Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 1

Learning Area 1: NUMBER BASES Worksheet 1.1

Learning Objective 1: Understand and use the concept of numbers in base two, eight and five.Learning Outcome (i) State zero, one, two, three, ……… in base : a) two.

Activity 1: Grouping in twos to state a number in base two

1. In each of the following cases, state the number of cubes in base two.

Number

in base ten

Groups of Numberin

base twoEights Fours Twos Units

0

1

2

3

4

5

6

7

8

9

10

11

12

2. Complete the table below.

2

2

2

2

2

2

2

2

2

2

2

2

2

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 2

Numberin

base ten

Groups of Numberin

base two2 1

0

1 1

2 1 0

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

Activity 2: Counting in base two

1. Count the number of objects in each diagram below in base two.

(a) (b)

1

02

2

012

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 3

The number of hexagons The number of stars

= =

(c) (d)

The number of pentagons The number of triangles

= =

2. Fill in the blanks to complete each sequence below in base two.

(a) 1 2 , 10 2 , ………… , ………… , ………… , ………… , …………

(b) 11 2 , 100 2 , …………. , …………. , ……………. , …………..

(c) 101 2 , 110 2 , …………. , …………. , ……………. , …………..

(d) 1000 2 , 1001 2 , …………. , …………. , ……………. , …………..

………….. , ………….. , …………….. , ………….. , ………….

Activity 3: Binary wizard

Imagine you are the binary wizard in the passage below.Fill in each blank with a suitable number in base two.

Hello, my dear friends.

NOTES

The digits used in writing numbers in base two are and .

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 4 As you can see, I have ………………. eyes and ………………. fingers ! Weird ? Wondering which world am I from?

In the world I’m staying in, there are ………………. days in a week and ………………. hours in a day! Jealous? Wondering how I spent my time?

Want to know my age? I’m ………………. years old! Surprised ? Wondering how I can look so young at such an age?

Just to let you know. I’m studying in Form ………………. now and I’ll will be sitting for my SPM examination at the end of this year, taking altogether a total of ………………. subjects. Stunned? Wondering whether this is the so called life-long learning?

Now, please don’t laugh. I aim to score ………………. As in my SPM examination. Wondering how I can make it?

Oh, no! Please stop wondering. Believe me, give me all the support you can, wish me good luck and I can do wonders!

Thank-you. I’m the binary wizard who thinks only in twos.

Learning Area 1: NUMBER BASES Worksheet 1.2

Learning Objective 1: Understand and use the concept of numbers in base two, eight and five.Learning Outcome (i) State zero, one, two, three, ……… in base : b) eight.

Activity 1: Grouping in eights to state a number in base eight

1. In each of the following cases, state the number of triangles in base eight.

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 5

Number

in base ten

Groups of Numberin

base eightEights Units

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

2. Complete the table below.

Numberin

base ten

Groups of Numberin

base eight8 1

192 3

20

21

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

8

328

8

8

8

8

8

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 6

23

25

28

30

34

37

39

41

43

46

50

53

56

63

64

65

67

70

72

Activity 2: Counting in base eight

1. Count the number of objects in each diagram below in base eight

(a) .(b)

The number of computers =The number of diskettes =

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 7

2. Fill in the blanks to complete each sequence below in base eight.

(a) 5 8 , 6 8 , ………… , ………… , ………… , ………… , …………

(b) 14 8 , 15 8 , …………. , …………. , ……………. , …………..

(c) 35 8 , 36 8 , …………. , …………. , ……………. , …………..

(d) 63 8 , 64 8 , …………. , …………. , ……………. , …………..

………….. , ………….. , …………….. , ………….. , …………. ,

………….. , ………….. , …………….. , ………….. , ……………

Activity 3: Octopus Genius

Imagine you are the octopus genius taking part in a quiz.Answer the following questions in base eight.

1. An octopus has ……………….. arms.

2. A dodecagon has ……………….. sides.

3. The Malaysian flag has ……………….. stripes.

4. Malaysia celebrated ……………….. years of independence in the year 2008.

5. There are ……………….. minutes in one hour.

6. A chessboard is marked off into ……………….. squares of ……………….. alternating colours.

7. A teacher bought a gross of pencils to be shared equally between two classes.

Each class gets ……………….. pencils.

8. A century is a period of ………………. years.

NOTES

The digits used in writing numbers in base eight are

, , , , , , and .

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 8 .

Learning Area 1: NUMBER BASES Worksheet 1.3

Learning Objective 1: Understand and use the concept of numbers in base two, eight and five.Learning Outcome (i) State zero, one, two, three, ……… in base : c) five.

Activity 1: Grouping in fives to state a number in base five

1. In each of the following cases, state the number of smiley faces in base five.

Numberin

base ten

Groups of Numberin

base fiveFives Units

0

1

2

3

4

5

6

7

5

5

5

5

5

5

5

5

5

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 9

8

9

10

11

12

13

14

15

16

17

18

2. Complete the table below.

Numberin

base ten

Groups of Numberin

base five5 1

19

20

22

25

28

30

33

36

39

41

44

47

49

5

5

5

5

5

5

5

5

5

5

5

5

5

5

5

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 10

51

62

74

83

91

110

125

136

200

Activity 2: Counting in base five

1. Count the number of cylinders in the diagram below in base five.

2. Fill in the blanks to complete each sequence below in base five.

(a) 2 5 , 3 5 , ………… , ………… , ………… , ………… , …………

(b) 13 5 , 14 5 , …………. , …………. , ……………. , …………..

The number of black cylinders =

The number of white cylinders =

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 11

(c) 32 5 , 33 5 , …………. , …………. , ……………. , …………..

(d) 41 5 , 42 5 , …………. , …………. , ……………. , …………..

………….. , ………….. , …………….. , ………….. , …………. ,

………….. , ………….. , …………….. , ………….. , ……………

Activity 3: 5-star surveyor

Congratulation! You are a well known 5-star surveyor.The diagram below shows the plan of a plot of land. Measure, to the nearest cm, the required lengths in base five.

NOTES

The digits used in writing numbers in base five are

, , , and .

PQ = …………………. cm

QR = …………………. cm

RS = …………………. cm

ST = …………………. cm

TP = …………………. cm

SQ = …………………. cm

SP = …………………. cm

P

Q

R

T

S

Program Waja Negeri Perak Tahun 2009FORM 5 MATHEMATICS Module 1 : Page 12