Miscellaneous Exercise 13

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

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

Solved by: Dr Lee Dr Lee Chu Keong ([email protected])

0

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

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

:

1

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



  

Question 1(d)

                       Question 1(e)

      

Question 1(f)

Rearranging gives:

        2

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

  ()         ()   Question 1(g)

                                      

Using the factor formulae:

Question 1(h)

Using the factor formulae:

           3

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

   ( ) 

    Question 2(a)

   ( ) 

        



Not applicable

Question 2(b)

                       (  ) 

Using the factor formulae:

Question 2(c)

    4

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

      ()  Question 2(d)

                

Question 4

                   

Divide throughout by

:

5

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

           Question 5(a)

Question 5(b)

Question 5(c)

                                                                    

Question 5(d)

6

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

                                   Question 5(e) For the question, the Factor Formulae has to be used:

                   

Question 5(f)

                                  7

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

Question 5(g)

                                                



Question 5(h)

                                               

Question 6

Question 6(a)

       √    √     ()    

Maximum:

8

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

Minimum:

Question 6(b)

                     

Question 7

Multiply throughout by 2:

         √    √   ()  √      √   (√ ) 9

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

           √     ()  

Question 8

Point R





-coordinate

Point P

Question 8(c)

                    10

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

Question 9

        √    √   ()  ()  √      √   (√ )   

Question 10 Using the formula:

                       √ 11

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

This happens when:

Question 11(b)

 √   ()  ()    √    √                         ()         

Question 12(a)

12

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



Divide both sides by

    :

Question 12(b)

  

        

Question 12(c)

        √   ()                    ()  

Question 12(d)

13

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

Question 14

Maximum value of

  √ 

        √    √   ()    √ 

The maximum value occurs when:

Question 14(b)

         √    √   (√ )   

Question 15 First, let’s write down what’s obvious from the diagram:

          

Now, let’s state the Addition Formula for

.

14

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

Examine the formula above, and you’ll realise that we’ve got every term except for



Let’s stuff what we’ve 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!):

       15

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

    √     √    √                                            

Now, apply the R-formula to

:

Question 18(a)

          

Question 18(b)

                                                     16

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

          √   ()  √      √   (√ )    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

17

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

      Question 19(b)

     

             [ ]   

Range:

 y 3

2

1

3 4

2

4

5 4

3 2

7

 x 2

4

1

Question 20

                18

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

Shaded Area:

      √    √     ( )           ( )                                 19

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

The latest version of this file can be downloaded from OpenlySolved.org.

20