SPM 2017 Add Maths Paper 2, Question 9Linear Law

Solved on video in English and Bahasa Melayu · 10 marks · Form 4, Linear Law · 6:19 video

The question

Use a graph paper to answer this question. 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 - sqrt(h) = hk/x, where h and k are constants. Table 1: x = 1.5, 2.0, 3.5, 4.5, 5.0, 6.0; y = 4.5, 5.25, 5.5, 6.3, 6.34, 6.5. (a) Plot xy against x, using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the xy-axis. Hence, draw the line of best fit. (b) Using the graph in 9(a), find (i) the value of h and of k, (ii) the correct value of y if one of the values of y has been wrongly recorded during the experiment.

[10 marks]

SPM 2017 Add Maths Paper 2, Question 9: the question as drawn in Eduly's video6:19

Step 1

Rearrange y - sqrt(h) = hk/x by multiplying both sides by x: xy = sqrt(h)·x + hk, i.e. Y = mX + c with Y = xy, X = x, gradient m = sqrt(h), intercept c = hk

Why this step

Plotting y against x gives a curve. Multiplying by x turns it into xy against x, a straight line whose gradient and intercept give h and k.

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

Final answer

(a) Line of best fit drawn; (b)(i) h ≈ 51.27, k ≈ −0.0780; (b)(ii) y = 6.0

Where students lose marks

Watch out: plot xy against x, and read h, k and the corrected y from the line of best fit, never the wrong point.

Watch every step of this question solved on video (6:19), with the reason behind each step and a box that checks your own answer.

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