Foundation November 2023 Paper 3 Q23
23 Jenna is asked to show the inequality \(\ -3 \lt x \leqslant 4\ \) on a number line.
Here is her answer.
(a) Write down two mistakes Jenna has made. (2)
(b) Work out the greatest integer that satisfies the inequality
\(5y - 7 \lt 16\) (2)
\(5y - 7 \lt 16\) (2)
| Answer | Mark | Mark scheme |
|---|---|---|
| Explanations | C2 | for two different correct explanations Acceptable examples She should have a solid/full/shaded/coloured circle at 4 It does not show that \(x\) could be equal to 4 She should have marked/drawn a (clear/empty) circle at \(-3\) The line should be drawn to \(-3\) Jenna started from \(-2\) not \(-3\) Not acceptable examples Both circles should be black One circle should be filled in (needs to say which circle) She shouldn’t have to reach number 4 Jenna has made no mistakes |
| (C1 | for one correct mistake described) |
Additional guidance
Any incorrect statement as part of a correct response can be ignored unless it contradicts the statement.
| Answer | Mark | Mark scheme |
|---|---|---|
| 4 | M1 | for a correct first step, eg for adding 7 to both sides \(5y - 7 + 7 \lt 16 + 7\) or for dividing throughout by 5 eg \(\dfrac{5y}{5} - \dfrac{7}{5} \lt \dfrac{16}{5}\) or for showing 4.6 (oe) as the critical value or for \(5 \times 4 - 7\) with 13 seen as answer |
| A1 | for 4 or \(y = 4\) with no incorrect working |
Additional guidance
Allow use of any inequality or as an equation for the first mark
Award 1 mark for 4.6 oe,
eg \(y = \dfrac{23}{5}\) or \(y \lt 4.6\)
An answer of 4 from incorrect working can score 1 mark at most.