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Mathematical Methods Textbook Worked Solutions Chapter 1- 9
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C H A P T E R
1
Functions and relations
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a)
b)
c)
d)
e)
f)
g)
h)
Exercise 1B Q3
a)
b)
c)
d)
e)
f)
g)
h)
i)
O
2 2
4
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Exercise 1C Q9
b)
Exercise 1C Q10
Exercise 1C Q11
Exercise 1C Q 12
a)
b)
Exercise 1C Q 13
a)
b)
Exercise 1C Q14
a)b)c)d)
e)f)Exercise 1C Q15
c)d) =e) =f)g)Exercise 1C Q16
Exercise 1C Q17
using the points given
Exercise 1D Q1
a) 8 b)8 c)2 d)-2 e) -2 f)4
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f)
Exercise 1F Q2
a)b)c)d)e)f)g)Exercise 1F Q3
a)b)c)d)
e)f)Exercise 1F Q4
a)b)c)d)Exercise 1F Q5
a)
b)=
c)
Exercise 1F Q6
a):
b) :
Exercise 1F Q7
a) the range of f is ,which is not a subset of the domain of ,
b) :y
Exercise 1F Q8
a)y
y
4
4
b)y
9
-3 3
2-2
0
4
40-4
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Exercise 1G Q7
a)
b)
c)
d)
e)
f)
g)
h)
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Exercise 1G Q8
a) C B D AExercise 1G Q9
b)
c)
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C H A P T E R
2
Revising linear functions andmatrices
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Exercise 2C Q2
a)
b)
c)
d)
e)
f)
Exercise 2C Q3
a)
b)
c)
d)
Exercise 2C Q4
a)
b)
c)
d)
Exercise 2C Q5
a)
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b)
c)
d)
Exercise 2C Q6
Exercise 2C Q7
a)
b)c)
Exercise 2C Q8
a)
b)
c)
d)
e)
f)
Exercise 2C Q9
a) i)
ii)
b) i)
ii)
Exercise 2C Q10
Exercise 2C Q11
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Exercise 2E Q2
a)
b)
c)
Exercise 2E Q3
a)
Exercise 2E Q4
a)
b)
c)
Exercise 2E Q5
a)
b)
Exercise 2E Q6
Exercise 2E Q7
a)
b)
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c)
d)
e)
f)
g)
h)
i)
j)
Exercise 2E Q8
a)
b)
c)
d)
e)
f)
Exercise 2E Q9
a)
b)
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Exercise 2E Q10
a)
b)
Exercise 2F Q1
a)
b)
c)
d)
Exercise 2F Q2
Exercise 2F Q3
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Exercise 2G Q8
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C H A P T E R
3
Functions of families
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Exercise 3A Q1
a)
b)
Exercise 3A Q2
a) i)
ii)
b) i)ii)
c) i)
ii)
d) i)
ii)
e)ii)
Exercise 3A Q3
a)
b)
Exercise 3A Q4
a) b) c)e)
y
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Exercise 3B Q1
a)
b)
c)
d)
Exercise 3B Q2
a)
b)
c)
d)
e)
f)
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Exercise 3B Q3
Exercise 3B Q4
Exercise 3B Q5
a)b)c)
Exercise 3B Q6
a)
b)
c)
d)
e)
f)
g)
Exercise 3C Q1
Exercise 3C Q2
Exercise 3C Q3
a)b)c)d)e)f)g)Exercise 3C Q4
a) b) c)e)g)
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Exercise 3D Q1
a)
b)
c)
d)
e)
f)
g)
h)
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i)
j)
k)
l)
m)
Exercise 3D Q2
a)
b)
c)
d)
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e)
f)
Exercise 3D Q3
a)
b)
c)
Exercise 3D Q4
a)
b)
c)
d)
e)
f)
g)
Exercise 3E Q1
a)
b) i) = 2 3 x 3 4
ii) = 2 3 x 3 + 4
iii) = 2 3 x 3 4
iv) = 2 3 x 3 8
v) = 2 3 x 3 + 8
vi) = 2 3 x 3 + 8
c) i) =2
(x 3)34 ii) =
2
(x 3)3+ 4
iii) =2
(x 3)34
iv) =2
(x 3)38 v) =
2
(x 3)3+ 8
vi) =2
(x 3)3+ 8
d) i) = 2(x 3)4
4 ii) = 2(x 3)4
+ 4
iii) =2
(x 3)44
iv) =2
(x 3)48 v) =
2
(x 3)4+ 8
vi) =2
(x 3)4+ 8
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e) i) =2
3x 3
4 ii) =2
3x 3
+ 4
iii) =2
3x 3
4
iv) =2
3x 3
8 v) =2
3x 3
+ 8
vi) = 23x 3
+ 8
f) i) = 2 (x 3)2/3 4
ii) = 2 (x 3)2/3 + 4
iii) = 2 (x 3)2/3 4
iv) = 2 (x 3)2/3 8
v) = 2 (x 3)2/3 + 8
vi) = 2 (x 3)2/3 + 8
g) i) = 2(x 3)3/4
4
ii) =2
(x 3)3/4+ 4
iii) y=2
(x 3)3/44
iv) =2
(x 3)3/48
v) =2
(x 3)3/4
+ 8
vi) =2
(x 3)3/4+ 8
Exercise 3E Q2
Exercise 3E Q3
Exercise 3E Q4
a)
b)
Exercise 3E Q5
a)
O
8 2
5 4
3
O
4 3
8
3
O
2 1
3
3
2
5
2
O
(1
2, 2)
1
7
2
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b)
Exercise 3F Q1
a)
b)
c)
d)
e)
f)
Exercise 3F Q2
a)
b) -1
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c)
d)
e)
f) +3
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g)
h)
i)
j)
k)
Exercise 3F Q4
a)
b)
c)
Exercise 3F Q5
a)
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b)
Exercise 3F Q6
a)
b)
c)
d)
e)
f)
Exercise 3G Q1
a)
b)
c)
d)
e)
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Exercise 3H Q6
Exercise 3I Q1
Exercise 3I Q2
Exercise 3I Q3
Exercise 3I Q4
Exercise 3I Q5
a)
b)
Exercise 3J Q1
a)
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e)
f)
Exercise 3J Q3
a)
b)
c)
d)
e)
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Exercise 3J Q4
a)
b)
c)
Exercise 3J Q5
a)
b)
c)
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Exercise 4B Q2
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
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g)
h)
i)
j)
Exercise 4B Q5
a)b)Exercise 4B Q6
a)b)c)d)Exercise 4B Q7
a)b)
Exercise 4B Q8
Exercise 4B Q9
a)
b)
Exercise 4B Q10
Exercise 4C Q1
a)
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g)
h)
i)
j)
,
k)
l)
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Exercise 4E Q2
a)
b)
Exercise 4F Q1
a)
b)
Exercise 4F Q2
a)
b)
c)
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Exercise 5A Q1
a)
b)
c)
d)
Exercise 5A Q2
a)
b)
c)
d)
e)
f)
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Exercise 5B Q2
a)b)c)d)Exercise 5B Q3
a) b) i)
ii) iii)
Exercise 5C Q1
a)b)c)d)
e)
f)
g)
h)i)
Exercise 5C Q2
a)
b)
c)
d)
e)
f)
g)
h)
i)
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Exercise 6A Q1
a)=
b)=
c)=
d)=
e)=
f)=
Exercise 6A Q2
a)b)c)d)e)f)Exercise 6A Q3
a)
b)c)d)e)f)
Exercise 6A Q4
a)b)c)d)e)f)Exercise 6B Q1
0
-
a)b)c)d)e)f)Exercise 6B Q2
a)b)c)d)e)
-1
1-1
1
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Exercise 6E Q1
a)
b)
c)
d)
e)
f)
Exercise 6E Q2
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
o)
p)
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Exercise 6F Q2
a)
b)
c)
d)
e)
Exercise 6F Q3
Exercise 6F Q4
Exercise 6F Q5
Exercise 6F Q6
Exercise 6F Q7
Exercise 6F Q8
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Exercise 6G Q1
a)
b)
c)
d)
e)
f)
g)
h)
i)
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Exercise 6G Q2
a)
b)
c)
Exercise 6G Q3
a)
b)
c)
d)
Exercise 6H Q1
a)
b)
c)
d)
e)
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Exercise 6H Q2
a)
b)
c)
d)
e)
f)
g)
h)
Exercise 6I Q1
Exercise 6I Q2
Exercise 6I Q3
Exercise 6I Q4
Exercise 6I Q5
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b)
Exercise 7C Q6
a)
b)
c)
Exercise 7C Q7
Exercise 7C Q8
Exercise 7C Q9
a)
b)
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c)
Exercise 7E Q15
a)
b)
c)
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C H A P T E R
9
Differentiation ofpolynomials, power functions
and rational functions
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Exercise 9F Q6
Exercise 9F Q7
Exercise 9F Q8
Exercise 9F Q9
Exercise 9G Q1
a)
b)
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c)
d)
e)
f)
g)
h)
Exercise 9G Q2
a)
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Exercise 9H Q3
Exercise 9H Q4
Exercise 9H Q5
a)
b) i)ii)
Exercise 9H Q6
a)b)Exercise 9H Q7
a) i)
ii)
iii)
b)
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b)
c)
d)
e)
f)
Exercise 9J Q2
Exercise 9J Q3
Exercise 9J Q4
Exercise 9J Q2
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Exercise 9K Q16
Exercise 9K Q17
Exercise 9K Q18
Exercise 9K Q19
Exercise 9K Q20
Exercise 9K Q21
Exercise 9K Q22
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