OCR A Level Mathematics A H240/02 Pure Mathematics and Statistics (2025) | Question Paper with Marking Scheme

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2025 OCR A Level Mathematics A
H240/02 Pure Mathematics and Statistics
Verified Question paper with Marking Scheme Attached




Oxford Cambridge and RSA


Thursday 12 June 2025 – Afternoon
A Level Mathematics A
H240/02 Pure Mathematics and Statistics
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 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 non-exact numerical answers correct to 3 significant figures unless a different degree
of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is needed
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.




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2
Formulae
A Level Mathematics A (H240)


Arithmetic series
S = 1 n^a + lh = 1 n"2a +^n - 1hd,
n 2 2



Geometric series
a^1 - rnh
Sn =
1-r
a
S3= for r 1 1
1-r

Binomial series
^a + bhn = an + nC1 a n- 1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
JN n!
n Cr = n Cr = K On =
wher r r!^n - rh!
e
LP
n^n - 1h 2 n^n - 1h f ^n - r + 1h r ^ x 1 1, n e Rh
^1 + xhn = 1 + nx + x +f+ x +f
2! r!

Differentiation
f^xh f l^xh
tan kx k sec2kx
sec x sec x tan x
cot x -cosec2x
cosec x -cosec x cot x

u dy v du - u dv
Quotient rule y = v , = dx 2 dx
dx v

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^xh
n 1 n+1
; f l^xhaf^xhk dx = n +a1f^xhk + c

dv du
Integration by ;u dx = uv - ; v dx
parts
dx dx

Small angle approximations
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3
sin i ≈ i , cos i ≈ 1 - 1 i2, tan i ≈ i where i is measured in radians
2




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4
Trigonometric identities
sin^A ! Bh = sin A cos B ! cos A sin B

cos^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan^A ! Bh = aA ! B ! ^k + 1h2rk
1 " tan A tan B

Numerical methods
b b-a
Trapezium rule: y 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 = xn -
n +1 f l^xnh

Probability
P^A U Bh = P^Ah+P^Bh- P^A + Bh
P^A + Bh
P^A + Bh = P^AhP^B Ah = P^BhP^A Bh or P^A Bh =
P^Bh

Standard deviation
xh2 2
f ^x xh2
n = n or =


The binomial distribution
JnN
If X + B^n, ph then P^X = xh = K Op x ^1 - phn-x , mean of X is np, variance of X is np^1 - ph
x
LP
Hypothesis test for the mean of a normal distribution
J v2N X-n
2
If X + N^n, v h then X + NKn, O and ~ N^0, 1h
L n P v n

Percentage points of the normal distribution
If Z has a normal distribution with mean 0 and variance 1 then, for each value of p, the table gives
the value of z such that P^Z G zh = p.

p 0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
z 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291


Kinematics
Motion in a straight line Motion in two dimensions
v = u + at s = vt - 1 at2
s = ut + 1 at2
2

s = 12^u + vht
v2 = u2 + 2as

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