Intermediate November 2022 Unit 1 Q23
23. On Monday morning, Twm picked \(n\) apples from a tree.
Ceri picked 5 times as many apples as Twm.
On Monday afternoon, Twm picked 19 more apples.
Ceri gave 7 of her apples to Twm.
Ceri still had more apples than Twm.
Write down an inequality in terms of \(n\) to show the above information.
Use your inequality to find the least possible number of apples Twm picked on Monday morning.
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(5n - 7 > n + 26\) or equivalent. | B2 | Award B2 for \(5n - 7 > n + 19 + 7\). Award B1 for one of the following:
|
| (Least number of apples Twm picked =) 9 | B2 | An answer must be given following work from an inequality. Award B2 for \(n\) = 9. FT for B2 or B1, from ‘their inequality’, if of equivalent difficulty (must be at least 3 terms with at least 2 ‘\(n\)’ terms and a constant). |
Notes
The rest of the comments for the second B2, printed in the Comments column in the original:
Possible scenarios:
| 1st B2 | 2nd B2 | |
|---|---|---|
| Inequality used | B2 awarded for: | B1 awarded for: |
| \(\boldsymbol{5n - 7 > n + 26}\) B2 awarded | 9 | Sight of:
|
| \(\boldsymbol{5n - 7 > n + 19}\) B1 awarded | 7 | Sight of:
|
| \(\boldsymbol{5n \;\; > n + 26}\) B1 awarded | ||
| \(\boldsymbol{5n - 7 < n + 26}\) B1 awarded | Sight of:
| |
Unsupported answers or no inequality shown
If B0 B0, award SC1 for an unsupported answer of 9 without showing any working or no inequality shown.
Use of equations
If an equation is used throughout, a possible first B1 (see bullet points) and then B0 is awarded.
If B1 for an equation is awarded (see bullet points), a second B2 or B1 could be awarded if there is evidence that the equation has then been turned to an inequality (e.g. \(n\) > 8·25, so answer is 9).
If an inequality is shown and then equation used, B2 B2 is possible.
The second header row of the scenarios table was shaded in the original.