The Windsor Boys’ School
Pure 2 Chapter 4 – Binomial Expansion
This paper is out of 40
f ( x)  (3  2 x) 3 ,
1.
3
x .
2
Find the binomial expansion of f(x), in ascending powers of x, as far as the term in x3.
Give each coefficient as a simplified fraction.
(Total 5 marks)
2.
(a)
Find the binomial expansion of
(1  8 x) ,
1
x  ,
8
in ascending powers of x up to and including the term in x3, simplifying each term.
(4)
(b)
Show that, when x =
1
, the exact value of √(1 – 8x) is
100
23
.
5
(2)
(c)
1
into the binomial expansion in part (a) and hence obtain an
100
approximation to √23. Give your answer to 5 decimal places.
Substitute x 
(3)
(Total 9 marks)
The Windsor Boys' School
1
3.
(a)
Expand
1
(4  3x)
, where x 
4
, in ascending powers of x up to and including the term
3
2
in x . Simplify each term.
(5)
(b)
Hence, or otherwise, find the first 3 terms in the expansion of
x8
(4  3 x)
as a series in
ascending powers of x.
(4)
(Total 9 marks)
4.
1
f(x) =
(4  x)
,
│x│ < 4
Find the binomial expansion of f (x) in ascending powers of x, up to and including the term in
x3. Give each coefficient as a simplified fraction.
(Total 6 marks)
5.
f ( x) 
(a)
3x 2  16
(1  3x)(2  x)
2

A
B
C


,
(1  3x) (2  x) (2  x) 2
x  13
Find the values of A and C and show that B = 0.
(4)
(b)
Hence, or otherwise, find the series expansion of f(x), in ascending powers of x, up to and
including the term in x3. Simplify each term.
(7)
(Total 11 marks)
The Windsor Boys' School
2