CIE IGCSE ADDITIONAL MATHEMATICS
(0606)
TOPICAL PRACTICE QUESTIONS
TOPIC 12:
SERIES
Compiled from:
Paper 1
Variants 1, 2 and 3
2016- 2020
"Discipline is doing what
needs to be done, even if
you don't feel like doing it."
Source: 0606/11/M/J/18 - Question No. 9
1
8
J
1 NO
K
(i) Find the first 3 terms in the expansion of K2x O in descending powers of x.
16xP
L
8
J
N2
1 NO JK 1
OO .
1
+
(ii) Hence find the coefficient of x4 in the expansion of KK2x O K 2
x
16
x
L
P L
P
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[3]
[3]
Compilation: www.mystudycompass.com
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Source: 0606/11/M/J/19 - Question No. 4
2
(i)
The first 3 terms, in ascending powers of x, in the expansion of `2 + bxj
a + 256x + cx2. Find the value of each of the constants a, b and c.
(ii)
Using the values found in part (i), find the term independent of x in the expansion of
8
`2 + bxj b2x - 3l .
x
8
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2
can be written as
[4]
[3]
Compilation: www.mystudycompass.com
Source: 0606/11/M/J/20 - Question No. 9
3
Page 3
(a) An arithmetic progression has a second term of - 14 and a sum to 21 terms of 84. Find the first
term and the 21st term of this progression.
[5]
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Compilation: www.mystudycompass.com
Source: 0606/11/M/J/20 - Question No. 9
Page 4
(b) A geometric progression has a second term of 27p 2 and a fifth term of p 5 . The common ratio, r, is
such that 0 1 r 1 1.
(i) Find r in terms of p.
[2]
(ii) Hence find, in terms of p, the sum to infinity of the progression.
[3]
(iii) Given that the sum to infinity is 81, find the value of p.
[2]
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Compilation: www.mystudycompass.com
Source: 0606/11/O/N/16 - Question No. 4
4
5
J
1N
2
K
O
(i) Find the first 3 terms in the expansion of 2x , in descending powers of x.
3xP
L
5
J
1N
1 NJ
(ii) Hence find the coefficient of x7 in the expansion of K3 + 3OK2x 2 - O .
3xP
x PL
L
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[3]
[2]
Compilation: www.mystudycompass.com
Source: 0606/11/O/N/18 - Question No. 3
5
Page 6
The coefficient of x2 in the expansion of (2 - x) (3 + kx) 6 is equal to 972. Find the possible values of the
constant k.
[6]
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Compilation: www.mystudycompass.com
Source: 0606/11/O/N/20 - Question No. 10
6
Page 7
(a) An arithmetic progression has a second term of 8 and a fourth term of 18. Find the least number of
terms for which the sum of this progression is greater than 1560.
[6]
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Compilation: www.mystudycompass.com
Source: 0606/11/O/N/20 - Question No. 10
Page 8
(b) A geometric progression has a sum to infinity of 72. The sum of the first 3 terms of this progression
333
is
.
8
(i) Find the value of the common ratio.
[5]
(ii) Hence find the value of the first term.
[1]
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Compilation: www.mystudycompass.com
Source: 0606/12/M/J/16 - Question No. 2
7
1 5
(i) The first 3 terms in the expansion of c2 - m are
4x
integers a, b and c.
a+
b c
+ . Find the value of each of the
x x2
[3]
(ii) Hence find the term independent of x in the expansion of c2 -
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1 m5 ^
3 + 4xh.
4x
[2]
Compilation: www.mystudycompass.com
Source: 0606/12/M/J/17 - Question No. 4
83
Page 10
n
J
x NO x-axis and y-axis2respectively.
Vectors
j areinunit
vectors parallel
- the
The
firsti 3and
terms
the expansion
of KK3 to
O are 81 + ax + bx . Find the value of each of the constants
6P
n, a and b.
[5]
L
(a) The vector v has a magnitude of 3 5 units and has the same direction as i - 2 j. Find v giving
your answer in the form a i + b j, where a and b are integers.
[2]
(b) The velocity vector w makes an angle of 30° with the positive x-axis and is such that w = 2 .
Find w giving your answer in the form c i + d j, where c and d are integers.
[2]
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Compilation: www.mystudycompass.com
Source: 0606/12/M/J/18 - Question No. 5
9
Page 11
5
J
1 ON
b c
K
(i) The first three terms in the expansion of K3 - O can be written as a + + 2 . Find the value
x x
9xP
of each of the constants a, b and c.
[3]
L
(ii) Use your values of a, b and c to find the term independent of x in the expansion of
N5
J
KK3 - 1 OO (2 + 9x) 2 .
9x P
L
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[3]
Compilation: www.mystudycompass.com
Source: 0606/12/M/J/20 - Question No. 3
Page 12
x 6
10 (a) Find the first 3 terms in the expansion of b4 - l in ascending powers of x. Give each term in
16
its simplest form.
[3]
(b) Hence find the term independent of x in the expansion of b4 -
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2
x 6b
l x - 1l .
x
16
[3]
Compilation: www.mystudycompass.com
Source: 0606/12/O/N/16 - Question No. 4
11
5
J
1N
2
K
O
(i) Find the first 3 terms in the expansion of 2x , in descending powers of x.
3xP
L
5
J
1N
1 NJ
(ii) Hence find the coefficient of x7 in the expansion of K3 + 3OK2x 2 - O .
3xP
x PL
L
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[3]
[2]
Compilation: www.mystudycompass.com
Source: 0606/12/O/N/17 - Question No. 3
12
5
J
x 2NO
K
(i) Find, in ascending powers of x, the first 3 terms in the expansion of K2 - O .
4P
L
5
2
J
x 2NO JK1 3 NO
K
(ii) Hence find the term independent of x in the expansion of K2 - O K - 2O .
4 P Lx x P
L
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[3]
[3]
Compilation: www.mystudycompass.com
Source: 0606/12/O/N/18 - Question No. 5
13
Page 15
The 7th term in the expansion of (a + bx) 12 in ascending powers of x is 924x 6 . It is given that a and b are
positive constants.
(i)
1
Show that b = .
a
[2]
The 6th term in the expansion of (a + bx) 12 in ascending powers of x is 198x 5 .
(ii)
Find the value of a and of b.
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[4]
Compilation: www.mystudycompass.com
Source: 0606/12/O/N/19 - Question No. 3
Page 16
x 14
14 The first three terms in the expansion of b1 - l (1 - 2x) 4 can be written as 1 + ax + bx 2 . Find the value
7
of each of the constants a and b.
[6]
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Compilation: www.mystudycompass.com
Source: 0606/12/O/N/20 - Question No. 4
Page 17
15 The 7th and 10th terms of an arithmetic progression are 158 and 149 respectively.
(a) Find the common difference and the first term of the progression.
[3]
(b) Find the least number of terms of the progression for their sum to be negative.
[3]
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Compilation: www.mystudycompass.com
Source: 0606/12/O/N/20 - Question No. 5
3
2
16 Find the coefficient of x 2 in the expansion of bx - lbx + l .
x
x
5
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[5]
Compilation: www.mystudycompass.com
Source: 0606/13/M/J/18 - Question No. 9
17
8
J
1 NO
K
(i) Find the first 3 terms in the expansion of K2x O in descending powers of x.
16xP
L
8
J
N2
1 NO JK 1
OO .
1
+
(ii) Hence find the coefficient of x4 in the expansion of KK2x O K 2
x
16
x
L
P L
P
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Page 19
[3]
[3]
Compilation: www.mystudycompass.com
Source: 0606/13/M/J/20 - Question No. 8
Page 20
18 (a) An arithmetic progression has a first term of 7 and a common difference of 0.4. Find the least
number of terms so that the sum of the progression is greater than 300.
[4]
(b) The sum of the first two terms of a geometric progression is 9 and its sum to infinity is 36. Given
that the terms of the progression are positive, find the common ratio.
[4]
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Compilation: www.mystudycompass.com
Source: 0606/13/O/N/16 - Question No. 4
19
6
J
xN
K
O
(i) Find, in ascending powers of x, the first 3 terms in the expansion of 2 .
4P
L
6
J
xN
2 3 NJ
(ii) Hence find the term independent of x in the expansion of K4 + + 2OK2 - O .
x x PL
4P
L
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[3]
[3]
Compilation: www.mystudycompass.com
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Source: 0606/13/O/N/17 - Question No. 7
20
2 6
x
(i) Find, in ascending powers of x, the first 3 terms in the expansion of c2 - m . Give each term in
4
its simplest form.
[3]
(ii)
2
6
x2 1
Hence find the coefficient of x in the expansion of c2 - m c + xm .
x
4
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2
[4]
Compilation: www.mystudycompass.com
Source: 0606/13/O/N/18 - Question No. 1
21
(a) In the expansion of (2 + px) 5 the coefficient of x 3 is equal to -
(b) Find the term independent of x in the expansion of e2x 2 +
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8
1
o .
4x 2
Page 23
8
. Find the value of the constant p.
25
[3]
[3]
Source: 0606/13/O/N/20 - Question No. 5
Page 24
25
xn
r
the expansion
of point
is
, find the value of the
(1 + at
x) btime
1 - tls is given
22 Given
thatdisplacement,
the coefficient
ofofx 2a in
(b) The
x m,
particle
from a fixed
4 by x = 6 cos b3t + 3 l.
2
positive integer n.
[5]
2r
Find the acceleration of the particle when t =
.
[3]
3
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