MRSM Trial 2025 Add Maths Paper 2, Question 11Linear Law

Table 1.1 shows the values of two variables x and y obtained from an experiment. The variables are related by y = px + r/(px), where p and r are constants. Table 1.1: x = 1, 2, 3, 4, 5, 6 ; y = 5.9, 4.2, 4.3, 4.6, 5.1, 5.9.

(a)(i) Based on Table 1.1, complete Table 1.2 (the xy row, given the x² row = 1, 4, 9, 16, 25, 36).

Table 1.1 gives x = 1, 2, 3, 4, 5, 6 and y = 5.9, 4.2, 4.3, 4.6, 5.1, 5.9 for y = px + r/(px).

(a)(ii) Plot xy against x², using a scale of 2 cm to 5 units on both axes. Hence, draw the line of best fit.

Using the straight-line graph of xy against x² (from y = px + r/(px), where xy = p·x² + r/p):

(b)(i) Using the graph in (a)(ii), find p.

Using the straight-line graph of xy against x² (xy = p·x² + r/p, with p = 0.8429):

(b)(ii) Using the graph in (a)(ii), find r.

The variables are related by y = px + r/(px), with p = 0.8429 and r = 4.214.

(c) Hence, find the values of the gradient and y-intercept for another possible linear form for y = px + r/(px).