miscellaneous exercise 2
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MathsTRANSCRIPT
Dr Lee Chu Keong (http://ascklee.org/)
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Solutions to Miscellaneous Exercise 2 (Ho Soo Thong & Khor Nyak Hiong’s Panpac Additional Mathematics)
Solved by: Dr Lee Chu Keong ([email protected])
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)
(√ √ )(√ √ )
(√ ) (√ )
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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!
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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(d)
Question 14
( )
( )
( ( ))
( )
( )
(
)
√
Question 15
( )
( )
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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)
( ) ( )
( ) ( )
( ) ( )
( ) ( )
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( ) ( )( )
( ) ( )( )
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