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1 Revision Exercise 3

Solutions to Revision Exercise 3 (Ho Soo Thong & Khor Nyak Hiongs Panpac Additional Mathematics)

Solved by: Dr Lee Chu Keong (ascklee@gmail.com)

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2 Revision Exercise 3

Revision Exercise 3 This PDF file only contains solutions. For the questions, please refer to Ho Soo Thong

and Khor Nyak Hiongs textbook, Additional Mathematics.

Question 1(a)

Some rearrangements are needed so that the equations to be solved match the

matrix given.

this equation is okay dont do anything to it!

this equation needs to be rearranged to

Therefore the two equations to be solved simultaneously using the matrix method are:

and

(note that this is the rearranged version)

Now, the two equations match the matrix, [

].

[

] [ ] [

]

[

] ( ( )) (( ) )

( )

[

]

[

]

[

]

Solving for and :

[ ] [

] [ ]

[

]

[ ]

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3 Revision Exercise 3

Question 1(b)

(1)

From (1)

(2)

(3)

Substituting (1) into (3), we get:

(

) ( )

( )( )

When

( )

When ,

( )

Question 2(a)

( )

( ) ( )

( ) ( )

Let

( )( )

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4 Revision Exercise 3

Question 2(b)

( )( )

( )( )

Therefore,

(

)

( )

Question 3(a)

( ) ( )

(

)

(

)

( )( )

( )( )

Question 3(b)

For this question, remember the Change-of-Base Law:

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5 Revision Exercise 3

(

)

Question 3(c)

( )

( )

( )

( )

( )

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6 Revision Exercise 3

( )

( )

Question 4(a)

( )

Collecting like terms:

( )

( )( )

Question 4(b)

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7 Revision Exercise 3

(

)

( )

(

)

(

)

When

When

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8 Revision Exercise 3

Question 5(a)

( )( )

( )( )

Question 5(b)

( )

( )( )

Question 6(a)(i)

The roots of the equation are and .

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9 Revision Exercise 3

(

)

(

)

Question 6(a)(ii)

( )

(

)

( )

(

)

(

)

(

)

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10 Revision Exercise 3

Question 6(b)(i)

( )

( )

Question 6(b)(ii)

( ) (( ) ( ))

( )( )

( )

( )

( )

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