SPM 2023 Add Maths Paper 1, Question 3Linear Law

Solved on video in English and Bahasa Melayu · Form 4, Linear Law · 4:22 video

The question

(a)

Diagram 2 shows two straight lines, L₁ and L₂, drawn based on five plotted points on a plane of 1/y against x². (a) Which straight line is a suitable line of best fit? Give a reason for your answer.

(b)

Diagram 2 shows the straight line graph of 1/y against x² with line of best fit passing through (6, 7) and (10, 9). (b) Given that (10, 9) lies on the line of best fit, express y in terms of x.

SPM 2023 Add Maths Paper 1, Question 3: the question as drawn in Eduly's video4:22

Part (a)

Step 1

A line of best fit should pass through the distribution of points so that the points are as close as possible to the line and evenly distributed on both sides.

Why this step

The line doesn't have to touch points. What counts is overall closeness and balance, so 'passes through more points' loses the mark.

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

Final answer

L₁, as the points lie nearest to it and are evenly spread

Where students lose marks

Watch out: don't say the line 'passes through more points'. Say the plotted points are closest to L₁ and evenly spread about it.

Part (b)

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

Final answer

y = 2/(x² + 8)

Where students lose marks

Watch out: find the gradient from (6, 7) and (10, 9), then finish by inverting 1/y so y is the subject.

Watch every step of this question solved on video (4:22), with the reason behind each step and a box that checks your own answer.

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