SPM 2021 Add Maths Paper 2, Question 10Linear Law

Solved on video in English and Bahasa Melayu · Form 4, Linear Law · 5:53 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 + √h = k²/x, where h and k are constants. The values are x: 1, 2, 3, 4, 5, 6 and y: 3.25, 1.28, 0.58, 0.25, 0.05, −0.09. (a) Plot xy against x, using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 0.5 unit on the xy-axis. Hence, draw the line of best fit.

(b)

Using the graph of xy against x in part (a), where y + √h = k²/x: (b)(i) Find the value of x when y² = 4/x². (b)(ii) Write y + √h = k²/x in linear form, hence find the value of h and of k.

SPM 2021 Add Maths Paper 2, Question 10: the question as drawn in Eduly's video5:53

Part (a)

Step 1

Compute xy for each x:

Why this step

Multiplying the equation by x gives xy = −√h·x + k², which is a straight line. So we plot xy, not y, against x.

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

Final answer

xy: 3.25, 2.56, 1.74, 1.00, 0.25, −0.54; plot and line (see video)

Where students lose marks

Watch out: plot every point accurately, then draw a balanced line, with roughly equal numbers of points and distances on each side.

Part (b)

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

Final answer

(i) x ≈ 2.7; (ii) xy = −√h·x + k², h = 9/16, k = 2

Where students lose marks

Watch out: in xy = −√h·x + k², the gradient is −√h and the Y-intercept is k². Use the gradient too, to find h.

Watch every step of this question solved on video (5:53), with the reason behind each step and a box that checks your own answer.

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