Forming Equations: WJEC GCSE Higher November 2022 Unit 1 Q10

Higher November 2022 Unit 1 Q10

WJECHigherCurrent spec6 marksForming Equations Linear Inequalities

10. In this question, you will be assessed on the quality of your organisation, communication and accuracy in writing.

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 + 2 OCW]

Mark scheme

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: Sight of \(5n - 7\) Sight of \(n + 26\) Sight of \(n + 19 + 7\)
(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).
Organisation and Communication.	OC1	For OC1, candidates will be expected to: present their response in a structured way explain to the reader what they are doing at each step of their response lay out their explanation and working in a way that is clear and logical write a conclusion that draws together their results and explains what their answer means
Accuracy of writing.	W1	For W1, candidates will be expected to: show all their working make few, if any, errors in spelling, punctuation and grammar use correct mathematical form in their working use appropriate terminology, units, etc.

Notes

Possible scenarios:

1^st B2	2nd B2
Inequality used	B2 awarded for:	B1 awarded for:
\(\boldsymbol{5n - 7 > n + 26}\) B2 awarded	9	Sight of: \(4n > 33\) \(n > \dfrac{33}{4}\) or equiv 8(·25) One slip in solving the inequality, but final answer rounded correctly
\(\boldsymbol{5n - 7 > n + 19}\) B1 awarded	7	Sight of: 4n > 26 \(n > \dfrac{26}{4}\) or equiv 6(·5) One slip in solving the inequality, but final answer rounded correctly
\(\boldsymbol{5n \;\, > n + 26}\) B1 awarded	7
\(\boldsymbol{5n - 7 < n + 26}\) B1 awarded		Sight of: \(4n < 33\) \(n < \dfrac{33}{4}\) or equiv

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. \(n > 8{\cdot}25\), so answer is 9).

If an inequality is shown and then equation used, B2 B2 is possible.