A Level Mathematics A H240/03 Pure Mathematics And Mechanics Sample Question Paper

A Level Mathematics A
H240/03 Pure Mathematics And Mechanics
Sample Question Paper

Date – Morning/Afternoon Version 2.1
Time Allowed: 2 Hours


You Must Have:
• Printed Answer Booklet

You May Use:
• A Scientific Or Graphical Calculator




* 0 0 0 0 0 0 *




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 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.
• You Are Permitted To Use A Scientific Or Graphical Calculator In This Paper.
• 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. Unless Otherwise Instructed,
When A Numerical Value Is Needed, Use G = 9.8.

INFORMATION

• The Total Number Of Marks For This Paper Is 100.
• The Marks For Each Question Are Shown In Brackets [ ].
• You Are Reminded Of The Need For Clear Presentation In Your Answers.
• The Printed Answer Booklet Consists Of 16 Pages. The Question Paper Consists Of 12 Pages.




© OCR 2018 H240/03 Turn Over
603/1038/8 B10022.5.6

, 2

Formulae
A Level Mathematics A (H240)

Arithmetic Series
Sn = 12 N(A + L) =2 1 N{2a + (N −1)D}

Geometric Series
A(1 − R N
)
Sn =
1− R
A
S = For R  1
1− R

Binomial Series
N N N N N−2 2
(A + B)N−1= A + C1 A B + C2 A B + + n C r a n−r br + + bn (n  ) ,
N N!
Where
=
N
C C = =
R N  r  R !(N − R)!
R  
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( F ( X)
X)
Tan Kx K Sec 2 Kx
Sec X Sec X Tan X
Cotx − Cosec 2 X
Cosec X − Cosec X Cot X
Du
U V − U
Quotient Y = , Dv Dy = Dx
Rule V Dx Dx V2

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

1
 F ( X) ( F ( X)) ( F ( X) )
N N+1
Dx = +C
N +1
Dv
Integration By Parts
 U
Du
Dx = Uv − V
Dx

Dx Dx

© OCR 2018 H240/03

,Small Angle Approximations 3
1 2
Sin    , Cos   1 − , Tan    Where Θ Is Measured In Radians
 2




© OCR 2018 H240/03 Turn over

, 4

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
Tan( A  B)
B ( A  B  (K + 1 ) )
= 2
1 tan A tan B

Numerical Methods
B B−
A 2 N
N−1
A
N
Trapezium Y Dx  1 H{( Y0 + ) + 2( Y1 + Y2 + … + ) }, Where H
Rule: Y Y =

F( Xn
)
The Newton-Raphson Iteration For Solving F( X) = Xn+1 = Xn
0: − 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 )

Standard Deviation

 F( −X )
) (X − X
2
2  X2 Fx 2
= −X 2
X = − X2
Or 
N N  F
F

The Binomial Distribution
N
If X ~ B(N, P) Then P( X = X) =  P X (1 − P) N− X , Mean Of X Is Np, Variance Of X Is Np(1 – P)
 x

Hypothesis Test For The Mean Of A Normal Distribution
  2 X −
( )
If X ~ N  ,  2 Then X ~ N  ,
  And ~ N(0, 1)
 N  / N

Percentage Points Of The Normal Distribution
If Z Has A Normal Distribution With Mean 0 And Variance 1 Then, For Each Value Of P, The Table
Gives The
Value Of Z Such P(Z  Z) = P.
That

P 0.75 0.90 0.95 0.975 0.99 0.995 0.9975 0.999 0.9995
Z 0.674 1.282 1.645 1.960 2.326 2.576 2.807 3.090 3.291
© OCR 2018 H240/03