2025 OCR AS Level Mathematics B (MEI) H630/01 Pure Mathematics and Mechanics
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Thursday 15 May 2025 – Afternoon
AS Level Mathematics B (MEI)
H630/01 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 70.
• 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 [603/0991/X] OCR is an exempt Charity
DC (SL/SG) 350671/7 Turn over
*1856846909*
, 2
Formulae AS Level Mathematics B (MEI) (H630)
Binomial series
(a + b) n = an + nC1 an–1b + nC2 an–2b2 + ... + nCr an–rbr + ... +b n ^n e Nh,
n
JnN n!
Cr = nCr = K O =
where r r!^n - rh!
L P
n n^n - 1h 2 n^n - 1h...^n - r + 1h r
^1 + xh = 1 + nx + x + ... + x + ... ^ x 1 1, n e Rh
2! r!
Differentiation from first principles
f^x + hh - f(x)
f l(x) = lim
h"0 h
Sample variance
2 1 2 2 ^/ xih2 2 2
s =n S where Sxx = /(xi - x)
- = / xi - n = / xi - n-x
- 1 xx
Standard deviation, s = variance
The binomial distribution
If X ~ B^n, ph then P (X = r) = nCr p r q n-r where q = 1 - p
Mean of X is np
Kinematics
Motion in a straight line
v = u + at
s = ut + 1 at2
2
s= 1 (u + v) t
2
v2 = u2 + 2as
s = vt - 1 at2
2
© OCR 2025 H630/01 Jun25
, 3
1 Expand (2a - b) 4 . You must simplify your answer. [3]
2 Triangle ABC is shown in the diagram. The length of AC is 2p cm and the length of BC is 3p cm,
where p is a positive constant. The angle ABC is 25°.
C
3p cm
2p cm
25°
B
A
Calculate the size of the obtuse angle CAB. [2]
3 In this question you must show detailed reasoning.
The graph below shows the line y = 3x - 4 and the line through P and Q where P is (–1, 3) and Q
is (5, 0).
y
P
Q
O 5 x
–4
Use an algebraic method to find the coordinates of the point of intersection of the two lines. [4]
© OCR 2025 H630/01 Jun25 Turn over
Combined Question Paper & Final Marking Scheme
Oxford Cambridge and RSA
Thursday 15 May 2025 – Afternoon
AS Level Mathematics B (MEI)
H630/01 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 your final answers to a degree of accuracy that is appropriate to the context.
• 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 70.
• 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 [603/0991/X] OCR is an exempt Charity
DC (SL/SG) 350671/7 Turn over
*1856846909*
, 2
Formulae AS Level Mathematics B (MEI) (H630)
Binomial series
(a + b) n = an + nC1 an–1b + nC2 an–2b2 + ... + nCr an–rbr + ... +b n ^n e Nh,
n
JnN n!
Cr = nCr = K O =
where r r!^n - rh!
L P
n n^n - 1h 2 n^n - 1h...^n - r + 1h r
^1 + xh = 1 + nx + x + ... + x + ... ^ x 1 1, n e Rh
2! r!
Differentiation from first principles
f^x + hh - f(x)
f l(x) = lim
h"0 h
Sample variance
2 1 2 2 ^/ xih2 2 2
s =n S where Sxx = /(xi - x)
- = / xi - n = / xi - n-x
- 1 xx
Standard deviation, s = variance
The binomial distribution
If X ~ B^n, ph then P (X = r) = nCr p r q n-r where q = 1 - p
Mean of X is np
Kinematics
Motion in a straight line
v = u + at
s = ut + 1 at2
2
s= 1 (u + v) t
2
v2 = u2 + 2as
s = vt - 1 at2
2
© OCR 2025 H630/01 Jun25
, 3
1 Expand (2a - b) 4 . You must simplify your answer. [3]
2 Triangle ABC is shown in the diagram. The length of AC is 2p cm and the length of BC is 3p cm,
where p is a positive constant. The angle ABC is 25°.
C
3p cm
2p cm
25°
B
A
Calculate the size of the obtuse angle CAB. [2]
3 In this question you must show detailed reasoning.
The graph below shows the line y = 3x - 4 and the line through P and Q where P is (–1, 3) and Q
is (5, 0).
y
P
Q
O 5 x
–4
Use an algebraic method to find the coordinates of the point of intersection of the two lines. [4]
© OCR 2025 H630/01 Jun25 Turn over
