SPM 2020 Add Maths Paper 2, Question 8Linear Law

Solved on video in English and Bahasa Melayu · Form 4, Linear Law · 5:46 video

The question

(a)

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(2.8)^(-q/x), where p and q are constants. Table 1: x = 1.5, 2.0, 3.0, 4.2, 6.3, 10.0 with corresponding y = 6.6, 11.7, 16.2, 26.3, 30.2, 47.9. (a) Based on Table 1, construct a table for the values of 1/x and log10 y.

(b)

2 unit on the log10 y-axis. Hence, draw the line of best fit.

(c)(i)

(c) Using the graph in 8(b), find the value of (i) p.

(c)(ii)

(c)(ii) Using the graph in 8(b), find the value of q.

SPM 2020 Add Maths Paper 2, Question 8: the question as drawn in Eduly's video5:46

Part (a)

Step 1

Compute 1/x: 1/1.5 = 0.67, 1/2.0 = 0.50, 1/3.0 = 0.33, 1/4.2 = 0.24, 1/6.3 = 0.16, 1/10.0 = 0.10.

Why this step

Two decimal places keep the plotted points accurate. Writing 0.2 instead of 0.24 shifts the point and spoils the line of best fit.

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

Final answer

1/x: 0.67, 0.50, 0.33, 0.24, 0.16, 0.10; log10 y: 0.82, 1.07, 1.21, 1.42, 1.48, 1.68

Where students lose marks

Watch out: give 1/x to at least two decimal places. Writing 0.2 instead of 0.24 distorts the plotted points.

Part (b)

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

Final answer

Graph plotted, best-fit line drawn (see video)

Where students lose marks

Watch out: balance the line of best fit, with about equal points above and below it, not pulled toward one outlier.

Part (c)(i)

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

Final answer

p ≈ 57.5

Where students lose marks

Watch out: extend the line to 1/x = 0 and read the intercept carefully. It is log10 p, so undo the log.

Part (c)(ii)

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

Final answer

q ≈ 3.12

Where students lose marks

Watch out: gradient = −q × log10 2.8, not −q. Use two points actually on your line and keep the minus sign.

Watch every step of this question solved on video (5:46), with the reason behind each step and a box that checks your own answer.

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