b n ^n e Nh,
n n!
where n C = C = c m =
r n r r r!^n - rh!
n ^n - 1h 2 n ^n - 1hf ^n - r + 1h r
^1 + xhn = 1 + nx + x +f+ x +f ^ x 1 1, n e Rh
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
u dy v du - u dv
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
de dx = ln f^xh + c
f^ x h
n 1 n +1
; f l^xhaf^xhk dx = n + 1af^xhk + c
dv du
Integration by ;u dx = uv - ; v dx
parts
dx dx
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