Module PMR

CHAPTER 6 : INDICES

NUMBERS IN INDEX FORM

Example:Express in the form of repeated multiplication.

1) 2) 3)

4) 5) 6) 7)

Example: Write in index notation.h x h x h x h x h x h =

8) g x g x g x g 9). 10)

11) 7 x 7 x7 x 7 x 7 12) (-11)(-11)(-11) 13) 14)

Example:Evaluate

= 32

15) 16) 17)

18) 19) 20) 21)

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LAWS OF INDICES

LAW 1

Example: Simplify

1) 2) 3)

Example: Simplify

4) 5) 6)

Example: Simplify

7) 8) 9)

Example: Simplify

10) 11) 12)

LAW 2

Example: Simplify

1) 2)

3)

Example: Simplify 45 42

= 45 - 2

= 43

4) 54 53

5) 6)

Example: Simplify

7) 8)

9)

Example:Simplify

10) 11) 12)

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LAW 3

Example: Simplify

1) 2) 3)

Example:Simplify

4) 5) 6)

Example: Simplify

7) 8) 9)

LAW 4

Example: Simplify

1) 2) 3)

Example: Simplify

=

4) 5) 6)

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Example: Simplify

= = = = =

7) 8) 9)

LAW 5

Example: 1) =

2) = 3) =

LAW 6 FRACTIONAL INDICES

Example: Rewrite by using the root and power symbol

1) 2) 3)

Example: Write in the form of index

1) 2) 3)

Example: Evaluate

1) 2) 3)

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Module PMR

Example: Simplify

1) 2) 3)

COMBINATION OF LAWS

Example:Simplify

1) 2)

3)

Simplify 4) 5) 6)

Evaluate

7) 8) 9)

Evaluate 10) 11) 12)

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Module PMR

13) 14)

15) 16)

17) 18)

19) 20) Given Find .

21) Given that Find . 22) If . Find .

Common Errors

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Module PMR

Errors Correct Steps

1. = = = 2

1. = = = 1

2. = =

2. = = =

3.

= =

3.

= = =

Questions based on PMR Format

1. Evaluate

2. Evaluate

3. Find the value of

4. Given that .Find the value of

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Module PMR

5. If , find the value of

6. Simplify

7. Simplify

8. Simplify

9. Simplify

10. Simplify

PMR past year questions

2004

1. Given that , calculate the value of . ( 2 marks )

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Module PMR

2. Simplify . ( 3 marks )

2005

1. Evaluate .

( 3 marks )

2. Given calculate the value of . ( 2 marks )

2006

1. Simplify .

( 2 marks )

2. Find the value of .

( 3 marks )

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Module PMR

2007

1. a). Find the value of .

b). Simplify . ( 3 marks )

2008

1. Simplify .

( 2 marks )

2. Find the value of a).

b).

( 3 marks )

CHAPTER 6 : INDICESANSWERS

1. 2. 3.

4.

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5. 6. 7.

8.

9. 10.

11. 12.

13. 14. 15. 1000 16. 81

17. 18. 19. or 20. 0.064

21. 0.0025 LAW 11. 2. 3. 4.

5. 6. 7. 8.

9. 10. 11. 12.

LAW 21. 2. 3. 4. 55. 72 6. 7. 8.

9. 10. u13 11. 12.

LAW 31. 2. 3. 4. 5. 6. 7. 8. 9.

LAW 4

1. 2. 3.

4. 5. 6.

7. 8 8. 9.

LAW 51. 1 2. 1 3. 1

LAW 61. 2. 3.

1. 2. 3.

1. 3 2. 4 3. 27

4. 5. 6.

COMBINATION OF LAWSIndices 74

Module PMR

1. 2. 3. 4. 5. 6. 7. 8.

9. 10. 128 11. 243 12. 8

13. 32 14. 81 15. 81 16. 17. 18. 1 19. 20. 21. 6 22. 4

Questions Based on PMR Format

1. 2. 3. 32 4. 3

5. 7 6. 7. 8.

9. 10.

PMR QUESTIONS

YEAR SOLUTION AND MARK SCHEMESUB

MARKFULL MARK

2004 or 11 2

2004 111 3

2005 1

1

1

3

2005

1

1 2

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Module PMR

2006 11 2

2006

1

1

1

3

2007 a)

b)

11

13

2008

1

1

2

2008 a)

b)

1

1

1

3

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