SPM 2023 Add Maths Paper 2, Question 11Linear Law

Solved on video in English and Bahasa Melayu · Form 4, Linear Law · 4:59 video

The question

(a)

Table 2 shows the values of two variables, x and y, obtained from an experiment. The variables are related by x^a = by, where a and b are constants. x: 2.40, 3.16, 3.98, 6.31, 10.00, 18.20 y: 1.26, 1.59, 2.52, 3.98, 8.91, 19.96

(a) Based on Table 2, construct a table for the values of log10 x and log10 y.

(b)

Using the log10 x and log10 y values from part (a):

(b) Plot log10 y against log10 x, using a scale of 2 cm to 0.2 unit on both axes. Hence, draw the line of best fit.

(c)

The variables are related by x^a = by.

(c) Write x^a = by in linear form. Hence, by using the graph in (b), find the value of a and of b.

SPM 2023 Add Maths Paper 2, Question 11: the question as drawn in Eduly's video4:59

Part (a)

Step 1

Compute log10 x: log 2.40 = 0.38, log 3.16 = 0.50, log 3.98 = 0.60, log 6.31 = 0.80, log 10.00 = 1.00, log 18.20 = 1.26.

Why this step

Plotting y against x gives a curve. Taking log10 of both variables is what will straighten the power law, so we need these values before plotting.

1 more step, with the reason for it, in the full solution

Final answer

log10 x: 0.38, 0.50, 0.60, 0.80, 1.00, 1.26; log10 y: 0.10, 0.20, 0.40, 0.60, 0.95, 1.30

Where students lose marks

Watch out: recheck each log10 value. One slip, like log 8.91 written as 1.26 instead of 0.95, ruins the whole graph.

Part (b)

2 more steps, each with the reason for it, in the full solution

Final answer

Graph of log10 y against log10 x with line of best fit (see video)

Where students lose marks

Watch out: put log10 x across and log10 y up, using the given scale. Balance the points above and below the line.

Part (c)

4 more steps, each with the reason for it, in the full solution

Final answer

log10 y = a log10 x − log10 b; a ≈ 1.49, b ≈ 3.47

Where students lose marks

Watch out: read a and b from the line of best fit, not table points. Gradient is a, y-intercept is −log10 b.

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