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

0

Solutions to Miscellaneous Exercise 2 (Ho Soo Thong & Khor Nyak Hiong’s Panpac Additional Mathematics)

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

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

1

Miscellaneous Exercise 2 Question 2(a)

√ √

√

√ √ √ (

√ √

√ ) (

√ √

√ )

√

√

√

(

)√

√

Question 2(b)

√ (

√ √

√ √ √ √

)

√

√ √

√ (

√ √

√ ) √

√

√

(

)√

√

√

Question 3

√ √

( ) ( )√

( )

( )

Substitute ( ) into ( ):

( )

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( ) √( ) ( )( )

( )

√

( )

(

)

Question 4(a)

√ Squaring both sides gives:

Question 4(b)

√ √

√ ( )

√

Squaring both sides of the equation:

( )( )

Question 4(c)

√

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√

Squaring both sides of the equation:

( )( )

Question 4(d)

√

√

( )( )

Question 4(e)

√ √

Squaring both sides of the equation:

√

√

√

Squaring both sides of the equation:

Question 4(f)

(√ √ )(√ √ )

(√ ) (√ )

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

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√

Question 6 (1)

(2)

From (1) (3)

From (2) ( ) ( ) (4)

Substituting (3) into (4) ( ) (5)

From (3)

( )

Question 7(a)

( )

( )

( )

( )

( )

Question 7(b)

( ) ( )

Let :

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( )( )

Question 7(c)

( )

( )

Question 7(d)

( )

( )( )

(

)

Reject!

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

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Question 8(a) ( )

Question 8(b)

( ) ( )

( ) ( )

( ( )) ( )

( ) ( )

( ) ( ( ))

Question 8(c)

( )( )

Question 9(a)

( )

( )

( )

( )

( ) (

)

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( )

( )

Substitute ( ) into ( ):

( )

( )

Question 9b(i)

( ) ( )

( ) ( )

[( )( )]

( )( )

Question 9b(ii)

(

)

( )

Question 10(a)

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Question 10(b)

( )

( )

Substitute ( ) into ( ):

Substitute into ( ):

Question 11b

( )

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Question 11d

( )

Question 11e

( )

Question 11h

Question 11j

( )

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Question 13(a)

Question 13(b)

Question 13(c)

( )

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Question 13(d)

Question 14

( )

( )

( ( ))

( )

( )

(

)

√

Question 15

( )

( )

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

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(

)

(

)

( )

(

)

(

)

( )

Question 16a

( )( ) ( ) ( )

( ) ( )

( ) [ ( )]

( ) [ ( )]

( ) ( )

( ) ( )

Question 16b(i)

( ) When :

( )

Question 16b(ii)

( )

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Question 16c

( ) Question 17a(i)

At ,

( )

Question 17a(ii)

At ,

( )

( )

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( )

( )

Question 17(b)

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) ( )

( ) [ ( )]

( ) ( )

Question 17(c)

( )

( ) ( )

Let :

( )( )

( )

(

)

Therefore, Question 18(a)

( )

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( )

( ) ( )

( )

Question 18(b)

( )

( ) ( ) ( )

Let :

( )( )

Question 19(a)

( )

( )

(

)

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Question 19(b)

( ) ( )

( )

( )

( )

Question 20(a)

( ) ( )

( ) ( )

[( ) ( )]

( )( )

( )

Question 20(b)

( ) ( )

( ) ( )

( ) ( )

( ) ( )

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

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( ) ( )( )

( ) ( )( )

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