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1 Revision Exercise 11

Solutions to Revision Exercise 11 (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 11

Revision Exercise 11 This PDF file only contains solutions. For the questions, please refer to Ho Soo Thong

and Khor Nyak Hiongs textbook, Additional Mathematics.

Question 1(c)

Use the Factor Formulae

1(b)

(

)

1(c)

Using factor formulas:

( )

( )

2(a)

( )

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3 Revision Exercise 11

[ ]

(

) (

)

( )

(

)

2(b)(i)

Amplitude

Period

2(b)(ii)

Question 3(a)

( )

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4 Revision Exercise 11

(

)

Question 3(b)

( )

( )

( )

( )

Question 3(c)

( )

(

)

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5 Revision Exercise 11

Question 3(d)

( )

Divide throughout by 2:

( )( )

Reject!

( )

Question 4(a)

Quadrant No. 3 (cosine and secant is negative)

Question 4(b)

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6 Revision Exercise 11

Question 4(c)

( )

( (

)

)

(

)

Question 4(d)

( )

(

)

(

)

( )

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7 Revision Exercise 11

Question 5(a)

Using

Using

Length of OP:

Question 5(b)

( )

Question 5(c)

( )

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8 Revision Exercise 11

( )

Question 6(a)

( ) ( )

( )

Collecting like terms:

But we are given (in the question) that

And so:

Question 6(b)(i)

( )

( )

( )

( )

Factoring out and :

( )

( )

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9 Revision Exercise 11

Question 6(b)(ii)

( )

( ) ( )

( )

Question 6(b)(iii)

The part of the equation can be simplified using the appropriate R-

Formula.

Of the four, use:

( )

So, ( )

( ) ranges between and

( ) ranges between and

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10 Revision Exercise 11

( ) ranges between and

The maximum value is therefore 9

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