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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
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OCR A/AS Level question
OCR AS paper,
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the complete
A H230-02
Question
Pure Mathematics
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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
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A H230-02
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Pure Mathematics
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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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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
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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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,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
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Scheme
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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
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Question
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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
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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]
© OCR 2025 H230/02 Jun25 Turn over
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the 2025
including
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complete
Level question
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,the 2025UK.STUDIES//2025
OCR A/AS Level question
OCR AS paper,
Levelincluding
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the complete
A H230-02
Question
Pure Mathematics
Paper with Exam-Ready
and Mechanics
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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
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