4MA0 Foundation January 2017 Paper 1 Q20

EdexcelFoundationOld spec7 marksDrawing & Using Graphs Linear Inequalities

(a) On the grid, draw the graph of \(y = -2x + 4\) for values of \(x\) from −1 to 5

Coordinate grid with x from -2 to 6 and y from -7 to 7

(4)

(b) Show by shading on the grid, the region defined by all three of the inequalities \[\begin{aligned} y &\leqslant -2x + 4 \\ y &\geqslant -4 \\ x &\geqslant 1 \end{aligned}\] Label your region R. (3)

Mark scheme (a)

Scheme	Marks
(−1, 6) (0, 4) (1, 2) (2, 0) (3, −2) (4, −4) (5, −6) Answer: Correct line between \(x = -1\) and \(x = 5\)	B4
	B3
	B2
	B1
	(4)

Notes

B4: For a correct line between \(x = -1\) and \(x = 5\)

B3: For a correct line through at least 3 of (−1, 6) (0, 4) (1, 2) (2, 0) (3, −2) (4, −4) (5, −6)
OR
for all of (−1, 6) (0, 4) (1, 2) (2, 0) (3, −2) (4, −4) (5, −6) plotted but not joined.

B2: For at least 2 correct points plotted

B1: For at least 2 correct points stated (may be in a table) or seen in working
OR
for a line drawn with a negative gradient through (0, 4)
OR
for a line with the correct gradient.

Mark scheme (b)

Scheme	Marks
	M1
	M1
For correct region identified	A1ft
	(3)
	(7 marks)

Notes

M1: for \(y = -4\) drawn; accept full or dashed line
NB A shaded rectangle implies a choice of lines so M0

M1: for \(x = 1\) drawn; accept full or dashed line
NB A shaded rectangle implies a choice of lines so M0

A1ft: for correct region identified.
Condone no label if region clear.
ft from an incorrect straight line in part (a)