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2025 OCR A Level Mathematics A
H240/01 Pure Mathematics
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Wednesday 4 June 2025 – Afternoon
A Level Mathematics A
H240/01 Pure Mathematics
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 page 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 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [603/1038/8] OCR is an exempt Charity
DC (PQ/CB) 356902/3 Turn over
2025 OCR
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A Levelthe
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Mathematics
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A H240-01
the
Question
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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
© OCR 2025 H240/01 Jun25
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A Levelthe
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A H240-01
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3
sin i ≈ i , cos i ≈ 1 - 1 i2 , tan i ≈ i where i is measured in radians
2
© OCR 2025 H240/01 Jun25 Turn over
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A H240-01
the
Question
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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
2 2
xh f ^x xh
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
Ln 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
© OCR 2025 2 H240/01 Jun25
2025 OCR
Download
A Levelthe
Mathematics
2025 OCR2025
A
A/AS
H240-01
OCR
Level
APure
question
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Mathematics
paper, including
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A H240-01
the
Question
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Scheme
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2025 OCR A Level Mathematics A
H240/01 Pure Mathematics
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Wednesday 4 June 2025 – Afternoon
A Level Mathematics A
H240/01 Pure Mathematics
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 page 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 8 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [603/1038/8] OCR is an exempt Charity
DC (PQ/CB) 356902/3 Turn over
2025 OCR
Download
A Levelthe
Mathematics
2025 OCR2025
A
A/AS
H240-01
OCR
Level
APure
question
LevelMathematics
Mathematics
paper, including
Verified
A H240-01
the
Question
complete
Pure paper
Mathematics
Question
with Marking
Paper
Verified
with
Scheme
Question
Exam-Ready
Attached.pdf
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the 2025the
OCR
2025
A/AS
OCRLevel
A/ASquestion
Level question
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Question
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Paper with
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Exam-Ready
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Examiner
Mark Scheme
Mark Scheme
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
© OCR 2025 H240/01 Jun25
2025 OCR
Download
A Levelthe
Mathematics
2025 OCR2025
A
A/AS
H240-01
OCR
Level
APure
question
LevelMathematics
Mathematics
paper, including
Verified
A H240-01
the
Question
complete
Pure paper
Mathematics
Question
with Marking
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Verified
with
Scheme
Question
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the 2025the
OCR
2025
A/AS
OCRLevel
A/ASquestion
Level question
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Question
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Mark Scheme
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3
sin i ≈ i , cos i ≈ 1 - 1 i2 , tan i ≈ i where i is measured in radians
2
© OCR 2025 H240/01 Jun25 Turn over
2025 OCR
Download
A Levelthe
Mathematics
2025 OCR2025
A
A/AS
H240-01
OCR
Level
APure
question
LevelMathematics
Mathematics
paper, including
Verified
A H240-01
the
Question
complete
Pure paper
Mathematics
Question
with Marking
Paper
Verified
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Scheme
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OCR
2025
A/AS
OCRLevel
A/ASquestion
Level question
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the complete
Question
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Examiner
Examiner
Mark Scheme
Mark Scheme
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
2 2
xh f ^x xh
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
Ln 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
© OCR 2025 2 H240/01 Jun25
2025 OCR
Download
A Levelthe
Mathematics
2025 OCR2025
A
A/AS
H240-01
OCR
Level
APure
question
LevelMathematics
Mathematics
paper, including
Verified
A H240-01
the
Question
complete
Pure paper
Mathematics
Question
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