Oxford Cambridge and RSA - 2025
Wednesday 4 June 2025 – Afternoon
A Level Mathematics A
H240/01 Pure Mathematics
Time allowed: 2 hours
(Verified Question Paper With Mark
Scheme Combined June 2025)
, 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
OCR is an exempt
[603/1038/8] DC
Charity Turn over
(PQ/CB) 356902/3
, 2
Formulae
A Level Mathematics A (H240)
Arithmetic series
S = 1 n^a + lh = 1 n"2a +^n - 1hd,
n 2 2
Geometric series
Sn =
a^1 -
rnh
1- r
a
S =1 - r for r 1 1
3
Binomial series
^a + bhn = an + nC1 a n-1b + nC2 a n- 2b2 +f+ nCr a n- rbr +f+
bn ^ n e Nh
J N n!
n Cr = n Cr = Kn O =
where r r!^n - rh!
L P
1h n n^n - 1h 2 n^n - 1h f ^n - r +
^1xr++f
xh = 1 + nx + x +f+ ^ x 1 1, n e Rh
2! r!
Differentiation
f^xh
tan kx ^x2h
fk lsec kx
sec x sec x tan x
cot x -cosec2x
cosec x -cosec x cot x
u dy v du - u dv
Quotient rule y = , = dx dx
v dx
v2
Differentiation from first principles
f^x + hh - f^xh
f l^xh h="lim
0 h
Integration
c f l^xh
d dx = ln f^xh + c
e f ^ x h
n 1 n +1
; f l^xhaf^xhk ndx+ = af^xhk +c
1
© OCR H240/01
2025 Jun25
, 3
Integration by parts dv du
;u dx = uv - ; v dx
dx dx
Small angle approximations
2
sin i ≈ i , cos i ≈ 21 - 1
i , tan i ≈ i where i is measured in radians
© OCR H240/01 Turn over
2025 Jun25
Wednesday 4 June 2025 – Afternoon
A Level Mathematics A
H240/01 Pure Mathematics
Time allowed: 2 hours
(Verified Question Paper With Mark
Scheme Combined June 2025)
, 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
OCR is an exempt
[603/1038/8] DC
Charity Turn over
(PQ/CB) 356902/3
, 2
Formulae
A Level Mathematics A (H240)
Arithmetic series
S = 1 n^a + lh = 1 n"2a +^n - 1hd,
n 2 2
Geometric series
Sn =
a^1 -
rnh
1- r
a
S =1 - r for r 1 1
3
Binomial series
^a + bhn = an + nC1 a n-1b + nC2 a n- 2b2 +f+ nCr a n- rbr +f+
bn ^ n e Nh
J N n!
n Cr = n Cr = Kn O =
where r r!^n - rh!
L P
1h n n^n - 1h 2 n^n - 1h f ^n - r +
^1xr++f
xh = 1 + nx + x +f+ ^ x 1 1, n e Rh
2! r!
Differentiation
f^xh
tan kx ^x2h
fk lsec kx
sec x sec x tan x
cot x -cosec2x
cosec x -cosec x cot x
u dy v du - u dv
Quotient rule y = , = dx dx
v dx
v2
Differentiation from first principles
f^x + hh - f^xh
f l^xh h="lim
0 h
Integration
c f l^xh
d dx = ln f^xh + c
e f ^ x h
n 1 n +1
; f l^xhaf^xhk ndx+ = af^xhk +c
1
© OCR H240/01
2025 Jun25
, 3
Integration by parts dv du
;u dx = uv - ; v dx
dx dx
Small angle approximations
2
sin i ≈ i , cos i ≈ 21 - 1
i , tan i ≈ i where i is measured in radians
© OCR H240/01 Turn over
2025 Jun25
