OCR AS Level Mathematics A H230/02 Pure Mathematics and Mechanics

Formulae

AS Level Mathematics A (H230)

Binomial series

a b a a C C b a b a C b b n n n n n n n

r

n r r n

1

1

2 + = + + 2 2 + + f f+ + - - - ^ h ^n ! Nh,

where C

! !

n !

r r n r

n C

n

r n r = = = - c ^ m h

Differentiation from first principles

x lim h

x h x

f

f f

h 0 = + -

" l^ ^ ^ h h h

Standard deviation

n

x x

n

x

x

2 2

2 - = - /^ h /

 or f

f x x

f

fx

x

2 2

2 - = - ^ h

/

/

/

/

The binomial distribution

If X n + B^ , ph then X x

n

x

P p p 1 x n x = = - - ^ h c m ^ h , mean of X is np, variance of X is np^1-ph

Kinematics

v u = +at

s ut at 2

1 2 = +

s u v t 2

1 = + ^ h

v u 2as

2 2 = +

s vt at 2

1 2 = -

3

© OCR 2022 H230/02 Jun22 Turn over

Section A: Pure Mathematics

Answer all the questions.

1 Write the solution of the inequality ( ) x x - + 2 3 ( ) 2 0 using set notation. [2]

2 In this question you must show detailed reasoning.

Solve the equation 3 1 x x + = 4 . [4]

3 Give a counter example to disprove the following statement.

If x and y are both irrational then x y + is irrational. [2]

4 The circle x y 6 4 x y k 0 2 2 + -++ = has radius 5.

Determine the value of k. [3]

4

© OCR 2022 H230/02 Jun22

5

y

O x

( , 1 )2

1 -

The diagram shows a curve C for which y is inversely proportional to x. The curve passes through

the point 1, 2

1 a - k.

(a) (i) Determine the equation of the gradient function for the curve C. [3]

 (ii) Sketch this gradient function on the axes in the Printed Answer Booklet. [1]

(b) The diagram indicates that the curve C has no stationary points.

 State what feature of your sketch in part (a)(ii) corresponds to this. [1]

(c) The curve C is translated by the vector 2

0

-

c m.

 Find the equation of the curve after it has been translated.