MATHEMATICS - FORM 1

BASIC MEASUREMENTS 

                       -           

 

     

LENGTH

A) Determining the Metric Units of Length

1. Lenght is the distance between two points.

2. The relationships between the metric units

    of legth are shown below :
    

Worked Example 1

State the units of length suitable for measuring

(a) the thickness of a coin,

(b) the length of Sungai Pahang.

Solution

(a) mm              (b) km

B) Conversion between Metric Units of length

A unit of length can be converted to another

unit.

(a) 1 cm = 10 mm

(b) 1 m = 100 cm

(c) 1 m = 100 x 10 mm

           = 1 000 m

(d) 1 km = 1 000 m

(e) 1 km = 1 000 x 100 cm

             = 100 000 cm

(f) 1 km = 100 000 x 10 mm

            = 1 000 000 mm

  

Worked Example 2

Convert

(a) 31 m to cm,
       4

(b) 26 cm 2 mm to mm

Solution



Worked Example 3

Convert

(a) 62.3 cm to m,

(b) 1 km 25 m to km.

Solution



Worked Example 4

Convert

(a) 85 mm to cm and mm,

(b) 6 054

Solution



Worked Example 5

Convert

(a) 73 m to m and cm,
       4

(b) 0. 52 km to cm.

Solution



C) Measuring the Lengths of Objects

Worked Example 6

Measure the length of the straight line PR with

a ruler.

       

Solution

PR = 2.8 cm or 2 cm 8 mm

Worked Example 7

Mesure the curve MN.

       

Solution

Use a piece of thread and place it on the curve

from M to N. Mark the point N on it. Stretch the

thread on a ruler to mesure the length of the

curve MN.

     

MN = 4.6 cm or 4 cm 6 mm

D) Drawing Straight Lines

Use  A straight line can be drawn by using a

ruler and a pencil if the length is given.

Worked Example 8

Draw the straight line PR with the length of

(a) 41 cm     (b) 6 cm 4 mm.
       2

Solution

   

E) Estimating the Lengths of Objects

When estimating the length of an object,

an appropriate unit of length must be used.

For example :-

The appropriate unit of measurement for estimating

the thickness of a coin is mm. Other units of length

such as m and km are not suitable in this case. m

and km are used for larger measurement.

Worked Example 9

Estimate the length of the fluorescent tube in metres.

Solution

The estimated length of the fluorescent tube is 1. 5 m.

The actual length is 1. 22 m.

F) Addition, Subtraction, Multiplication
and Division involving Length


Estimate Before performing addition, subtraction,

multiplication or division involving lengths of different

units, we have to change all the measurements to the

same unit first.

Worked Example 10

Solve

(a) 15 m 42 cm + 6 m 25 cm

(b) 24. 9 cm + 4 mm.

Solution



Therefore, 15 m 42 cm + 6 m 25 cm

                  = 21 m 67 cm




Worked Example 11

Solve

(a) 6 cm - 2. 015 cm,

(b) 51 mm - 23 mm,
       2           10

(c) 33. 52 m - 16 cm.

Solution

(a)        6. 000 cm
         -  2. 015 cm
            3. 985 cm  

Therefore, 6 cm - 2. 015 cm = 3. 985 cm






Worked Example 12

Solve

(a) 64 mm x 8
       8

(b) 4 km 20 m 12 cm x 5

Solution

(a) 64 mm x 8
       8

     = 52 mm x 8
         8

     = 52 mm



Therefore, 4 km 20 m 12 cm x 5

                 = 20 km 100 m 60 cm

Worked Example 13

Solve

(a) 18. 2 cm ÷ 5        (b) 15 km 280 ÷ 4.

Solution



G) Problem Solving involing Length

Worked Example 14

A piece of black thread is 2 m 64 cm long and

a piece of red thread is 2. 4 m long. Find their

total length.

Solution

1. Understand the problem

    Length of the black thread = 2 m 64 cm

    Length of red thread is 4. 6 m

    Find : Total length of the two pieces of threads

2. Devise a plan

    Change 2 m 64 cm to m and then nuse addition.

3. Carry out the plan

    2 m 64 cm

    = 2 m + ( 64 ÷ 100) m

    = 2 m + 0. 64 m

    = 2. 64 m

    2. 64 m + 2. 4 m = 5. 04m

           2. 64 m
       +  2. 40 m
           5. 04 m

    Therefore, the total length is 5. 04 m.

4. Check

          5. 04 m
       -  2. 4   m
          2. 64 m  

MASS

A) Determining the Metric Units of Mass
 
1. Mass is the amount of matter in an object.

2. Mass is usually measured in grams (g),

    kilograms (kg) and tonnes in metric units.

3. A suitable unit of measured should be used

    for determining  the mass of an object.

Worked Example 15

State suitable unit for each of the following.

(a) The mass of a chicken

(b) The mass of an egg

Solution

(a) kg 
   
(b) g

B) Conversion between Metric Units of  Mass

The relationships between the units of

mass in the metric system are as follows. 

   
         

Worked Example 16

Convert

(a) 2. 45 kg to g,

(b) 3 106 kg to tonnes,

(c) 15 030 g to kg and g,

(d) 67. 05

Solution




C) Measuring the Mass of Objects

1. A weighing machine is used to measure

the mass of an object.

2. Before weighing the object, the pointer

    (needle) must be set at zero.

Worked Example 17

State the mass of each object on the weighing

machine below.

(a)                                  (b)
                                     

Solution

(a) 300 g                                (b) 1. 8 kg

D) Estimating the Mass of Object

When estimating the mass of an object, an

appopriate unit of mass must be used.

For Example :-

The unit suitable for measuring the mass of

a 20 sen coin is g. kg is not suitable in this

case as kg is used for larger measurements.

Worked Example 18

Estimate the mass of

(a) a bottle of 300 ml of mineral water,

(b) a ream of A4 papers.

Solution

(a) Using a packet of 300 g of sugar as a guide,

     the estimated mass of the bottle of mineral

     water is about 300 g. The actual mass of the

     bottle of mineral water is 310 g.

(b) Using a packet of flour weighing 1 kg as a

     guide, the mass of a ream of A4 paper is 

     estimated to be about 2 kg. The actual mass

     of a ream of A4 paper is 2. 38 kg.

E) Addition, Subtraction, Multiplication
 and Division involving Mass


Before performing addition, subtraction,multip-

lication and division involving mass, change all

the measurements to the same unit.

Worked Example 19

Solve

(a) 8 tonnes 350 kg + 6 tonnes 740 kg,

(b) 13 kg 70 g - 4 kg 520 g

(c) 720 g - 3 kg
                5

Solution



Worked Example 20

Solve

(a) 5 tonnes 410 kg x 6

(b) 22 kg ÷ 4
       5

(c) 20 kg 25 g ÷ 8

Solution


F) Problem Solving involving Mass

An empty vessel weights 530 g. When filled

with sugar, it weights 2. 58 kg. Find, in kg,

the mass of the sugar.


Solution

1. Understand the problem

    Given information :

    Mass of the empty vessel = 530 g

    Mass of the empty vessel + sugar = 2. 58 kg

    Find : Mass of sugar

2. Devise a plan

    Change the mass of the empty vessel to kg

    and then use subtraction.

3. Carry out the plan

    530 g

    = ( 530 ÷ 1 000 ) kg

    0. 53 kg                                2. 5 8 kg
                                             -  0. 5 3 kg
    Mass of sugar                      2. 0 5 kg

    = 2. 58 kg - 0. 53 kg

    = 2. 05 kg

    Therefore, the mass of the sugar is 2. 05 kg.

4. Check

         2. 05 kg
      + 0. 53 kg
         2. 58 kg

TIME

A) Determining the Appropriate Units of Time

1. Time is the period between two occurrences

    or events.

2. The units of time are seconds, minutes, hours,

    days, weeks, months, years, decades, centuries

    and millenniums.

Worked Example 22

State a suitable unit of time for each of the following.

(a) The age of a person

(b) The time taken to travel from Shah Alam to Kuala

     Pilah by car

Solution

(a) Years and months

(b) Hours and minutes

B) Conversion between Units of Time

State a The relationships between the units of time

are as follows :

               



Worked Example 23

Convert

(a) 51 days to hours,
       4

(b) 6 minute 18 seconds to seconds.

Solution

(a) 51 days = 21 x 24 hours
        4             4

                  = 126 hours

(b) 6 minute 12 seconds

     = ( 6 x 60 ) seconds + 18 seconds

     = ( 360 + 18 ) seconds

     = 378 seconds

Worked Example 24

Convert

(a) 36 months to years,

(b) 309 minutes to hours and minutes.

Solution

(a) 32 months = ( 36 ÷ 12 ) years

                      = 3 years



C) Measuring the Time taken for an Activity

A stop watch or a digital clock are always used to

measure he time taken for an activity. The units

used are usually in seconds, minutes and hours.

D) Estimating the Time of an Activity

Estimate the time taken to sing the national anthem,

"Negaraku".

Solution

30 seconds

E) Addition, Subtraction, Multiplication
and Division involving Time


Worked Example 26

Solve

(a) 5 minutes 42 seconds + 31 minutes.
                                             2

Solution

(a) 5 minutes 42 seconds + 31 minutes
                                             2
 
     = 5 minutes 42 seconds + 3 mminutes
       
        30 seconds

     = 9 minutes 12 seconds

       

Worked Example 27

Solve

(a) 14 weeks 2 days - 6 weeks 5 days

(b) 22. 3 minutes - 24 seconds

Solution



(b) 22. 3 minutes - 24 seconds

     = ( 22 + 0. 3) minutes - 24 seconds

     = 22 minutes + ( 0. 3 * 60 ) seconds -

        24 seconds

     = 22 minutes 18 seconds - 24 seconds

     = 21 minutes 54 seconds

       

Worked Example 28

Solve

(a) 8 days 15 hours x 4

Solution



Worked Example 29

Solve

(a) 7 hours ÷ 12

Solution

(a) 7 hours ÷ 12

     = ( 7 x 60 ) minutes  ÷ 12

     = 420 minutes ÷ 12

     = 35 minutes

                 

F) Problem Solving involving Time

Worked Example 30
                     
A bus took 6 hours 35 minutes to travel from

Seremban to Ipoh. It took another 2 hours 15

minutes to travel from Ipoh to Butterworth.

Calculate the total time taken to travel from

Seremban to Butterworth.

Solution

1. Understand the problem

    Given information :

    Seremban to Ipoh = 6 hours 35 minutes

    Ipoh to Butterworth = 2 hours 15 minutes

    Find : Total time from Shah Alam to

              Butterworth

2. Devise a plan

    Use addition.

3. Carry out the plan

            

4. Check

           

8.4 TWELVE-HOUR AND TWENTY-
FOUR-HOUR SYSTEM


A) Time in the 12-hour System

1. Time can be expressed in the 12-hour system

    or 24-hour system.


2. In the 12-hour system, we have to state clearly

    whether the time is in the morning, noon, after-

    noon, evening, night or midnight.

3. In the 12-hour system, a.m. is used for the time

between midnight and noon whereas p.m. is used

for the time between noon and midnight.

Solution

For example :-


Worked Example 31

Write the time for each of the following in the 12-

hour system.

(a)                               (b)                         
                     

Solution

(a) 8. 20 a.m.               (b) 3. 35 p.m.

B) Time in the 24-hour System

1. In the 24-hour system, four digits are used to

indicate time. The first two digits denote
hour

and the last two digits dennite minutes.          

For example :-



2. A day ends at 2400 hours. The next day begins

    at 0000 which is 12. 00 midnight.

Worked Example 32

Write the time for each of the following in the 24-

hour system.

(a)                              (b)
                     

Solution

(a) 0805 hours              (b) 1120 hours

C) Changing Time in the 12-hour System
to the 24-hour System and vice versa


The relationship between the times in two systems

is shown below.



Worked Example 33

Change each of the following to the 24-hour

 system.

(a) 8. 15 a.m.               (d) 10 .45 p.m.

(b) 11. 00 a.m.             (e) 12. 20 a.m.

(c) 4. 35 p.m.

Solution


Worked Example 34

Change each of the following to the 12-hour

system.

(a) 0925 hours          (c) 1705 hours

(b) 1235 hours          (d) 0045 hours

Solution


D) Determining the Interval between
Two given Times


Interval is the length of time between two given

times.

Worked Example 35

Find the interval between 09.15 a.m. and 3. 45 p.m.

on the same day.

Solution



Interval

= 2 hours 45 minutes + 3 hours 45 minutes

= 6 hours 30minutes

Worked Example 36

Find the interval between 11. 30 p.m. on Tuesday

and 4. 15 a.m. on Wednesday.

Solution



Interval

= 30 minutes + 4 hours 15 minutes

= 4 hours 45 minutes

E) Determining the Time in the 12-hour
 System or 24-hour System


Worked Example 37

Find the time which is 5 hours 25 minutes after

2. 15 p.m., in the 12-hour system.
     
Solution


The time is 7. 40 p.m..

Worked Example 38

Find the time which is 5 hours 55 minutes before

2. 10 p.m., in the 12-hour System.

Solution

2. 10 p.m. = 1410 hours

     

The time is 8. 15 a.m..

Worked Example 39

Find the time which is 4 hours 50 minutes after

2120 hours, in the 12-hour system.
     
Solution

   
The time is 0210 hours, the next day.

F) Problem Solving involving Time

A show starts at 8. 45 a.m. and ends at 3. 20 p.m.

How long is the show?
   

Solution

1. Understand the problem

    Given information :

    The show starts at 8. 45 a.m..

    The show ends st 3. 20 p.m..

    Find : Duration of the show

2. Devise a plan

    Change the times to the 24-hour system and

    then use subtraction.

3. Carry out the plan

    8. 45 a.m. = 0845 hours

    3. 20 p.m. = 1520 hours

       

    Therefore, the show lasts 6 hours 35 minutes.

4. Check