SPM Additional Mathematics 2019, Paper 2 (Question 11)


Question 11:
Use a graph paper to answer this question.
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 y= a x b , where a and b are constants.

Table 2

(a) Based on Table 2, construct a table for the values of log10x and log10y. [2 marks]

(b) Plot log10y against log10x, using a scale of 2 cm to 0.1 unit on the X-axis and 2 cm to 0.2 unit on the Y-axis.
Hence, draw the line of best fit. [3 marks]

(c) Using the graph in 11(b), find the value of [5 marks]
(i) a,
(ii) b.


Solution:
(a)

(b)

(c)
y= a x b log 10 y= log 10 ( a x b ) log 10 y= log 10 a log 10 x b log 10 y= log 10 a log 10 x 1 b log 10 y= 1 b log 10 x+ log 10 a Y= log 10 y, m= 1 b , X= log 10 x, c= log 10 a

(c)(i)
c= log 10 a 0.44= log 10 a a= 10 0.44   =2.754

(c)(ii)
m= 1.16 0.44    =2.636 1 b =2.636     b=0.3794

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