O-LevelMathematicsAlgebra and graphs4024/22 · May/June 2022 · Q68 Marks

The line y = x+2 is drawn on the grid. [Figure with coordinate grid and line y=x+2 drawn]

(a)On the grid, draw the line x+2y = 7.[2]
(b)Use your graph to find the solution of these simultaneous equations. y=x+2 x+2y = 7[1]
(c)(i)The region R is defined by these three inequalities. y≤x+2 x+2y ≥ 7 x ≤5 Shade and label region R.[2]
(c)(ii)(a)The point Z is in region R. The x-coordinate and the y-coordinate of point Z are both integers. Point Z does not lie on the boundary of region R. Find the number of possible positions of point Z.[1]
(c)(ii)(b)The y-coordinate of point Z is one more than its x-coordinate. Write down all the possible coordinates for point Z.[2]

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Mark scheme

Marking points from the official mark scheme (May/June 2022). The mark or mark type is shown in brackets.

[2] B1 for short or unruled line or for two correct coordinates soi
[1] FT where their line crosses y = x + 2 provided it crosses on given grid
[2] FT provided their region is a triangle using x < 5, y ≤ x + 2 and their x + 2y ≥ 7 B1 for line x = 5 drawn correctly
[1] 7
[2] B1FT for at least one correct and maximum of one incorrect

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