F5_2 Linear Law

8/13/2019 F5_2 Linear Law

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A linearequation is of the form

Y = mX+ CY& Xare variables

mand Care constants

2. LINEAR LAW F5


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A linearequation is of the form

Y = mX+ Cm is the gradient

Cis theY-intercept

2. LINEAR LAW F5


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Y = mX+ C

Students are advised to work

using this l inear formand

NOT the non-l inear or iginal

equation.

2. Linear Law[Paper 1, short quest ion : 4 marks]

F5


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How to answer this question ?

Look at the labelof theVERTICAL

axisof the given diagram. Convert the non-linear equation to

the linear form, Y = mX + C

Remember that your Y must be thesame as the VERTICALaxisof thegiven diagram.

2. Linear Law[Paper 1, short quest ion : 4 marks]

F5


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How to answer this question ?

Follow instruction :Plot Yagainst X :1. Convert the non-linear equation to the

linear form, Y = mX+ C

2. Create a new table of valuesin YOURanswer script / graph paper, usingXand Y

2. Linear Law[Paper 2, Q7 : 10marks]

F5


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How to plot the graph ?

Follow instruction !Plot Yagainst X :1. Follow the scale given

2. Remember to label the axes

3. Plot all the points carefully almost all of

them should lie in a straight line

4. Draw the line of best fit

2. Linear Law[Paper 2, Q7 : 10marks]

F5

Note : ANDA SUDAH DAPAT 4 MARKAH !


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Still remember .

Y = mX+ Cm is the gradient

Cis theYintercept ?

2. LINEAR LAW F5


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Use your graph to find

1. the Y-intercept : just READwhere your line

cuts the vertical axis!2. Find the gradient of the line of best fit, using

the formula :

2. Linear Law[Paper 2, Q7 : 5-6 markah lagi !]

F5

2 1

2 1

my y

x x


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You still need to decide :

Y = mX+ Cwhich unknown ism,

and which isC!

2. LINEAR LAW F5


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Y = mX+ C

Cis the constant,

and the other must be m

2. LINEAR LAW F5


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Ex.1 : If you are given coordinates ofTWOpointson the straight line

Y

X

(4, 11)

3

O

y/x

x

1. Label the axes X and Y onthe diagram

2. Find gradient of line

3. Find Y-intercept of line

m=

= 2

11 3

4 0

C = 3

4. So, Y = 2X +3

5. 2 3y

xx

6. y = 2x2+3x


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Y = mX+ C

Students are advised to workusing this l inear formand

NOT the non-l inear or iginal

equation.

2. Linear LawF5


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Examples (SPM 2007)

F5

Y

X

*(3, q)

(p, 0)

*O

y2/x

x

Given non-linear equation :

y2= 2x(10x) , find p and q.

y2 = =2x(10x)

y2/x = 202x

Rewrite as y2/x = 2x + 20

Compare with linear formY = mX + C,

Y= y2/x, X= x, m = -2

So, Y = 2X + 20X = 3, Y = q: q = 2 (3)+ 20

= 14

And X = p, Y = 0: 0 = 2p+ 20

p= 10


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Y

X

Bear in mind that ......

1. Scale must be uniform

2. Scale of both axes may defer :

FOLLOW given instructions !

3. Horizontal axis should start from 0 !

4. Plot against .

Linear Law (Paper 2)

Vertical Axis Horizontal

Axis

F5


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Exercise 1

The table below records the values of an experiment for

two variables x and y which are related by

where p and q are constants.

(a) Plotxyagainstx3using a scale of 2 cm to 1 uni ton the x3-axisand 2 cm to 10 uni tson the xy-axis.

Hence, draw the line of best fit [5marks ]

(b) From the graph, estimate the value of

(i) p and q

(i i) x when y = [5marks]

X 0.8 1.0 1.3 1.4 1.5 1.7

y 108.8 79.0 45.9 36.5 25.7 8.2

45

x

2 qy pxx


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Do not create your new X-Y valueson your question paper !!!

Better to be at the topof your graph paper

Wheres your TABLE of values???

Linear Law (Paper 2)

F5

x3 0.5 1.0 2.2 2.7 3.4 4.9

xy 87.0 79.0 59.7 51.1 38.6 13.9


17/240 1 2 3 4 5 6

x3

10

20

30

40

50

60

70

80

XY

x

x

x

x

F5

x

x

x3 0.5 1.0 2.2 2.7 3.4 4.9

xy 87.0 79.0 59.7 51.1 38.6 13.9

90

Plot all points carefully

Draw line of best fit usingLONG RULER !


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3 0 1 0 2 2 2 3 4 4 9


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0 1 2 3 4 5 6x3

10

20

30

40

50

60

70

80

XY

x

x

x

x

F5

Read this value !!!

Find the

gradient !

(x2, y2)

(x1, y1)

x

x

x3 0.5 1.0 2.2 2.7 3.4 4.9

xy 87.0 79.0 59.7 51.1 38.6 13.9

90


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0 1 2 3 4 5 6x3

10

20

30

40

50

60

70

80

XY

x

x

x

x

F5

C = 95 or 96

(x2, y2)

(x1, y1)

x

x

90

Find the gradient

Using m = 2 1

2 1

y y

x x

m - 16.67

2 q


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Values of p & q.

xy = px3 + q

This is in the form Y = mX + C

So, the gradient is m = p , and C = q

(i ) p -16.67, q 95,

(ii)xy = 45 ( Y = 45 )

From graph, x3= 3,

x 1.44

2 qy px

x

2 qy px

x


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Dont make this mistake!F5

0 1 x

Y

x

x

x

x

(x2, y2)

(x1, y1)

x

x

Gradient = k

k 8.5 1.5

3.2 1.2

7

3

Experimental results cannot be exact,

so : use DECIMALS !


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Kunci Mencapai Keputusan

CEMERLANG...

Belajar secara konsisten

Tabahkan hati Rajin tanya cikgu

Rajin buat latihan Jaga kesihatan anda !!!


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THANK Q &Selamat maju jaya !

F5_2 Linear Law

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