Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 10Linear Law

Solved on video in English · Form 4, Linear Law · 4:59 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 = q(x + 2)^p, where p and q are constants.

Table 1: x : 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 y : 3.61, 3.88, 4.13, 4.35, 4.56, 4.76

(a) Plot log₁₀ y against log₁₀(x + 2), using a scale of 2 cm to 0.1 unit on both axes. Hence, draw the line of best fit.

(b)(i)

Table 1 gives x and y related by y = q(x + 2)^p, where p and q are constants, and a straight-line graph of log₁₀ y against log₁₀(x + 2) has been drawn in part (a).

(b) By using your graph in 10(a): (i) write y = q(x + 2)^p in linear form.

(b)(ii)

(b)(ii) Hence, find the value of p and of q.

Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 10: the question as drawn in Eduly's video4:59

Part (a)

Step 1

Compute log₁₀(x + 2) for each x: 0.40, 0.48, 0.54, 0.60, 0.65, 0.70.

Why this step

The equation has (x + 2), not x, so the horizontal values must be log₁₀(x + 2). Using log₁₀ x is the common slip.

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

Final answer

log₁₀(x + 2): 0.40, 0.48, 0.54, 0.60, 0.65, 0.70; log₁₀ y: 0.56, 0.59, 0.62, 0.64, 0.66, 0.68; graph with line of best fit (see video)

Where students lose marks

Watch out: plot log₁₀ y against log₁₀(x + 2), not log₁₀ x, and keep 2 cm to 0.1 unit on both axes.

Part (b)(i)

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

Final answer

log₁₀ y = p·log₁₀(x + 2) + log₁₀ q

Where students lose marks

Watch out: p comes down as the gradient, and q becomes log₁₀ q as the intercept. Don't leave q without its log.

Part (b)(ii)

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

Final answer

p ≈ 0.4143, q ≈ 2.451 to 2.512 (values read from your line)

Where students lose marks

Watch out: the intercept is log₁₀ q, not q, so use q = 10^c. Take the gradient from two points on your line.

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