2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
VerifiedMark
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Scheme.
paper
Covers
with Marking
all examinable
SchemePage
content
Attached.pdf
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with Verifie
2025 OCR AS Level Mathematics A
H230/02 Pure Mathematics and Mechanics
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 23 May 2025 – Afternoon
AS Level Mathematics A
H230/02 Pure Mathematics and Mechanics
Time allowed: 1 hour 30 minutes
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 75.
• 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 [603/0933/7] OCR is an exempt Charity
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andMechanics
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MechanicsVerified
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, 2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
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paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
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converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
VerifiedMark
Question
Scheme.
paper
Covers
with Marking
all examinable
SchemePage
content
Attached.pdf
2 of 50
with Verifie
2
Formulae
AS Level Mathematics A (H230)
Binomial series
^a + bhn = an + nC1 a n-1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
n n!
where nC = C = c m =
r n r r r!^n - rh!
Differentiation from first principles
f^x + hh - f^xh
f l^xh = lim
h "0 h
Standard deviation
f ^x
= 2 or =
n n
The binomial distribution
n
If X ~ B^n, ph then P^X = xh = c mpx^1 - phn - x , mean of X is np, variance of X is np^1 - ph
x
Kinematics
v = u + at
s = ut + 1 at2
2
s = 12^u + vht
v2 = u2 + 2as
s = vt - 12at2
© OCR 2025 H230/02 Jun25
S Level question
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2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
, 2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
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converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
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Question
Scheme.
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3
Section A
Pure Mathematics
1 Determine the equation of the line that passes through the point (1, 3) and is perpendicular to
the line with equation 3x + 6y - 5 = 0. Give your answer in the form ax + by + c = 0 where a, b
and c are integers to be determined. [3]
2 In this question you must show detailed reasoning.
D C
12 cm2
A (3 - 3) cm B
The diagram shows the rectangle ABCD where AB = (3 - 3) cm.
The area of ABCD is 12 cm2.
Find the perimeter of ABCD. Give your answer in the form (a + b 3) cm, where a and b are
integers to be determined. [4]
3 In a triangle ABC, AB = 9 cm, BC = 7 cm and AC = 4 cm.
(a) Show that cos CAB = 23. [2]
(b) Hence find the exact value of sin CAB. [2]
(c) Find the exact area of triangle ABC. [2]
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AS
ASLevel
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Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
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PureMathematics
Mathematics
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andMechanics
Mechanics
MechanicsVerified
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, 2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
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paperwith
with
withMarking
Marking
MarkingScheme
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Attached
Attached---converted.pdf
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the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
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4
4 The cubic polynomial 2x3 - kx2 + 4x + k , where k is a constant, is denoted by f(x).
It is given that f l(2) = 16.
(a) Show that k = 3. [4]
For the remainder of the question, you should use this value of k.
(b) Use the factor theorem to show that (2x + 1) is a factor of f(x). [2]
(c) Hence show that the equation f(x) = 0 has only one real root. [4]
5 In this question you must show detailed reasoning.
G H
F E
(2x + 1) cm B C
(x - 2) cm
A 3 cm D
The diagram shows the cuboid ABCDEFGH where AD = 3 cm, AF = (2x + 1) cm and
DC = (x - 2) cm.
The volume of the cuboid is at most 9 cm3.
Find the range of possible values of x. Give your answer in interval notation. [5]
© OCR 2025 H230/02 Jun25
S Level question
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AS
ASLevel
Level
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Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
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PureMathematics
Mathematics
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andMechanics
Mechanics
MechanicsVerified
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2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
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converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
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Scheme.
paper
Covers
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Attached.pdf
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2025 OCR AS Level Mathematics A
H230/02 Pure Mathematics and Mechanics
Verified Question paper with Marking Scheme Attached
Oxford Cambridge and RSA
Friday 23 May 2025 – Afternoon
AS Level Mathematics A
H230/02 Pure Mathematics and Mechanics
Time allowed: 1 hour 30 minutes
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 75.
• 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 [603/0933/7] OCR is an exempt Charity
DC (DE/TC) 356289/3 Turn over
S Level question
Downloadpaper,
the 2025
including
OCRthe
A/AS
complete
Level question
Questionpaper,
Paperincluding
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Page
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50 Mark Paper
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2025
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2025OCR
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OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
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Attached
Attached---converted.pdf
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converted.pdf
, 2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
VerifiedMark
Question
Scheme.
paper
Covers
with Marking
all examinable
SchemePage
content
Attached.pdf
2 of 50
with Verifie
2
Formulae
AS Level Mathematics A (H230)
Binomial series
^a + bhn = an + nC1 a n-1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
n n!
where nC = C = c m =
r n r r r!^n - rh!
Differentiation from first principles
f^x + hh - f^xh
f l^xh = lim
h "0 h
Standard deviation
f ^x
= 2 or =
n n
The binomial distribution
n
If X ~ B^n, ph then P^X = xh = c mpx^1 - phn - x , mean of X is np, variance of X is np^1 - ph
x
Kinematics
v = u + at
s = ut + 1 at2
2
s = 12^u + vht
v2 = u2 + 2as
s = vt - 12at2
© OCR 2025 H230/02 Jun25
S Level question
Downloadpaper,
the 2025
including
OCRthe
A/AS
complete
Level question
Questionpaper,
Paperincluding
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the complete
Page
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Question
50 Mark Paper
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Covers all examinable
Examinercontent
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Answers
all examinable
2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
, 2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
VerifiedMark
Question
Scheme.
paper
Covers
with Marking
all examinable
SchemePage
content
Attached.pdf
3 of 50
with Verifie
3
Section A
Pure Mathematics
1 Determine the equation of the line that passes through the point (1, 3) and is perpendicular to
the line with equation 3x + 6y - 5 = 0. Give your answer in the form ax + by + c = 0 where a, b
and c are integers to be determined. [3]
2 In this question you must show detailed reasoning.
D C
12 cm2
A (3 - 3) cm B
The diagram shows the rectangle ABCD where AB = (3 - 3) cm.
The area of ABCD is 12 cm2.
Find the perimeter of ABCD. Give your answer in the form (a + b 3) cm, where a and b are
integers to be determined. [4]
3 In a triangle ABC, AB = 9 cm, BC = 7 cm and AC = 4 cm.
(a) Show that cos CAB = 23. [2]
(b) Hence find the exact value of sin CAB. [2]
(c) Find the exact area of triangle ABC. [2]
© OCR 2025 H230/02 Jun25 Turn over
S Level question
Downloadpaper,
the 2025
including
OCRthe
A/AS
complete
Level question
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2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
, 2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
Mathematics
the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
Examiner
VerifiedMark
Question
Scheme.
paper
Covers
with Marking
all examinable
SchemePage
content
Attached.pdf
4 of 50
with Verifie
4
4 The cubic polynomial 2x3 - kx2 + 4x + k , where k is a constant, is denoted by f(x).
It is given that f l(2) = 16.
(a) Show that k = 3. [4]
For the remainder of the question, you should use this value of k.
(b) Use the factor theorem to show that (2x + 1) is a factor of f(x). [2]
(c) Hence show that the equation f(x) = 0 has only one real root. [4]
5 In this question you must show detailed reasoning.
G H
F E
(2x + 1) cm B C
(x - 2) cm
A 3 cm D
The diagram shows the cuboid ABCDEFGH where AD = 3 cm, AF = (2x + 1) cm and
DC = (x - 2) cm.
The volume of the cuboid is at most 9 cm3.
Find the range of possible values of x. Give your answer in interval notation. [5]
© OCR 2025 H230/02 Jun25
S Level question
Downloadpaper,
the 2025
including
OCRthe
A/AS
complete
Level question
Questionpaper,
Paperincluding
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Covers all examinable
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2025
2025
2025OCR
OCR
OCRAS
AS
ASLevel
Level
LevelMathematics
Mathematics
MathematicsAAAH230-02
H230-02
H230-02Pure
Pure
PureMathematics
Mathematics
Mathematicsand
and
andMechanics
Mechanics
MechanicsVerified
Verified
VerifiedQuestion
Question
Questionpaper
paper
paperwith
with
withMarking
Marking
MarkingScheme
Scheme
SchemeAttached
Attached
Attached---converted.pdf
converted.pdf
converted.pdf
