SPM 2022 Add Maths Paper 2, Question 11Linear Law

Solved on video in English and Bahasa Melayu · 10 marks · Form 4, Linear Law · 5:56 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 ay = b√x + 1/√x, such that a and b are constants.

x: 1.0, 2.0, 3.5, 4.5, 6.0, 7.0 y: −4.70, −0.79, 1.29, 2.64, 3.51, 4.61

(a) Plot y√x against x, using a scale of 2 cm to 1 unit on the x-axis and 2 cm to 2 units on the y√x-axis. Hence, draw the line of best fit.

[4 marks]

(b)

Using the graph in 11(a):

(b) (i) find the value of y when x = 5.7, (ii) write ay = b√x + 1/√x in linear form, hence find the value of a and of b.

[6 marks]

SPM 2022 Add Maths Paper 2, Question 11: the question as drawn in Eduly's video5:56

Part (a)

Step 1

Compute Y = y√x for each x (this is the variable to plot on the vertical axis):

Why this step

Plotting y√x against x turns the curve into a straight line, so we work out this new variable first. The gradient and intercept then give a and b.

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

Final answer

y√x = −4.70, −1.12, 2.41, 5.60, 8.60, 12.20 (then plot and draw the line)

Where students lose marks

Watch out: draw one straight line passing evenly through the points, with roughly equal numbers of points on each side.

Part (b)

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

Final answer

y ≈ 3.43; y√x = (b/a)x + 1/a; a ≈ −0.143, b ≈ −0.39 (depends on your line)

Where students lose marks

Watch out: the graph gives y√x, not y, so divide by √5.7. Draw an accurate line, as a and b depend on it.

Watch every step of this question solved on video (5:56), with the reason behind each step and a box that checks your own answer.

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