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of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
Mark Scheme
2025 OCR A Level Mathematics A
H240/03 Pure Mathematics and Mechanics
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Thursday 19 June 2025 – 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 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 16 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [603/1038/8] OCR is an exempt Charity
DC (DE/FC) 357974/4 Turn over
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2025
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A H240-03
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PurePaper
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OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
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 H240/03 Jun25
S Level question
2025 OCR
2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
Mathematics
Purewith
Mathematics
Exam-Ready
and Mechanics
andExaminer
Mechanics
Verified
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with
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Attached.pdf
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Attached.pdf
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, Page 32025
of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
Mark Scheme
3
sin i ≈ i , cos i ≈ 1 - 1 i2 , tan i ≈ i where i is measured in radians
2
© OCR 2025 H240/03 Jun25 Turn over
S Level question
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2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
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Purewith
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and Mechanics
andExaminer
Mechanics
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of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
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Examiner
OCR
Mechanics
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Mark
Level
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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
x ^1 - phn-x , mean of X is np, variance of X is np^1 - ph
If X + B^n, ph then P^X = xh = K Op
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
nL n
Pv
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 H240/03 Jun25
S Level question
2025 OCR
2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
Mathematics
Purewith
Mathematics
Exam-Ready
and Mechanics
andExaminer
Mechanics
Verified
Mark
Verified
Question
Scheme.
Question
paper
Coverspaper
with
allMarking
examinable
with Marking
Scheme
content
Scheme
Attached.pdf
with
Attached.pdf
Verified Answers
of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
Mark Scheme
2025 OCR A Level Mathematics A
H240/03 Pure Mathematics and Mechanics
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Thursday 19 June 2025 – 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 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 16 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [603/1038/8] OCR is an exempt Charity
DC (DE/FC) 357974/4 Turn over
S Level question
2025 OCR
2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
Mathematics
Purewith
Mathematics
Exam-Ready
and Mechanics
andExaminer
Mechanics
Verified
Mark
Verified
Question
Scheme.
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Coverspaper
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Attached.pdf
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, Page 22025
of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
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 H240/03 Jun25
S Level question
2025 OCR
2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
Mathematics
Purewith
Mathematics
Exam-Ready
and Mechanics
andExaminer
Mechanics
Verified
Mark
Verified
Question
Scheme.
Question
paper
Coverspaper
with
allMarking
examinable
with Marking
Scheme
content
Scheme
Attached.pdf
with
Attached.pdf
Verified Answers
, Page 32025
of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
Mark Scheme
3
sin i ≈ i , cos i ≈ 1 - 1 i2 , tan i ≈ i where i is measured in radians
2
© OCR 2025 H240/03 Jun25 Turn over
S Level question
2025 OCR
2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
Mathematics
Purewith
Mathematics
Exam-Ready
and Mechanics
andExaminer
Mechanics
Verified
Mark
Verified
Question
Scheme.
Question
paper
Coverspaper
with
allMarking
examinable
with Marking
Scheme
content
Scheme
Attached.pdf
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Attached.pdf
Verified Answers
, Page 42025
of 812025
OCR AOCR
LevelA/AS
Mathematics
Level | Question
A H240-03
Paper
Pure
with
Mathematics
Exam-Ready
2025
and
Examiner
OCR
Mechanics
A/AS
Mark
Level
Verified
Scheme
| Question
QuestionPaper
paperwith
withExam-Ready
Marking Scheme
Examiner
Attached.pdf
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
x ^1 - phn-x , mean of X is np, variance of X is np^1 - ph
If X + B^n, ph then P^X = xh = K Op
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
nL n
Pv
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 H240/03 Jun25
S Level question
2025 OCR
2025
paper,
AOCR
Level
including
A Mathematics
Levelthe
Mathematics
complete
A H240-03
Question
A H240-03
PurePaper
Mathematics
Purewith
Mathematics
Exam-Ready
and Mechanics
andExaminer
Mechanics
Verified
Mark
Verified
Question
Scheme.
Question
paper
Coverspaper
with
allMarking
examinable
with Marking
Scheme
content
Scheme
Attached.pdf
with
Attached.pdf
Verified Answers
