math(f5) gradient and area under a graph

GRADIENT AND AREA UNDER A GRAPH

Distance-Time Graph How to draw a graph? Recall previous knowledge

• x axis represent time• y axis represent distance

Note : When a distance-time graph is drawn, the

gradient of the graph gives the speed.

Example

The following table shows the distance travelled and time taken by Amin to his office. Draw the distance-time graph made by Amin

Time (hours)

0.1 0.2 0.3

Distance (km)

5 10 15

The Gradient of a Distance-Time GraphWhat is gradient?

- Is the change of the quantity on the vertical axis with respect to the change of the quantity on the horizontal axis

How to find gradient? Recall the formula of gradient :

m =

Example :…………..

What is the general equation of straight line?

The gradient of distance-time graph represent speed

12

12

xx

yy

Please do worksheet 1…Exercise 6.1 B and

6.1 C with your partner

Exercise

How to find speed for a period of time from a distance-time graph

Notes:

Time

DistanceSpeed

Taken Time Total

Travelled Distance TotalSpeed Average

The distance-time graph shows the distance covered by a boy from the starting point to another point and back.

Example:

a) Find the speed for the first 15 seconds.

b) How long did he rest?

c) Find the speed where the boy back to starting point.

d) Find the average speed for the whole journey.

From the graph,

a)Find the speed for the first 15 seconds.Answers:a) Speed for the first 15 seconds:

sm

s

m

/3

20

0-15

0-100

Time

DistanceSpeed

Answers:b) How long did he rest?

Time taken = 30s – 15s = 15 seconds

-He takes 15 seconds to rest

Answers:c) The speed where the boy back to the starting

point:

sms

ms

m

/ 5 20

100

30-50

100-0

Time

DistanceSpeed

Negative sign indicates the

direction of the journey is reversed

Answers:d)

sms

m

/ 2 50

100

Taken Time Total

Travelled Distance TotalSpeed Average

Please do worksheet 1. Exercise 6.1 D

Exercise

Answers for Worksheet 1 (6.1D) a) Speed from technician workshop to the

house of the first customer:

154

6010

9

Time

DistanceSpeed

kmh

hours

km

b) Speed from 1st customer house to the 2nd customer house (BC):

124

603040

95

Time

DistanceSpeed

kmh

hours

kmkm

c)

143.15

6070

81

Taken Time Total

Travelled Distance TotalSpeed Average

kmh

hours

km

Please do worksheet 2

Exercise

Submit it after the end of the class

SUMMARY Gradient of a graph is the rate of change

in the quantity on the vertical axis with respect to the change in the quantity on the horizontal axis.

Gradient of the distance-time graph represents the speed.

Formula used:

12

12mxx

yy

Taken Time Total

Travelled Distance TotalSpeed Average

Time

DistanceSpeed

homework (ex6.1(d) , no 3&4)