Page 9 - Grab Me SPM Add Mathematics Form 4,5

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Example 8 6.3 Application of Linear Law
The diagram below shows part of the graph
log (1 – y) against log x. Given the variables Example 9
10
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x and y are related by the equation y = 1 – ax .
b
log (1 – y) The table below shows the values of two variables
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u and v obtained from an experiment. Given that
(3, 2) the variables u and v are related by the equation
uv = pu + qv, where p and q are constants.
u 20 25 30 35 40 45
log x
0 (1, 0) 10 v 20.0 16.7 15.0 14.0 13.3 12.8
Find the constants a and b.
(a) Based on the above table, construct a table for
Solution the values of .
v
2 – 0 u
From the graph, m = = 1. Thus, Y = X + c.
3 – 1 v
At point (1, 0), 0 = 1 + c Ú c = –1 (b) Plot v against v u using a scale of 2 cm to
Hence, log (1 – y) = log x – 1 …  0.2 unit on the u -axis and 2 cm to 2 units on
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Given y = 1 – ax , thus 1 – y = ax b the v-axis. Hence, draw the line of best fit.
b
log (1 – y) = log a + b log x … 
10
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Compare  with : log a = –1 (c) Using the graph in (b), find the values of p and
10 q.
a = 1 , b = 1
10
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Ch 6_Grab Me SPM AddMaths F4.indd 69 13/05/2022 9:02 AM