(a) On the number line, show the inequality \(x \lt 4\)(2)
\(3 \lt y \leqslant 7\) where \(y\) is an integer.
(b) Write down all the possible values of \(y\). (2)
(c) Solve \(3x + 5 \geqslant x + 17\) (3)
Mark scheme (a)
Answer
Mark
Mark scheme
Inequality shown
B2
for fully correct solution with all three aspects with no ambiguity Aspect 1: circle at 4 Aspect 2: circle not shaded Aspect 3: arrow pointing left or line extending beyond \(-5\), starting from their circle
(B1
for any two aspects)
Additional guidance
Circling the number 4 alone scores B0 Aspect 1 and Aspect 2 must relate to the same circle.
Mark scheme (b)
Answer
Mark
Mark scheme
4,5,6,7
B2
for all four numbers in any order
(B1
for 2 or 3 correct values with no errors or 4 correct values with one extra)
Mark scheme (c)
Answer
Mark
Mark scheme
\(x \geqslant 6\)
M1
for a correct intention to subtract 5 from both sides or a correct intention to subtract \(x\) from both sides
M1
for a full method to solve the inequality or showing a critical value of 6
A1
cao
Additional guidance
Can work with an equation for both M marks
Award 2 marks for an answer of \(x\ ?\ 6\) where ? is an = or any incorrect inequality symbol, or for an answer shown as just 6.
