Mathematical Methods Textbook Worked Solutions Chapter 1- 9

7/27/2019 Mathematical Methods Textbook Worked Solutions Chapter 1- 9

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C H A P T E R

1

Functions and relations

1


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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

3


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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

10


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Exercise 1G Q7

a)

b)

c)

d)

e)

f)

g)

h)

14


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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

-6

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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)

34


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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)

47


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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)

50


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Exercise 4B Q2

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

55


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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)

60


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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)

70


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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

88


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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)

90


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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)

94


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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)

108


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c)

Exercise 7E Q15

a)

b)

c)

114


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C H A P T E R

9

Differentiation ofpolynomials, power functions

and rational functions

115


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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)

127


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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

a)

b)137


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Mathematical Methods Textbook Worked Solutions Chapter 1- 9

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