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Name of student
Subject
Topic
Sub-topic
SPM Add Math
Chapter 6 Linear Law
Prepared by Cheng WL
Teacher’s Name
Class
Lesson no
Date
Day/Time
Cheng Wui Leap
F4 AM
11
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Lesson 1
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Lesson 1
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Lesson 1
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xy
1 The variables x and y are related by the equation
xy = 12.x- 4x3.A straight line graph is obtained by
plotting y against x 2 as shown in Diagram 1.
(p, 17)
Pembolehubah x dan y dihubungkanolehpersamaan
xy = 12x - 4x3• Grafgaris lurus diperolehdengan memplot y
melawanx2 sepertiyang ditunjukkan dalam Rajah 1.
1 The variables x and
y are related by the equation
y
5
xy
-------x3
0
xy = 12.x- 4x3.A straight line graph is obtained by
plotting y against x 2 as shown in Diagram 1.
(p, 17) 3
Diagram 3/ Rajah
Pembolehubah x dan y dihubungkanolehpersamaan
xy = 12x - 4x3• Grafgaris lurus diperolehdengan memplot y
melawanx2 sepertiyang ditunjukkan dalam Rajah 1.
Find the values of p and n.
Cari nilai p dan5 n.
y
4
Diagram
1/Rajah
B
1
(a) Convert the equation xy = 12x - 4x3 to the
linear form to obtain the straight line graph as
shown in Diagram 1.
Tukarkanpersamaanxy = 12x - 4x3 kepadabentuk
linear untuk memperolehgraf garis lurus sepertiyang
Diagram
1/Rajah
ditunjukkan
dalamRajah
1. 1
(a)(b)Convert
the equation xy = 12x - 4x3 to the
State/ Nyatakan
y = x + ; 2 , where
u is 3/
a constant.
Diagram
Rajah 3 Diagram 4
Cari nilai p dan n.
(y - x) against
B
menunjukkan
grafline
garisgraph
lurus yang
diperoleh
shows
a straight
obtained
bydengan
plotting
1
(y - x)1-.
melawan-.
(ymemplot
- x) against
x2
x2
y-x
Pembolehubah x dan y dihubungkanolehpersamaan
y = x + ..!!:_,dengankeadaanu ialahpemalar.Rajah 4
x2
menunjukkan graf garis lurus yang diperolehdengan
1
memplot (y - x) melawan-.
x2
y-x
_o
_______
Rajah 2 menunjukkan graf garis lurus yang diperoleh
(ii) coordinates of G.
dengan memplot (y - x) melawanx 2•
koordinatG.
y-x
[3 marks/markah]
Diagram
x2
1
4/Rajah
Ungkapkank dalamsebutan u dan t.
_o
_______
Rajah 2 menunjukkan graf garis lurus yang diperoleh
dengan memplot (y - x) melawanx 2•
y
X
Express
in terms ofgraf
u and
Rajah5 kmenunjukkan
garist.lurus yang diperoleh
2
Ungkapkank dalamxsebutan
u dan
1 t.
dengan memplot - melawan
[3 marks/ markah]
y
X
5 Diagram 5 shows axzstraight line graph obtained
y
. x2
•
1
by p 1ottmg - agamst -.
2
Express yin terms of x.
Ungkapkany dalam sebutanx.
[3 marks/ markah]
3 The variables x and y are related by the equation
Diagram
2
y = 3x2 - : , where
n is2/aRajah
constant.
Diagram 3
1016Express yin terms of x.
P
shows a straightsebutan
line graph
obtained by plotting
Ungkapkany dalam
x.
xy against x3•
[3 marks/ markah]
Pembolehubahx dan y dihubungkan olehpersamaan
3 The
variables x and y are related by the equation
y = 3x2 - n dengankeadaann ialahpemalar.Rajah3
y menunjukkan
= 3x2 - : , where
n islurus
a constant.
Diagram
3
graf garis
yang diperoleh
dengan
y
X
(6, 5)
Rajah5 menunjukkan graf garis lurus yang diperoleh
x2
1
dengan memplot - melawan
y
X
xz
y
(6, 5)
Diagram
5/ Rajah
5
Express yin terms of x.
Ungkapkany dalamsebutan x.
[3 marks/ markah]
memplot
xy melawan
shows
a straight
linex3.
graph obtained by plotting
xy against x
[3 marks/ markah]
x2
1
5 Diagram 5 shows a straight line graph obtained
. x2
•
1
agamst 4/
-.Rajah 4
by p 1ottmg - Diagram
y-x
3
4
Express k in terms of u and t.
2 Diagram 2 shows a straight line graph obtained
by plotting (y- x) against x 2 •
P
[3 marks/ markahJ
denganukeadaan
u ialahpemalar.
Rajah
y y= =x x++;..!!:_,
is a constant.
Diagram
44
, where
x2
2
2 Diagram 2 shows a straight line graph obtained
(i) the gradient of the straight
line,
by plotting
(y- x) against x 2 •
kecerunangaris lurus itu,
1016
1-.
x2
Pemboleh
ubahxx and
dan yydihubungkan
persamaan
4 The
variables
are related oleh
by the
equation
koordinat
G.
linear untuk
memperoleh
graf garis lurus sepertiyang
[3 marks/markah]
ditunjukkan dalamRajah 1.
(b) State/ Nyatakan
2/Rajah
by the equation
Find
the avalues
of pline
andgraph
n. obtained by plotting
shows
straight
(i) the
gradient
of the
linear
form
to obtain
the straight
straight line,
line graph as
garis lurus
shownkecerunan
in Diagram
1. itu,
Tukarkan
persamaanxy
(ii) coordinates
of =G.12x - 4x3 kepadabentuk
Diagram
[3 marks/ markahJ
-------x3
The variables0 x and y are related
•
Pembolehubahx dan y dihubungkan olehpersamaan
Diagram
y = 3x2 - n dengankeadaann ialahpemalar.Rajah3
menunjukkan graf garis lurus yang diperolehdengan
memplot xy melawanx3.
Prepared by Cheng WL
5/ Rajah
5
Express yin terms of x.
Ungkapkany dalamsebutan x.
[3 marks/ markah]
Lesson 1
Page 14
xz
Express yin terms of x.
y
Ungkapkany dalam sebutanx.
[3 marks/ markah]
(6, 5)
3 The variables x and y are related by the equation
y = 3x2 P
1016
: ,
where n is a constant. Diagram 3
shows a straight line graph obtained by plotting
xy against x3•
Pembolehubahx dan y dihubungkan olehpersamaan
Diagram
y = 3x2 - n dengankeadaann ialahpemalar.Rajah3
5/ Rajah
5
Express yin terms of x.
Ungkapkany dalamsebutan x.
menunjukkan graf garis lurus yang diperolehdengan
memplot xy melawanx3.
[3 marks/ markah]
xy
uation
ned by
1.
(p, 17)
an
emplot y
1.
5
quation
tained by
1.
xy
-------x3
0
(p, 17)
Diagram 3/ Rajah 3
maan
n memplot y
h 1.
Find the values of p and n.
Cari nilai p dan n. 5
[3 marks/ markahJ
-------x3
0
4 The variables x and y are related by the equation
B
the
raph as
ntuk
rtiyang
o the
graph as
bentuk
pertiyang
markah]
ined
eh
s/markah]
btained
roleh
3/ Rajah Diagram
3
y = x + ; 2 , whereDiagram
u is a constant.
4
Find athe
values line
of pgraph
and n.obtained by plotting
shows
straight
Cari nilai p dan n.
(y - x) against
1-.
x2
[3 marks/ markahJ
4Pemboleh
The variables
x and
y are related
by the equation
ubah x dan
y dihubungkan
olehpersamaan
B y =y x=+x..!!:_,
+ ;dengan
where
u is au ialah
constant.
Diagram
keadaan
pemalar.
Rajah 4 4
x2
2
,
shows a straight
line
graph
by plotting
menunjukkan
graf garis
lurus
yang obtained
diperolehdengan
1
memplot
(y
x)
melawan
-.
(y - x) against 1-.
x2
x2
y-x
Pembolehubah
x dan y dihubungkanolehpersamaan
y = x + ..!!:_,dengankeadaanu ialahpemalar.Rajah 4
x2
menunjukkan graf garis lurus yang diperolehdengan
1
memplot (y - x) melawan-.
x2
y-x
_o
_______
Diagram
x2
1
4/Rajah
4
Express k in terms of u and t.
Ungkapkank dalamsebutan u dan t.
_o
_______
x2
[3
1 marks/ markah]
5 Diagram 5 shows a straight line graph obtained
. x 2 Diagram
•
1
-. 4/Rajah 4
by p 1ottmg - agamst
y
X
Express k in terms of u and t.
Rajah5 menunjukkan graf garis lurus yang diperoleh
Ungkapkank dalam
sebutan u dan t.
x2
1
[3 marks/ markah]
dengan memplot - melawan
y
X
xz a straight line graph obtained
5 Diagram 5 shows
. x2 y •
1
by p 1ottmg - agamst -.
markah]
uation
3
otting
s/ markah]
an
quation
h3
m3
an
plotting
y
X
5) yang diperoleh
Rajah5 menunjukkan graf garis(6,lurus
x2
1
dengan memplot - melawan
y
X
xz
y
(6, 5)
Diagram
5/ Rajah
5
Express yin terms of x.
Prepared
by
Cheng
WLx.
Ungkapkan
y dalam
sebutan
Lesson 1
[3 marks/ markah]
Page 15
Diagram
4/Rajah
4
Express k in terms of u and t.
Ungkapkank dalamsebutan u dan t.
[3 marks/ markah]
5 Diagram 5 shows a straight line graph obtained
. x2
•
1
by p 1ottmg - agamst -.
y
X
Rajah5 menunjukkan graf garis lurus yang diperoleh
x2
1
dengan memplot - melawan
y
X
xz
y
s/ markah]
(6, 5)
quation
m3
plotting
aan
Diagram
5/ Rajah
ah3
Express yin terms of x.
gan
Ungkapkany dalamsebutan x.
5
[3 marks/ markah]
Prepared by Cheng WL
Lesson 1
Page 16
Table 1 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation y =
J,
where p and t are constants.
{pi~9Jadual1 menunjukkan nilai-nilaibagidua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubah x dan y
dihubungkanolehpersamaany =
dengankeadaanp dan t ialahpemalar.
4
6
8
10
12
14
2.45
1.86
1.38
1.04
0.78
0.59
Table 1/Jadual 1
(a) Based on Table 1, construct a table for the values of log 10 y. Give your answer correct to two significant
figures.
BerdasarkanJadualt bina satu jadual baginilai-nilailog 10 y. Berikanjawapan anda betul kepadadua angka bererti.
[1 mark/ markah]
(b) Plot log 10 y against x, using a scale of 2 cm to 2 units on the x-axis and 2 cm to 0.1 unit on the log 10 y-axis.
Hence, draw the line of best fit.
Plot log 10 y melawanx, menggunakanskala2 cm kepada2 unit padapaksi-x dan 2 cm kepada0.1 unit padapaksi-Iog10 y.
Seterusnya,lukis garis lurus penyuaian terbaik.
[3 marks/ markah]
(c) Use the graph in (b) to find the value of
Gunakangraf di (b) untuk mencarinilai
(i) t,
(ii) p.
[6 marks/ markah]
•
2 Table 2 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation hx = ky + 2xy, where h and k are constants.
Jadual2 menunjukkan nilai-nilaibagidua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubah x dan
y dihubungkanolehpersamaanhx =ky + 2xy, dengan keadaanh dan k ialahpemalar.
1.5
2.0
3.0
4.0
5.0
6.0
2.72
0.83
0.49
0.41
0.38
0.35
Table
2/Jadual 2
1
1
(a) Based on Table 2, construct a table for the values of - and-.
X
y
BerdasarkanJadual2, bina satu jadual baginilai-nilail_ dan
X
1
y
[2 marks/ markah]
(b) Plot l against l, using a scale of 2 cm to 0.1 unit on the l-axis and 2 cm to 0.5 unit on the l-axis.
y
X
y
X
Hence, draw the line of best fit.
Plot l_ rnelawan
1
dengan menggunakanskala2 cm kepada0.1 unit padapaksi-l_ dan 2 cm kepada0.5 unit padapaksi-l_.
y
X
y
Seterusnya,lukis garis lurus penyuaian terbaik.
[3 marks/ markah]
(c) Using the graph in (b), find the value of
Menggunakangraf di (b), cari nilai
(i) h,
(ii) k.
[5 marks/ markah]
3 Table 3 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation y = 3ax + b , where a and b are constants.
6X
Jadual3 menunjukkan nilai-nilai bagidua pembolehubah, x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubahx dan
Y dihubungkanolehpersamaany
=
3ax + :x' dengankeadaana dan b ialahpemalar.
1
2
3
4
5
6
14.65
8.28
6.59
6.06
6.00
6.18
Table 3/ Jadual 3
Prepared by Cheng WL
Lesson 1
Page 17
Gunakangraf di (b) untuk mencarinilai
(i) t,
(ii) p.
[6 marks/ markah]
•
2 Table 2 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation hx = ky + 2xy, where h and k are constants.
Jadual2 menunjukkan nilai-nilaibagidua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubah x dan
y dihubungkanolehpersamaanhx =ky + 2xy, dengan keadaanh dan k ialahpemalar.
1.5
2.0
3.0
4.0
5.0
6.0
2.72
0.83
0.49
0.41
0.38
0.35
Table
2/Jadual 2
1
1
(a) Based on Table 2, construct a table for the values of - and-.
X
y
BerdasarkanJadual2, bina satu jadual baginilai-nilail_ dan
X
1
y
[2 marks/ markah]
(b) Plot l against l, using a scale of 2 cm to 0.1 unit on the l-axis and 2 cm to 0.5 unit on the l-axis.
y
X
y
X
Hence, draw the line of best fit.
Plot l_ rnelawan
1
dengan menggunakanskala2 cm kepada0.1 unit padapaksi-l_ dan 2 cm kepada0.5 unit padapaksi-l_.
y
X
y
Seterusnya,lukis garis lurus penyuaian terbaik.
[3 marks/ markah]
(c) Using the graph in (b), find the value of
Menggunakangraf di (b), cari nilai
(i) h,
(ii) k.
[5 marks/ markah]
3 Table 3 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation y = 3ax + b , where a and b are constants.
6X
Jadual3 menunjukkan nilai-nilai bagidua pembolehubah, x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubahx dan
Y dihubungkanolehpersamaany
=
3ax + :x' dengankeadaana dan b ialahpemalar.
1
2
3
4
5
6
14.65
8.28
6.59
6.06
6.00
6.18
Table 3/ Jadual 3
Prepared by Cheng WL
Lesson 1
Page 18
(c) Using the graph in (b), find the value of
Menggunakangraf di (b), cari nilai
(i) h,
(ii) k.
[5 marks/ markah]
3 Table 3 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation y = 3ax + b , where a and b are constants.
6X
Jadual3 menunjukkan nilai-nilai bagidua pembolehubah, x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubahx dan
Y dihubungkanolehpersamaany
=
3ax + :x' dengankeadaana dan b ialahpemalar.
1
2
3
4
5
6
14.65
8.28
6.59
6.06
6.00
6.18
Table 3/ Jadual 3
(a)_ Based on Table 3, construct a table for the values of x2 and xy.
BerdasarkanJadual3, bina satu jadual baginilai-nilaix 2 dan xy.
[2
(b) Plot xy against x 2, using a scale of 2 cm to 5 units on both axes. Hence, draw the line of best fit.
Plot xy melawanx2, dengan menggunakanskala2 cm kepada5 unit pada kedua-duapaksi. Seterusnya,lukis garis lurus
penyuaian terbaik.
[3
(c) Using the graph in (b), find the value of
Menggunakangraf di (b), cari nilai
(i) al
(ii) b.
[5
4 Table 4 shows the values of two variables, x and y, obtained from an experiment. A straight line graph is
obtained by plotting
Y
against l.
X
X
Jadual4 menunjukkannilai-nilaibagi dua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Grafgaris lurus
1
diperolehdenganmemplot melawan-.
X
X
1.25
1.43
2.00
2.5
4.00
5.00
4.29
4.26
4.18
4.12
3.94
3.84
Table 4/ Jadual 4
1
y2
X
X
(a) Based on Table 5 construct a table for the values of - and-.
1
2
BerdasarkanJadual5, bina satu jadual baginilai-nilai_!_dan Y •
X
(b) Plot
y_
against l
X
X
1
X
[2
using a scale of 2 cm to 0.1 unit on the !-axis and 2 cm to 2 units on the Y-axis.
X
X
Hence draw the line of best fit.
1
2
Plot Y melawan1-,menggunakanskala2 cm kepada0.1 unit padapaksi-_!_dan 2 cm kepada2 unit padapaksi-y
X
X
X
2
X
•
Seterusnya, lukis garis lurus penyuaian terbaik.
[3 marks/ markah]
(c) Using the graph in (b),
Menggunakangraf di (b),
(i) find the value of y when x = 3.6,
(ii) express yin terms of x.
carinilai y apabilax = 3.6,
ungkapkany dalamsebutan x.
[5 marks/ markahJ
1 Table 1 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation y - {p = P.!_where p and t are constants.
X
1
Jaduall menunjukkan nilai-nilaibagidua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubahx dan
y dihubungkanolehpersamaany -{p = pt, dengankeadaanp dan t ialahpemalar.
X
Prepared by Cheng WL
1.2
2.0
3.5
4.5
5.0
6.0
4.15
5.16
5.81
5.68
6.06
6.19
Table Lesson
1/ Jadual 1
1
Page 19
(a) Plot xy against x, using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the xy-axis. Hence,
(c) Using the graph in (b), find the value of
Menggunakangraf di (b), cari nilai
(i) al
(ii) b.
[5
4 Table 4 shows the values of two variables, x and y, obtained from an experiment. A straight line graph is
obtained by plotting
Y
against l.
X
X
Jadual4 menunjukkannilai-nilaibagi dua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Grafgaris lurus
1
diperolehdenganmemplot melawan-.
X
X
1.25
1.43
2.00
2.5
4.00
5.00
4.29
4.26
4.18
4.12
3.94
3.84
Table 4/ Jadual 4
1
y2
X
X
(a) Based on Table 5 construct a table for the values of - and-.
1
2
BerdasarkanJadual5, bina satu jadual baginilai-nilai_!_dan Y •
X
(b) Plot
y_
against l
X
X
1
X
[2
using a scale of 2 cm to 0.1 unit on the !-axis and 2 cm to 2 units on the Y-axis.
X
X
Hence draw the line of best fit.
1
2
Plot Y melawan1-,menggunakanskala2 cm kepada0.1 unit padapaksi-_!_dan 2 cm kepada2 unit padapaksi-y
X
X
X
2
X
•
Seterusnya, lukis garis lurus penyuaian terbaik.
[3 marks/ markah]
(c) Using the graph in (b),
Menggunakangraf di (b),
(i) find the value of y when x = 3.6,
(ii) express yin terms of x.
carinilai y apabilax = 3.6,
ungkapkany dalamsebutan x.
[5 marks/ markahJ
1 Table 1 shows the values of two variables, x and y, obtained from an experiment. The variables x and y are
related by the equation y - {p = P.!_where p and t are constants.
X
1
Jaduall menunjukkan nilai-nilaibagidua pembolehubah,x dan y, yang diperolehdaripadasatu eksperimen.Pembolehubahx dan
y dihubungkanolehpersamaany -{p = pt, dengankeadaanp dan t ialahpemalar.
X
1.2
2.0
3.5
4.5
5.0
6.0
4.15
5.16
5.81
5.68
6.06
6.19
Table 1/ Jadual 1
(a) Plot xy against x, using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the xy-axis. Hence,
draw the line of best fit.
Plot xy melawanx, menggunakanskala2 cm kepada1 unit padapaksi-x dan 2 cm kepada5 unit padapaksi-xy. Seterusnya,
lukis garis lurus penyuaian terbaik.
(b) Using the graph in (a), find
Menggunakan graf di (a), cari
(i) the values of p and t,
nilai p dan t,
(ii) the correct value of y if one of the values of y has been wrongly re:orded during the experiment.
nilai betul bagiy jika satu daripadanilai y telahdirekodkansalahsemasaekspenmen.
#&U-i Applyin-;J
Prepared by Cheng WL
Lesson 1
Page 20