(a) Write down the greatest possible value of \(n\). (1)
(b) On the number line below, show the inequality \(-4 \leqslant m \lt 1\)(2)
(c) Solve \(\dfrac{2}{5}g - 4 \lt 6\) (3)
Mark scheme (a)
Answer
Mark
Mark scheme
4
B1
cao
Mark scheme (b)
Answer
Mark
Mark scheme
correct diagram
C2
for a fully correct diagram, eg
(C1
for drawing a line from −4 to 1 or (indep) for an open circle at 1 or (indep) for a closed circle at −4)
Additional guidance
Condone arrow heads or line ending to denote the ‘end’ of the line
Mark scheme (c)
Answer
Mark
Mark scheme
\(g \lt 25\)
M1
for a correct first step, eg adding 4 to both sides, eg \(\dfrac{2}{5}g \lt 6 + 4\) or multiplying throughout by 5, eg \(2g - 4 \times 5 \lt 6 \times 5\) or dividing throughout by 2, eg \(\dfrac{1}{5}g - 4 \div 2 \lt 6 \div 2\)
M1
for a correct second step, eg \(2g \lt \text{``}10\text{''} \times 5\) or \(\dfrac{1}{5}g \lt \text{``}10\text{''} \div 2\) or \(2g \lt \text{``}30\text{''} + \text{``}20\text{''}\) or \(g - \text{``}20\text{''} \div 2 \lt \text{``}30\text{''} \div 2\) or \(\dfrac{g}{5} \lt \text{``}3\text{''} + \text{``}2\text{''}\) or \(g - \text{``}2\text{''} \times 5 \lt \text{``}3\text{''} \times 5\)
or showing 25 oe as the critical value
A1
for \(g \lt 25\) oe
Additional guidance
Allow use of any inequality or as an equation for both method marks \(\dfrac{2}{5}g \lt 10\) \(2g - 20 \lt 30\) \(\dfrac{g}{5} - 2 \lt 3\)
