A Level Mathematics B (MEI) H640/02 Pure Mathematics and Statistics Sample Question Paper

MATHEMATICS OCR

A Level Mathematics B (MEI)
H640/02 Pure Mathematics and Statistics
Sample Question Paper

Date – Morning/Afternoon
Time allowed: 2 hours


OCR supplied materials:
• Printed Answer Booklet




EN
You must have:
• Printed Answer Booklet
• Scientific or graphical calculator
* 0 0 0 0 0 0 *
IM
INSTRUCTIONS
• Use black ink. HB pencil may be used for graphs and diagrams only.
• Complete the boxes provided on the Printed Answer Booklet with your name, centre number
EC

and candidate number.
• Answer all the questions.
• Write your answer to each question in the space provided in the Printed Answer Booklet.
• Additional paper may be used if necessary but you must clearly show your candidate number,
centre number and question number(s).
• Do not write in the bar codes.
SP



• You are permitted to use a scientific or graphical calculator in this paper.
• Final answers should be given to a degree of accuracy appropriate to the context.

INFORMATION
• The total number of marks for this paper is 100.
• The marks for each question are shown in brackets [ ].
• You are advised that an answer may receive no marks unless you show sufficient detail of the
working to indicate that a correct method is used. You should communicate your method with
correct reasoning.
• The Printed Answer Book consists of 20 pages. The Question Paper consists of 12 pages.




© OCR 2017 H640/02 Turn over
603/1002/9 B10026/4.1

, 2

Formulae A Level Mathematics B (MEI) H640


Arithmetic series
Sn  12 n(a  l )  12 n{2a  (n  1)d}

Geometric series
a(1  r n )
Sn 
1 r
a
S  for r  1
1 r

Binomial series
(a  b)n  a n  n C1 a n1b  n C2 a n2b2   n Cr a n  r b r   bn (n  ) ,
n n!
where n Cr    
 r  r !(n  r )!




EN
n(n  1) 2 n(n  1) (n  r  1) r
(1  x)n  1  nx 
2!
x  
r!
x  x  1, n  
Differentiation
f ( x) f ( x)
IM
tan kx k sec2 kx
sec x sec x tan x
cot x  cosec2 x
EC

cosec x  cosec x cot x
du dv
u dy v dx  u dx
Quotient Rule y  , 
v dx v2
SP



Differentiation from first principles
f ( x  h)  f ( x )
f ( x)  lim
h 0 h

Integration
f ( x)
 f ( x)
dx  ln f ( x)  c



 f (x) f ( x) dx  n  1 f ( x)
n 1 n 1
c



 
dv du
Integration by parts u dx  uv  v dx
dx dx

Small angle approximations
sin    , cos  1  12  2 , tan    where θ is measured in radians




© OCR 2017 H640/02

, 3

Trigonometric identities
sin( A  B)  sin A cos B  cos Asin B
cos( A  B)  cos A cos B sin Asin B
tan A  tan B
tan( A  B)  ( A  B  ( k  12 ) )
1 tan A tan B

Numerical methods
b ba
Trapezium rule: a y dx  12 h{( y0  yn )  2( y1  y2  …  yn1 ) }, where h  n
f( xn )
The Newton-Raphson iteration for solving f( x)  0 : xn 1  xn 
f ( xn )

Probability
P( A  B)  P( A)  P( B)  P( A  B)
P( A  B)
P( A  B)  P( A)P( B | A)  P( B)P( A | B ) or P( A | B) 
P(B )




EN
Sample variance
  xi   x2  nx 2
2
1
s 
2
S xx where S xx   ( xi  x )2   xi2  i
n 1 n
IM
Standard deviation, s  variance

The binomial distribution
EC

If X ~ B(n, p) then P( X  r )  n Cr p r q nr where q  1  p
Mean of X is np

Hypothesis testing for the mean of a Normal distribution
  2 X 
 
SP



If X ~ N  ,  2 then X ~ N   ,  and ~ N(0, 1)
 n  / n

Percentage points of the Normal distribution

p 10 5 2 1
z 1.645 1.960 2.326 2.575


Kinematics
Motion in a straight line Motion in two dimensions
v  u  at v  u  at
s  ut  12 at 2 s  ut  12 at 2
s  12  u  v  t s  12  u  v  t
v2  u 2  2as
s  vt  12 at 2 s  vt  12 at 2




© OCR 2017 H640/02 Turn over