Dr Lee Chu Keong (http://ascklee.org/)

0

Solutions to Miscellaneous Exercise 13 (Ho Soo Thong & Khor Nyak Hiongs Panpac Additional Mathematics)

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

http://ascklee.org/CV/CV.pdf

Dr Lee Chu Keong (http://ascklee.org/)

1

Miscellaneous Exercise 13 The solutions for question 1 and 2 have been worked to a point where the remainder of the solution is pretty obvious. Question 1(a)

( )

( )( )

(

)

(

)

Question 1(b)

( )

(

)

Question 1(c)

( )

( )

Divide both sides by :

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2

( )

Question 1(d)

( )

( )

Question 1(e)

( )

( )

Question 1(f)

Rearranging gives:

Dr Lee Chu Keong (http://ascklee.org/)

3

(

)

( )

( )

(

)

Question 1(g)

Using the factor formulae:

( )

( )

Question 1(h)

Using the factor formulae:

( )

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4

( )

(

)

Question 2(a)

( )( )

(

)

Not applicable

Question 2(b)

Using the factor formulae:

( )

( )

(

)

Question 2(c)

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5

( )

(

)

Question 2(d)

( )

( )

Question 4

( ) ( )

Divide throughout by :

( )

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6

Question 5(a)

( )

( )

Question 5(b)

( )

( )

Question 5(c)

( )

Question 5(d)

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Question 5(e)

For the question, the Factor Formulae has to be used:

Question 5(f)

( )( )

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8

Question 5(g)

( ) ( ) (

)

(

)

( )

( )( )

( )( )

Question 5(h)

( ) ( ) ( )( )

( ) ( )

( )( )

( )

Question 6

(

)

( )

Question 6(a)

( )

Maximum:

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( )

Minimum:

( )

Question 6(b)

( )

( )

Question 7

Multiply throughout by 2:

(

)

( )

( )

(

)

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10

Question 8

(

)

( )

Point R

-coordinate

( )

( )

( )

Point P

( )

( )

Question 8(c)

( )

( )

( )

Dr Lee Chu Keong (http://ascklee.org/)

11

Question 9

(

)

(

)

( )

( )

(

)

Question 10

Using the formula:

( )( )

( )( ) ( )

Dr Lee Chu Keong (http://ascklee.org/)

12

(

)

(

)

( )

This happens when:

( )

( )

(

)

Question 11(b)

( )

( )

Question 12(a)

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13

Divide both sides by :

( )

Question 12(b)

( )

( )

( )

Question 12(c)

(

)

( )

Question 12(d)

( )

( )( )

(

)

( )

Dr Lee Chu Keong (http://ascklee.org/)

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Question 14

(

)

( )

Maximum value of

The maximum value occurs when:

( )

( )

Question 14(b)

( )

( )

(

)

Question 15

First, lets write down whats obvious from the diagram:

( )

Now, lets state the Addition Formula for ( ).

( )

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15

Examine the formula above, and youll realise that weve got every term except for

Lets stuff what weve got into the Addition Formula, and see what we get

Cross multiplying, we get

( ) ( )

Collecting like terms, we get

( )

Question 16

( )

( )

Question 17 First, apply the factor formulae (twice!):

( )

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16

Now, apply the R-formula to :

( ) [ (

)]

(

)

(

)

(

)

Question 18(a)

( )

( )

Question 18(b)

(

)

( )

(

)

(

)

Dr Lee Chu Keong (http://ascklee.org/)

17

(

)

( )

( )

(

)

Question 19(a)

(

)

( )

Squaring both sides gives:

( ) [ ( )]

NOTE: For [ ( )] , the maximum value is 1, and the minimum value is 0.

Therefore, the maximum value of ( ) happens when

[ ( )]

( )

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18

( )

( )

Question 19(b)

( )

[

( )]

Range:

Question 20

4 2

3

4

5

4

3

2

7

42

x

1

1

2

3

y

Dr Lee Chu Keong (http://ascklee.org/)

19

(

)

( )

( )

( )

(

)

Shaded Area:

( )( )

( )( )

( )

Dr Lee Chu Keong (http://ascklee.org/)

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