CHAPTER 2: LINEAR LAW PAPER 1 xy
1.
n •
• ( 8, k ) x
0
Diagram 1 10 Diagram 1 shows part of a straight line graph drawn to represent y 1. Find the values of k and x n. [answer: n 10 k 2 ] [4 marks]
2.
log10 y ( 3,9 ) •
• ( 7,1) log10 x
0 Diagram 2
Diagram 2 shows part of a straight line graph drawn to represent y = 10kxn, where k and n are constants. Find the values of k and n. [answer: n = -2,k = 15] [4 marks]
1
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y x 3.
• 12, 7
1 x
0 • (2 , - 3 )
Diagram 3
Diagram 3 shows that the variables x and y are related in such away that when
y is plotted against x
1 , a straight line that passes through the points (12 , 7 ) and (2 , - 3 ) is obtained . Express y in x terms of x. [answer: y = 1-5x] [3 marks]
4.
log10 y
3 •
x
0
• ( 5 , -7 ) Diagram 4 Diagram 4 shows part of the graph of log10 y against x. The variables x and y are related by the a equation y x where a and b are constants. Find the values of a and b. b [answer: a = 1000, b = 100] [4 marks ]
2
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log10 y 5. 2
0
x
4 Diagram 5
Diagram 5 shows part of the graph of log10 y against x. The variables x and y are related by the bx
equation y = a (10 ) where a and b are constants. Find the values of a and b. [answer: a = 100, b = - 1/2]
[3 marks]
6.
log10 y
• 2
• -4
0
log10 x
Diagram 6
Diagram 6 shows part of a straight line graph when log10 y against log10 x is plotted. Express y in terms of x. [answer: y 100 x ]
[4 marks]
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7. The variable x and y are related by equation y pk 3 x , where k and p are constant. Diagram 7 shows the straight line obtained by plotting log 10 y against x . log 10 y
( 0, 8 )
(2,2) x
O Diagram 7
a) Reduce the equation y pk 3 x to linear form Y = mX + c. b) Find the value of, i) ii)
log 10 p ,
k.
[answer: log 10 p 8 ] [answer: k = 10 ]
[4 marks]
Orang-orang Berjaya mempunyai disiplin yang tinggi.
4
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PAPER 2 1. Use graph paper to answer this question. Table 1 shows the values of two variables , x and y obtained from an experiment. Variables x n and y are related by the equation y 2rx 2 x, where r and n are constants. r x y
2 8
3 13.2
4 20
5 27.5
6 36.6
7 45.5
Table 1 (a).
(b).
y against x , using a scale of 2 cm to 1 unit on both axes. x Hence, draw the line of best fit.
[5 marks]
Use your graph in (a), to find the value of (i). n, (ii). r, (iii). y when x = 1.5.
[5 marks]
Plot
2. Use graph paper to answer this question. Table 2 shows the values of two variables , x and y obtained from an experiment. Variables x h and y are related by the equation y kx, where h and k are constants. x x y
1 5.1
2 6.9
3 9.7
4 12.5
5 15.4
6 18.3
Table 2 (a).
(b).
Plot xy against x 2 , using a scale of 2 cm to 5 units on the x 2 -axis and 2 cm to 10 units on the xy-axis. Hence, draw the line of best fit.
[5 marks]
Use your graph in (a), to find the value of (i). h, (ii). k, (iii). y when x = 2.5.
[5 marks]
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3. Use graph paper to answer this question. Table 3 shows the values of two variables, x and y obtained from an experiment. Variables x n and y are related by the equation y w , where n and w are constants. x x y
3 103
4 87
5 76
6 68
7 62
8 57.4
Table 3 (a).
(b).
Plot log10 y against log10 x , using a scale of 2 cm to 0.1 unit on the log10 x -axis and 2 cm to 0.2 units on the log10 y -axis. Hence, draw the line of best fit. [5 marks] Use your graph in (a), to find the value of (i). n, (ii). w, (iii). y when x = 2.
[5 marks]
4. Use graph paper to answer this question. Table 4 shows the values of two variables, x and y obtained from an experiment. Variables x b and y are related by the equation y a x , where a and b are constants. x x y
0.2 12.40
0.4 8.50
0.6 6.74
0.8 5.66
1.2 4.90
1.4 3.87
Table 4 (a).
Plot y x against x , using a scale of 2 cm to 0.2 unit on the x -axis and 2 cm to 0.2 units on the y x -axis. Hence, draw the line of best fit. [5 marks]
(b).
Use your graph in (a), to find the value of (i). a, (ii). b, (iii). y when x = 0.9. 6
[5 marks]
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5. Use graph paper to answer this question. Table 5 shows the values of two variables, x and y obtained from an experiment. Variables x and y are related by the equation y  pm x , where m and p are constants. x y
1.5 2.51
3.0 3.24
4.5 4.37
6.0 5.75
7.5 7.76
9.0 10.00
Table 5 (a).
Plot log10 y against x , using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 0.1 units on the log10 y -axis. Hence, draw the line of best fit. [5 marks]
(b).
Use your graph in (a), to find the value of (i). m, (ii). p, (iii). x when y = 4.8.
[5 marks]
6. Use graph paper to answer this question. Table 6 shows the values of two variables, x and y obtained from an experiment. Variables x and y are related by the equation y  hk x , where h and k are constants. x y
3 10.2
4 16.4
5 26.2
6 42
7 67.1
8 107.4
Table 6 (a).
(b).
Plot log10 y against x , using a scale of 2 cm to 1 unit on the x -axis and 4 cm to 0.5 units on the log10 y -axis. Hence, draw the line of best fit. [5 marks] Use your graph in (a), to find the value of (i). h, (ii). k, (iii). x when y = 35.6. [5 marks]
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ANSWER
No. 1.
PAPER 1 Solution xy x 10 Calculate gradient from graph n 10 k 2
Marks 1 1 1 1
log10 y 2log10 x 15 Calculate gradient from graph n 2 k 15
1
c = -5 y 1 5 x x y 1 5x
1 1
4.
log10 y = - log10 b + log10 a Gradient = -2 b = 100 a = 1000
1 1 1 1
5.
log10 y = bx + log10 a or log10 y = bxlog10 10 + log10 a a = 100 b=-½
1 1 1
2.
3.
6. log10 x1/2
Gradient = ½ log10 y = ½ log10 x + 2 or log10 102 or log10 x1/2.102 y 100 x
1 1 1
1
1 1 1 1
7(a)
3 log 10 k 3
1
(b)(i)
log10 y (3log10 k ) x log10 p
1
8
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log 10 p 8 k 10
(ii)
1 1
PAPER 2 No. 1(a)
Solution x y x
(b) (i) (ii) (iii)
3 4.4
4 5
5 5.5
6 6.1
7 6.5
Uniform scale for x-axis and y-axis 6 points plotted correctly Draw the line of best fit Reduce non-linear to linear equation y n 2rx x r Calculate gradient from graph n = 0.77 r = 0.275 y From graph , 3.6 x y = 5.4
(b) (i) (ii) (iii)
2.(a)
2 4
x2 xy
1 4 5.1 13.8
9 29.1
16 50
25 77
Uniform scale for x-axis and y-axis 6 points plotted correctly Draw the line of best fit Reduce non-linear to linear equation xy kx 2 h Calculate gradient from graph h 2 k 3 From graph, xy = 20 y= 8
9
Marks 1
1 1 1 1
1 1 1 1 1 36 109.8
1
1 1 1 1 1 1 1 1 1
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3.(a)
log10 x
0.48 0.60
0.70
0.78
0.85
0.90
log10 y
2.01 1.94
1.88
1.83
1.79
1.76
(b) (i) (ii) (iii)
4.(a)
(b) (i) (ii) (iii)
x y x
1
Uniform scale for x-axis and y-axis 6 points plotted correctly Draw the line of best fit Reduce non-linear to linear equation log10 y w log10 x log10 n Calculate gradient from graph n 102.3 199.526 w 0.6 From graph, log10 y 2.12
1 1 1 1
y 102.12 131.825
1
0.2 0.4 5.55 5.38
0.6 5.22
0.8 5.06
1.2 4.9
Uniform scale for x-axis and y-axis 6 points plotted correctly Draw the line of best fit Reduce non-linear to linear equation y x ax b Calculate gradient from graph a - 0.8 b 5.7 From graph y x 4.9 y = 5.165
10
1 1 1 1
1.4 4.74
1
1 1 1 1 1 1 1 1 1
prepared by: cik shila 11/4/2012
5.(a)
(i) (ii) (iii)
x log10 y
1.5 3.0 0.4 0.51
6 0.76
7.5 0.89
1
9 1
Uniform scale for x-axis and y-axis 6 points plotted correctly Draw the line of best fit Reduce non-linear to linear equation log10 y x log10 m log10 p Calculate gradient from graph m 100.084 or m 1.2134 p 100.26 or1.8197 log10 4.8 0.68 x= 5
1 1 1 1
All values of log10 y are correct
1
6.(a) x log10 y
(i) (ii) (iii)
4.5 0.64
3 4 1.0 1.21
5 1.42
6 1.62
7 1.82
Uniform scale for x-axis and y-axis 6 points plotted correctly Draw the line of best fit Reduce non-linear to linear equation log10 y x log10 k log10 h Calculate gradient from graph k 100.2 or k 1.588 h 100.425 or h 2.66 log10 35.6 1.55 x = 5.7
11
1 1 1 1 1
8 2.03 1 1 1 1 1 1 1 1 1
prepared by: cik shila 11/4/2012