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

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Solutions to Miscellaneous Exercise 18 (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 18

Question 1(a)

( )

Question 1(b)

( ) (( ) ( ))

Question 1(c)

(( ) ) ( )

( )

Question 1(d)

(( ) ) (

)

( )

Question 1(e)

(( ) ( )) (( )

)

( ) ( )

Question 1(f)

( )

( )

( )

[

( )

]

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Question 2(a)

( ) ( )

( )

( )

( )

( )

( )

Question 2(b)

(( ) ) (

)

( )

( )

( )

( )

( )

Question 2(c)

(

) (

( ))

( )

Question 2(d)

√ [ (

( )

( )) ]

√ [

√ ]

√ [√

√ ]

Question 2(e)

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Question 2(f)

( )

Question 3(a)

( )

Question 3(b)

( )

Question 3(c)

( )

Question 3(d)

√ √

Question 3(e)

Question 3(f)

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( )

Question 3(g)

Question 3(h)

Question 3(i)

Question 3(j)

( )

( )

Question 3(k)

( )

(

)

( )

(

)

√

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Question 3(l)

( )

Question 4(a)

(

)

Question 4(b)

( ) ( )

( )

( )

( ) ( )

( )( )

( )( )

( )( )

Question 4(c)

( ) ( )

Question 4(d)

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( ) (

)

( )

( )

Question 4(e)

[ ( )]

[ ]

[ ]

Question 4(f)

[ √

]

√

(

) ( ) ( ) ( )

( )

√

√

( )

√

√

( )

( )

( )( )

( )( )

Question 4(g)

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[ ( )]

( ) ( )

( )

( )

( ( ) )

Question 4(h)

[ ( )]

( )

[

( )]

Question 4(i)

[ ( )]

Question 5

Take natural log on both sides:

( )

Question 6

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( ) ( )

( )

At :

( )

( )

( )

Question 7(a)

At the turning points,

.

Taking natural log on both sides:

(

)

(

)

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√

√

Coordinates of turning point: (

)

Question 7(b)

(

)

At stationary points,

:

Question 8

( ) ( )

( )

At :

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At :

( )

( )

( )

Note: Revise section 2.9 (Applications of Exponential and Logarithmic Functions) before

attempting questions 1214.

Question 9

( )

( ) (

)

( )

At :

( )

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

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( )

Question 10(a)

( ) (

)

( )

( )

( )

When :

( )

( )

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Question 10(b)

Question 11

(

)

S is a minimum point, and therefore,

:

( )

( )

(

)

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Question 12(a)

( )

Question 12(b)

Question 13(a)

( )

Question 13(b)

Initial value of x refers to the value of x when :

Question 13(c)

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Question 13(d)

At :

( )

As becomes very large, becomes very negative, and becomes very small. As a result,

also becomes very small, and the value of x, approaches 26.

Question 14(a)

The soup should be cooked 5.97 minutes before noon.

Question 14(b)

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( )

decreases at 1.08°C per minute.

As becomes very large, becomes very negative, and becomes very small. As a result,

also becomes very small, and the value of x, approaches 28.

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