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 H230/01 Jun22 Turn over
Section A: Pure Mathematics
Answer all the questions.
1 Find the term in x3
in the binomial expansion of ( ) 3 2x 5 - . [2]
2 In this question you must show detailed reasoning.
The cubic polynomial f(x) is defined by f x x5 4x ax 2 3 2 ^ h = - + - , where a is a constant.
You are given that ( ) x-2 is a factor of f(x).
(a) Find the value of a. [2]
(b) Find all the factors of f(x). [3]
3 The diagram in the Printed Answer Booklet shows part of the graph of y x 4 3 x
2 = - + .
(a) It is required to solve the equation x x3 1 0 2 - + = graphically by drawing a straight line with
equation y m = +x c on the diagram, where m and c are constants.
Find the values of m and c. [2]
(b) Use the graph to find approximate values of the roots of the equation x x3 1 0 2 - + = . [2]
(c) By shading, or otherwise, indicate clearly the regions where all of the following inequalities
are satisfied. You should use the values of m and c found in part (a).
x H 0 x G 4 y x 4 3 x
2 G - + y m H x c + [3]
4 In this question you must show detailed reasoning.
Solve the following equations, for 0° ° G Gx 360 .
(a) 2 1 tan x+ = 4 [3]
(b) 5 1 sin c x x 2 os2 - = [5]
5 The gradient of a curve is given by d
d
x x
x
y 3 2 = - . The curve passes through the point (6, 20).
(a) Determine the equation of the curve. [4]
(b) Hence determine y x d p
1
y in terms of the constant p.
Version | LATEST 2022 |
Release date | 2022-07-14 |
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Authors | Qwivy.com |
Pages | 8 |
Language | English |
Tags | OCR AS Level Mathematics A H23001 Pure Mathematics and Statistics 2022 |
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