OCR A Level Mathematics B (MEI) Pure Mathematics
and Mechanics (H640/02)
Oxford Cambridge and RSA
June 2026 – Afternoon
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Time allowed: 2 hours
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 ms–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 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, 2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
Sn = 12 n^a + lh = 21 n"2a +^n - 1hd,
Geometric series
a^1 - rnh
Sn = 1 - r
a
S = for r 1 1
3 1-r
Binomial series
^a + bhn = an + nCJ 1 N
a n-1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
n n n!
C = C = =
where KO
Lr P r!^n - rh!
r n r
n^n - 1h 2 n^n - 1hf^n - r + 1h r ^ x 1 1, n e Rh
^1 + xhn = 1 + nx + x +f+ x +f
2! r!
Differentiation
f^xh f l^xh
tan kx k sec2kx
sec x sec x tan x
cot x -cosec2x
cosec x - cosec x cot x
u dy v du - u dv
Quotient Rule y = v , = dx 2 dx
dx v
Differentiation from first principles
f^x + hh- f^xh
f l^xh = lim
h"0 h
Integration
c f l^xh
d dx = ln f^xh + c
ef x
^ h
n 1 af^xhkn +1 + c
; f l^xhaf^xhk dx =
n+1
dv du
Integration by parts ; u dx = uv - ; v dx
dx dx
Small angle approximations
sin i ≈ i, cos i ≈ 1 - 1 2i2, tan i ≈ i where i is measured in radians
, 3
Trigonometric identities
sin^A ! Bh = sin A cos B ! cos A sin B
cos^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan^A ! Bh = aA ! B ! ^k + 12hrk
1 " tan A tan B
Numerical methods
b-a
Trapezium rule: ; b y dx ≈ 1 h"^y + y h + 2^y + y +f+ y h,, where h =
a
2 0 n 1 2 n -1
f^x h n
n
The Newton-Raphson iteration for solving f^xh = 0: xn +1 = xn -
f l^xnh
Probability
P^A j Bh = P^Ah +P^Bh - P^A k Bh
P^A k Bh
P^A k Bh = P^AhP^B Ah = P^BhP^A Bh or P^A Bh =
P^Bh
Sample variance
2 1 2 ^/ xih2 2
s = n - 1 Sxx where Sxx = /^xi - xh = / x i - n = / x i - nx
- 2 2 -
Standard deviation, s = variance
The binomial distribution
If X + B^n, ph then P^X = rh = nCr prqn-r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J 2N X-n
2 v
If X + N^n, v h then X + NKn, n O and v ~ N^0, 1h
n
L P
Percentage points of the Normal distribution
p 10 5 2 1
1 p% 1 p%
z 1.645 1.960 2.326 2.576 2 2
z
Kinematics
Motion in a straight line Motion in two dimensions
v = u + at v = u + at
s = ut + 21 at2 s = ut + 12at2
s = 12^u + vht s = 12^u + vht
v2 = u2 + 2as
s = vt - 12 at2 s = vt - 12 at2
Turn over
, 4
Section A (20 marks)
1 (a) Sketch the function y = 2x - 3 . [2]
(b) In this question you must show detailed reasoning.
Solve the equation 2x - 3 = 4 - x. [3]
7x - 25
2 Express in partial fractions. [4]
2
(x - 1)(x - 4)
3 (a) Evaluate
4
1
r
r =1
giving your answer as a fraction in its lowest terms. [1]
(b) Write the sum 1 + 3 + 5 + 7 + 9 in a similar way to the series in part (a). [2]
(c) Explain why the sum to infinity of 1 + 3 + 5 + 7 + 9 +… is not well defined. [1]
4 The diagram shows part of a circle with centre O and radius 5 cm. The circle passes through the
points A and B. The length AB is 5 cm.
O
A 5 cm B
Calculate the area of the shaded region. [4]
and Mechanics (H640/02)
Oxford Cambridge and RSA
June 2026 – Afternoon
A Level Mathematics B (MEI)
H640/01 Pure Mathematics and Mechanics
Time allowed: 2 hours
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 ms–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 12 pages.
ADVICE
• Read each question carefully before you start your answer.
, 2
Formulae A Level Mathematics B (MEI) (H640)
Arithmetic series
Sn = 12 n^a + lh = 21 n"2a +^n - 1hd,
Geometric series
a^1 - rnh
Sn = 1 - r
a
S = for r 1 1
3 1-r
Binomial series
^a + bhn = an + nCJ 1 N
a n-1b + nC2 a n-2b2 +f+ nCr a n-rbr +f+ bn ^n e Nh,
n n n!
C = C = =
where KO
Lr P r!^n - rh!
r n r
n^n - 1h 2 n^n - 1hf^n - r + 1h r ^ x 1 1, n e Rh
^1 + xhn = 1 + nx + x +f+ x +f
2! r!
Differentiation
f^xh f l^xh
tan kx k sec2kx
sec x sec x tan x
cot x -cosec2x
cosec x - cosec x cot x
u dy v du - u dv
Quotient Rule y = v , = dx 2 dx
dx v
Differentiation from first principles
f^x + hh- f^xh
f l^xh = lim
h"0 h
Integration
c f l^xh
d dx = ln f^xh + c
ef x
^ h
n 1 af^xhkn +1 + c
; f l^xhaf^xhk dx =
n+1
dv du
Integration by parts ; u dx = uv - ; v dx
dx dx
Small angle approximations
sin i ≈ i, cos i ≈ 1 - 1 2i2, tan i ≈ i where i is measured in radians
, 3
Trigonometric identities
sin^A ! Bh = sin A cos B ! cos A sin B
cos^A ! Bh = cos A cos B " sin A sin B
tan A ! tan B
tan^A ! Bh = aA ! B ! ^k + 12hrk
1 " tan A tan B
Numerical methods
b-a
Trapezium rule: ; b y dx ≈ 1 h"^y + y h + 2^y + y +f+ y h,, where h =
a
2 0 n 1 2 n -1
f^x h n
n
The Newton-Raphson iteration for solving f^xh = 0: xn +1 = xn -
f l^xnh
Probability
P^A j Bh = P^Ah +P^Bh - P^A k Bh
P^A k Bh
P^A k Bh = P^AhP^B Ah = P^BhP^A Bh or P^A Bh =
P^Bh
Sample variance
2 1 2 ^/ xih2 2
s = n - 1 Sxx where Sxx = /^xi - xh = / x i - n = / x i - nx
- 2 2 -
Standard deviation, s = variance
The binomial distribution
If X + B^n, ph then P^X = rh = nCr prqn-r where q = 1 - p
Mean of X is np
Hypothesis testing for the mean of a Normal distribution
J 2N X-n
2 v
If X + N^n, v h then X + NKn, n O and v ~ N^0, 1h
n
L P
Percentage points of the Normal distribution
p 10 5 2 1
1 p% 1 p%
z 1.645 1.960 2.326 2.576 2 2
z
Kinematics
Motion in a straight line Motion in two dimensions
v = u + at v = u + at
s = ut + 21 at2 s = ut + 12at2
s = 12^u + vht s = 12^u + vht
v2 = u2 + 2as
s = vt - 12 at2 s = vt - 12 at2
Turn over
, 4
Section A (20 marks)
1 (a) Sketch the function y = 2x - 3 . [2]
(b) In this question you must show detailed reasoning.
Solve the equation 2x - 3 = 4 - x. [3]
7x - 25
2 Express in partial fractions. [4]
2
(x - 1)(x - 4)
3 (a) Evaluate
4
1
r
r =1
giving your answer as a fraction in its lowest terms. [1]
(b) Write the sum 1 + 3 + 5 + 7 + 9 in a similar way to the series in part (a). [2]
(c) Explain why the sum to infinity of 1 + 3 + 5 + 7 + 9 +… is not well defined. [1]
4 The diagram shows part of a circle with centre O and radius 5 cm. The circle passes through the
points A and B. The length AB is 5 cm.
O
A 5 cm B
Calculate the area of the shaded region. [4]
