O-LevelMathematicsCoordinate geometry4024/22 · Oct/Nov 2018 · Q810 Marks

The line 2y = x + 4 is drawn on the grid. [Figure 8.1]

(a)(i)On the grid, draw the line x + y + 2 = 0.[2]
(a)(ii)The region R is represented by these three inequalities. 2y ≥ x + 4 x + y + 2 ≥ 0 y ≤ 2 On the grid, shade and label the region R.[2]
(b)Line L is perpendicular to the line 2y = x + 4. Line L passes through the point (1, 8). Show that the equation of line L is y = 10 – 2x.[3]
(c)Use an algebraic method to find the coordinates of the point of intersection of the lines 2y = x + 4 and y = 23 – 2x.[3]

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Mark scheme

Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.

[2] B1 for ruled line from (–4, 2) to (0, –2)
[2] B1 for line y = 2 drawn
[2] B1 for correct region shaded
[3] B1 Gradient of 2y = x + 4 is 1/2 soi so Gradient of line L is –2
[3] M1 FT substitution of (1, 8) into y = their mx + c for L
[3] M1 for a correct method to eliminate one variable
[3] A1 for either x = 8.4 or y = 6.2 nfww
[3] After A0, SC1 for a pair of values that satisfy either equation or for correct answers with no working

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