(a) On the grid, show by shading, the region that satisfies all of these inequalities.\[x + y \lt 5 \qquad y \gt 1 \qquad x \gt 2 \qquad y \lt 3x - 2\]Label the region R.(4)
Ron says,
“I can remove one of the four inequalities from the grid so that the region R will not change.”
Ron is correct.
(b) Which inequality can be removed so that the region R will not change? (1)
Mark scheme (a)
Answer
Mark
Mark scheme
Region shown
B4
for a fully correct region identified
(B3
for drawing three correct lines)
(B2
for drawing two correct lines, must include at least one of \(x + y = 5\) or \(y = 3x - 2\))
(B1
for drawing \(x = 2\) and \(y = 1\) correctly OR for drawing \(x + y = 5\) correctly OR for drawing \(y = 3x - 2\) correctly)
Additional guidance
See diagram at end of mark scheme Can exclude \(y = 3x - 2\) for B4 Condone solid lines for all marks Region can be identified by shading in or shading out Lines need to be long enough to enclose the region
Mark scheme (b)
Answer
Mark
Mark scheme
\(y \lt 3x - 2\)
B1
(dep on B1 in (a)) for \(y \lt 3x - 2\) or ft their diagram if 1 line is redundant
Additional guidance
Condone use of ‘=’ or ‘\(\leqslant\)’ and \(3x - 2\)
