Oxford Cambridge and RSA - 2025
Thursday 15 May 2025 – Afternoon
AS Level Mathematics A
H230/01 Pure Mathematics and Statistics
Time allowed: 1 hour 30 minutes
(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 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 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
OCR is an exempt
[603/0933/7] DC
Charity Turn over
(SL/SG) 350669/4
, 2
Formulae
AS Level Mathematics A (H230)
Binomial series
n
^a + bh = an + nC1 a n-1b + nC2 a n-2b2 +f+ nCr a n- rbr +f+ ^n e Nh,
bn
where n n n!
C = C =c m=
r n r r r!^n - rh!
Differentiation from first principles
f^x + hh - f^xh
f l^xh h="lim
0 h
Standard deviation
/^x - / f ^x - xh2 / fx2
/ x2
xh2 n =
n -x
2 or /f = /f -x2
The binomial distribution
n n -x
If X ~ B^n, ph then P^X = xh = c mpx^1 - ph , mean of X is np, variance of X is np^1 - ph
x
Kinematics
v = u + at
s = ut + 21 at2
s = 2 1^u +
vht v2 = u2 +
2as s = 2vt -
1
at2
© OCR H230/01
2025 Jun25
, 3
Section A
Pure Mathematics
1 In this question you must show detailed reasoning.
Solve the following equations.
(a) x2 - 11 =5 [2]
(b) y6 + 7y3 - 8 =
[4]
0
[2]
(c) 2 3z-10 = 16
5
2 It is given that y0 (ax2 - 2x + 4) d x = 45 , where a is a constant.
Determine the value of a. [3]
3 (a) Express x2 - 6x in the form (x + p) 2 + q, where p and q are constants. [2]
(b) Hence or otherwise determine the centre and radius of the circle with equation
x2 + y2 - 6x - 16 = 0. [3]
cos i 1
4 (a) Show that - / tan i (where i ! 90n° for any odd integer n). [3]
1 - sin i cos i cos 3x 1
(b) Hence solve the equation - = 1 for 0 G x G 90°. [4]
1 - sin 3x cos 3x
5 (a) Find the coefficient of x7 in the expansion of (2x + 3) 9. [2]
(b) The following questions are about the binomial expansion of (1 + x) 21 in ascending
powers of x.
(i) Two consecutive terms have equal coefficients.
State the powers of x in these two terms. [1]
(ii) Given that the terms in xr and x r+5 have equal coefficients, find r. [2]
© OCR H230/01 Turn over
2025 Jun25
Thursday 15 May 2025 – Afternoon
AS Level Mathematics A
H230/01 Pure Mathematics and Statistics
Time allowed: 1 hour 30 minutes
(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 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 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
OCR is an exempt
[603/0933/7] DC
Charity Turn over
(SL/SG) 350669/4
, 2
Formulae
AS Level Mathematics A (H230)
Binomial series
n
^a + bh = an + nC1 a n-1b + nC2 a n-2b2 +f+ nCr a n- rbr +f+ ^n e Nh,
bn
where n n n!
C = C =c m=
r n r r r!^n - rh!
Differentiation from first principles
f^x + hh - f^xh
f l^xh h="lim
0 h
Standard deviation
/^x - / f ^x - xh2 / fx2
/ x2
xh2 n =
n -x
2 or /f = /f -x2
The binomial distribution
n n -x
If X ~ B^n, ph then P^X = xh = c mpx^1 - ph , mean of X is np, variance of X is np^1 - ph
x
Kinematics
v = u + at
s = ut + 21 at2
s = 2 1^u +
vht v2 = u2 +
2as s = 2vt -
1
at2
© OCR H230/01
2025 Jun25
, 3
Section A
Pure Mathematics
1 In this question you must show detailed reasoning.
Solve the following equations.
(a) x2 - 11 =5 [2]
(b) y6 + 7y3 - 8 =
[4]
0
[2]
(c) 2 3z-10 = 16
5
2 It is given that y0 (ax2 - 2x + 4) d x = 45 , where a is a constant.
Determine the value of a. [3]
3 (a) Express x2 - 6x in the form (x + p) 2 + q, where p and q are constants. [2]
(b) Hence or otherwise determine the centre and radius of the circle with equation
x2 + y2 - 6x - 16 = 0. [3]
cos i 1
4 (a) Show that - / tan i (where i ! 90n° for any odd integer n). [3]
1 - sin i cos i cos 3x 1
(b) Hence solve the equation - = 1 for 0 G x G 90°. [4]
1 - sin 3x cos 3x
5 (a) Find the coefficient of x7 in the expansion of (2x + 3) 9. [2]
(b) The following questions are about the binomial expansion of (1 + x) 21 in ascending
powers of x.
(i) Two consecutive terms have equal coefficients.
State the powers of x in these two terms. [1]
(ii) Given that the terms in xr and x r+5 have equal coefficients, find r. [2]
© OCR H230/01 Turn over
2025 Jun25
