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![Page 1: Question1 - WordPress.com · 2018-10-23 · 1 Find the value of the coefficient of 1 x in the expansion of 2x− 1 x 5.[3] 9709/01/M/J/03 BINOMIAL EXPANSION WORKSHEET AS MATHS BY:](https://reader031.vdocuments.site/reader031/viewer/2022011819/5e9ed74328ad763fce4d27fb/html5/thumbnails/1.jpg)
9709/1/O/N/02
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 1 -
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Question # 1
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![Page 2: Question1 - WordPress.com · 2018-10-23 · 1 Find the value of the coefficient of 1 x in the expansion of 2x− 1 x 5.[3] 9709/01/M/J/03 BINOMIAL EXPANSION WORKSHEET AS MATHS BY:](https://reader031.vdocuments.site/reader031/viewer/2022011819/5e9ed74328ad763fce4d27fb/html5/thumbnails/2.jpg)
1 Find the value of the coefficient of1x
in the expansion of (2x − 1x)
5. [3]
9709/01/M/J/03
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 2 -
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Question # 2
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4 Find the coefficient of x3 in the expansion of
(i) (1 + 2x)6, [3]
(ii) (1 − 3x)(1 + 2x)6. [3]
9709/01/M/J/04
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 3 -
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Question # 3
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1 Find the coefficient of x in the expansion of (3x − 2x)
5. [4]
9709/01/O/N/04
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 4 -
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Question # 4
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4 (i) Find the first 3 terms in the expansion of (2 − x)6 in ascending powers of x. [3]
(ii) Find the value of k for which there is no term in x2 in the expansion of (1 + kx)(2 − x)6. [2]
© UCLES 2005 9709/01/M/J/05
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 5 -
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Question # 5
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4 The first three terms in the expansion of (2 + ax)n, in ascending powers of x, are 32 − 40x + bx2. Findthe values of the constants n, a and b. [5]
© UCLES 2006 9709/01/M/J/06
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 6 -
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Question # 6
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1 Find the coefficient of x2 in the expansion of (x + 2x)6
. [3]
© UCLES 2006 9709/01/O/N/06
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 7 -
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Question # 7
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3 (i) Find the first three terms in the expansion of (2 + u)5 in ascending powers of u. [3]
(ii) Use the substitution u = x + x2 in your answer to part (i) to find the coefficient of x2 in the
expansion of (2 + x + x2)5. [2]
© UCLES 2007 9709/01/O/N/07
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 8 -
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Question # 8
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3 (i) Find the first 3 terms in the expansion, in ascending powers of x, of (2 + x2)5. [3]
(ii) Hence find the coefficient of x4 in the expansion of (1 + x2)2(2 + x2)5. [3
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 9 - © UCLES 2008 9709/01/M/J/08
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Question # 9
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![Page 10: Question1 - WordPress.com · 2018-10-23 · 1 Find the value of the coefficient of 1 x in the expansion of 2x− 1 x 5.[3] 9709/01/M/J/03 BINOMIAL EXPANSION WORKSHEET AS MATHS BY:](https://reader031.vdocuments.site/reader031/viewer/2022011819/5e9ed74328ad763fce4d27fb/html5/thumbnails/10.jpg)
1 Find the value of the coefficient of x2 in the expansion of (x2+ 2
x)
6. [3]
© UCLES 2008 9709/01/O/N/08
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 10 -
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Question # 10
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![Page 11: Question1 - WordPress.com · 2018-10-23 · 1 Find the value of the coefficient of 1 x in the expansion of 2x− 1 x 5.[3] 9709/01/M/J/03 BINOMIAL EXPANSION WORKSHEET AS MATHS BY:](https://reader031.vdocuments.site/reader031/viewer/2022011819/5e9ed74328ad763fce4d27fb/html5/thumbnails/11.jpg)
3 (i) Find the first 3 terms in the expansion of (2 + 3x)5 in ascending powers of x. [3]
(ii) Hence find the value of the constant a for which there is no term in x2 in the expansion of
(1 + ax)(2 + 3x)5. [2]
© UCLES 2009 9709/01/M/J/09
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 11 -
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Question # 11
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3 (i) Find the first 3 terms in the expansion of (2 − x)6 in ascending powers of x. [3]
(ii) Given that the coefficient of x2 in the expansion of (1 + 2x + ax2)(2 − x)6 is 48, find the value of
the constant a. [3]
© UCLES 2009 9709/11/O/N/09
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 12 -
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Question # 12
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(ii) Hence find the coefficient of x in the expansion of (1 +2
x2)(2x −
3
x)5
. [2]
© UCLES 2010 9709/11/M/J/10
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 13 -
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Question # 13
in descending powers of x. [3]x)2 (i) Find the first 3 terms in the expansion of (2x −
53
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6 (i) Find the first 3 terms in the expansion of (1 + ax)5 in ascending powers of x. [2]
(ii) Given that there is no term in x in the expansion of (1 − 2x)(1 + ax)5, find the value of the
constant a. [2]
(iii) For this value of a, find the coefficient of x2 in the expansion of (1 − 2x)(1 + ax)5. [3]
© UCLES 2010 9709/12/M/J/10 [Turn over
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 14 -
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Question # 14
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2 (i) Find the first three terms, in descending powers of x, in the expansion of (x − 2
x)6
. [3]
(ii) Find the coefficient of x4 in the expansion of (1 + x2)(x − 2
x)6
. [2]
© UCLES 2010 9709/13/M/J/10
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 15 -
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Question # 15
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1 Find the term independent of x in the expansion of (x −1
x2)9
. [3]
© UCLES 2010 9709/13/O/N/10
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 16 -
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Question # 16
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2 In the expansion of (1 + ax)6, where a is a constant, the coefficient of x is −30. Find the coefficient
of x3. [4]
© UCLES 2010 9709/11/O/N/10
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 17 -
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Question # 17
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1 (i) Find the first 3 terms in the expansion, in ascending powers of x, of (1 − 2x2)8. [2]
(ii) Find the coefficient of x4 in the expansion of (2 − x2)(1 − 2x2)8. [2]
© UCLES 2010 9709/12/O/N/10
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 18 -
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Question # 18
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2 (i) Find the terms in x2 and x3 in the expansion of (1 − 32x)6. [3]
(ii) Given that there is no term in x3 in the expansion of (k + 2x)(1 − 32x)6, find the value of the
constant k. [2]
© UCLES 2011 9709/12/M/J/11
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 19 -
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Question # 19
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1 Find the coefficient of x in the expansion of (x + 2
x2)7
. [3]
© UCLES 2011 9709/11/M/J/11
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 20 -
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Question # 20
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1 The coefficient of x3 in the expansion of (a + x)5 + (1 − 2x)6, where a is positive, is 90. Find the value
of a. [5]
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Question # 21
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1 Find the term independent of x in the expansion of (2x + 1
x2)6
. [3]
© UCLES 2011 9709/11/O/N/11
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 22 -
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Question # 22
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1 (i) Find the first 3 terms in the expansion of (2 − y)5 in ascending powers of y. [2]
(ii) Use the result in part (i) to find the coefficient of x2 in the expansion of (2 − (2x − x2))5. [3]
© UCLES 2011 9709/12/O/N/11
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Question # 23
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1 The coefficient of x2 in the expansion of (k + 13x)5
is 30. Find the value of the constant k. [3]
© UCLES 2011 9709/13/O/N/11
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 24 -
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Question # 24
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2 Find the coefficient of x6 in the expansion of (2x3 − 1
x2)7
. [4]
© UCLES 2012 9709/11/M/J/12
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 25 -
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Question # 25
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3 The coefficient of x3 in the expansion of (a + x)5 + (2 − x)6 is 90. Find the value of the positive
constant a. [5]
© UCLES 2012 9709/12/M/J/12
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 26 -
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Question # 26
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© UCLES 2012 9709/13/M/J/12
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Question # 27
3 The first three terms in the expansion of (1 − 2x) .
Find the values of the constants a and b. [6]
, in ascending powers of x, are 1 − x + bx26(1 + ax)2
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© UCLES 2012 9709/11/O/N/12
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Question # 28
. [2]6)in the expansion of (2 + x)(2x − x2(ii) Hence find the coefficient of x8
in ascending powers of x. [3]6)4 (i) Find the first 3 terms in the expansion of (2x − x2
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© UCLES 2012 9709/12/O/N/12
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Question # 29
is −280. Find the value of the constant a. [3], the coefficient of x57
x)−
a1 In the expansion of (x2
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© UCLES 2012 9709/13/O/N/12
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Question # 30
. [3]7
x)12
in the expansion of (2 −1 Find the coefficient of x3
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© UCLES 2013 9709/11/M/J/13
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Question # 31
is zero. Find the value
of p. [3]
6in the expansion of �1 − x��1 − px�(ii) It is given that the coefficient of x2
is
expanded in ascending powers of x. [2]
6, p is a non-zero constant. Find the first three terms when �1 − px�62 (i) In the expression �1 − px�
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2 Find the coefficient of x2 in the expansion of
(i)
@2x −
1
2x
A6
, [2]
(ii) �1 + x2�@2x −
1
2x
A6
. [3]
© UCLES 2013 9709/12/M/J/13
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 32 -
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Question # 32
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© UCLES 2013 9709/13/M/J/13
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Question # 33
5in the expansion of �1 + 2x��2 + ax�
54 (i) Find the first three terms in the expansion of �2 + ax� in ascending powers of x. [3]
(ii) Given that the coefficient of x2 is 240, find the possible
values of a. [3]
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© UCLES 2013 9709/11/O/N/13
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Question # 34
is zero. Find the value of a. [2], the coefficient of x26(ii) In the expansion of �1 + ax��2 + 3x�
is expanded in ascending powers of x. [3]61 (i) Find the first three terms when �2 + 3x�
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© UCLES 2013 9709/13/O/N/13 [Turn over
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Question # 35
��5. [4]
8 (i) Find the coefficient of x8 in the expansion of�x + 3x2
�4. [1]
(ii) Find the coefficient of x8 in the expansion of�x + 3x2
�5. [3]
(iii) Hence find the coefficient of x8 in the expansion of�1 +
�x + 3x2
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© UCLES 2014 9709/11/M/J/14
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Question # 36
. [4]8
2x
A+
14x33 Find the term independent of x in the expansion of
@
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© UCLES 2014 9709/12/M/J/14
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Question # 37
. [5]6A4
x2−x
@�in the expansion of �1 + x2
2 Find the coefficient of x2
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1 Find the coefficient of x in the expansion of
@x2
−2
x
A5
. [3]
© UCLES 2014 9709/13/M/J/14
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 38 -
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Question # 38
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1 In the expansion of �2 + ax�7, the coefficient of x is equal to the coefficient of x2. Find the value ofthe non-zero constant a. [3]
© UCLES 2014 9709/11/O/N/14
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 39 -
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Question # 39
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3 (i) Find the first 3 terms, in ascending powers of x, in the expansion of �1 + x�5. [2]
The coefficient of x2 in the expansion of�1 + �px + x2��5
is 95.
(ii) Use the answer to part (i) to find the value of the positive constant p. [3]
© UCLES 2014 9709/12/O/N/14
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 40 -
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Question # 40
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1 In the expansion of �2 + ax�6, the coefficient of x2 is equal to the coefficient of x3. Find the value ofthe non-zero constant a. [4]
© UCLES 2014 9709/13/O/N/14
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 41 -
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Question # 41
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3 (i) Find the first three terms, in ascending powers of x, in the expansion of
(a) �1 − x�6, [2]
(b) �1 + 2x�6. [2]
. [3]
© UCLES 2015 9709/11/M/J/15
(ii) Hence find the coefficient of x2 6in the expansion of ��1 − x��1 + 2x��
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 42 -
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Question # 42
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3 (i) Find the coefficients of x2 and x3 in the expansion of �2 − x�6. [3]
(ii) Find the coefficient of x3 in the expansion of �3x + 1��2 − x�6. [2]
© UCLES 2015 9709/12/M/J/15
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 43 -
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Question # 43
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3 (i) Write down the first 4 terms, in ascending powers of x, of the expansion of �a − x�5. [2]
(ii) The coefficient of x3 in the expansion of �1 − ax��a − x�5 is −200. Find the possible values of the
constant a. [4]
© UCLES 2015 9709/13/M/J/15
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 44 -
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Question # 44
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1 In the expansion of
@1 −
2x
a
A�a + x�5, where a is a non-zero constant, show that the coefficient of x2
is zero. [3]
© UCLES 2015 9709/11/O/N/15
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 45 -
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Question # 45
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2 In the expansion of �x + 2k�7, where k is a non-zero constant, the coefficients of x4 and x5 are equal.
Find the value of k. [4]
© UCLES 2015 9709/12/O/N/15
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 46 -
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Question # 46
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2 Find the coefficient of x in the expansion of
@x
3+
9
x2
A7
. [4]
© UCLES 2015 9709/13/O/N/15
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 47 -
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Question # 47
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1 (i) Find the coefficients of x4 and x5 in the expansion of �1 − 2x�5. [2]
(ii) It is given that, when �1 + px��1 − 2x�5 is expanded, there is no term in x5. Find the value of the
constant p. [2]
© UCLES 2016 9709/12/F/M/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 48 -
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Question # 48
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1 Find the term independent of x in the expansion of
@x −
3
2x
A6. [3]
© UCLES 2016 9709/11/M/J/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 49 -
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Question # 49
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![Page 50: Question1 - WordPress.com · 2018-10-23 · 1 Find the value of the coefficient of 1 x in the expansion of 2x− 1 x 5.[3] 9709/01/M/J/03 BINOMIAL EXPANSION WORKSHEET AS MATHS BY:](https://reader031.vdocuments.site/reader031/viewer/2022011819/5e9ed74328ad763fce4d27fb/html5/thumbnails/50.jpg)
4 Find the term that is independent of x in the expansion of
(i)
@x − 2
x
A6, [2]
(ii)
@2 + 3
x2
A @x − 2
x
A6. [4]
© UCLES 2016 9709/12/M/J/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 50 -
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Question # 50
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1 Find the coefficient of x in the expansion of
@1
x+ 3x2
A5. [3]
© UCLES 2016 9709/13/M/J/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 51 -
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Question # 51
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1 (i) Express x2 + 6x + 2 in the form �x + a�2 + b, where a and b are constants. [2]
(ii) Hence, or otherwise, find the set of values of x for which x2 + 6x + 2 > 9. [2]
© UCLES 2016 9709/11/O/N/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 52 -
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Question # 52
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![Page 53: Question1 - WordPress.com · 2018-10-23 · 1 Find the value of the coefficient of 1 x in the expansion of 2x− 1 x 5.[3] 9709/01/M/J/03 BINOMIAL EXPANSION WORKSHEET AS MATHS BY:](https://reader031.vdocuments.site/reader031/viewer/2022011819/5e9ed74328ad763fce4d27fb/html5/thumbnails/53.jpg)
4 In the expansion of �3 − 2x�01 +
x
2
1n, the coefficient of x is 7. Find the value of the constant n and
hence find the coefficient of x2. [6]
© UCLES 2016 9709/12/O/N/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 53 -
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Question # 53
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2 The coefficient of x3 in the expansion of �1 − 3x�6 + �1 + ax�5 is 100. Find the value of the constant a.
[4]
© UCLES 2016 9709/13/O/N/16
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 54 -
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Question # 54
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2 In the expansion of
@1
ax+ 2ax2
A5, the coefficient of x is 5. Find the value of the constant a. [4]
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© UCLES 2017 9709/12/F/M/17 [Turn over
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 55 -
Question # 55
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1 The coefficients of x2 and x3 in the expansion of �3 − 2x�6 are a and b respectively. Find the value ofa
b. [4]
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© UCLES 2017 9709/11/M/J/17
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 56 -
Question # 56
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1 (i) Find the coefficient of x in the expansion of
@2x −
1
x
A5. [2]
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(ii) Hence find the coefficient of x in the expansion of �1 + 3x2�@2x −
1
x
A5. [4]
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© UCLES 2017 9709/12/M/J/17
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 57 -
Question # 57
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1 The coefficients of x and x2 in the expansion of �2 + ax�7 are equal. Find the value of the non-zero
constant a. [3]
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© UCLES 2017 9709/13/M/J/17
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 58 -
Question # 58
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1 Find the term independent of x in the expansion of
@2x −
1
4x2
A9. [4]
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© UCLES 2017 9709/12/O/N/17
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 59 -
Question # 59
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3 (i) Find the term independent of x in the expansion of
@2
x− 3x
A6. [2]
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(ii) Find the value of a for which there is no term independent of x in the expansion of
�1 + ax2�@2
x− 3x
A6. [3]
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© UCLES 2017 9709/13/O/N/17
BINOMIAL EXPANSION WORKSHEET AS MATHS BY: MR. AFDAL - Page 60 -
Question # 60
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