Numeracy Foundation November 2023 Unit 1 Q3
3. Luca always has his eyes tested at the local optician.
He needs to have an eye test in December.
- Luca works from Monday to Saturday every week.
- Luca can only go for an eye test after he finishes work at 4 p.m.
- Luca cannot go for an eye test on a Tuesday or Friday.
- The local optician does not open on Wednesday afternoon or Saturday afternoon.
- The local optician is closed every Sunday and on 25th and 26th December.
The calendar below is for December 2023.
| December 2023 | ||||||
|---|---|---|---|---|---|---|
| Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday |
| 1 | 2 | |||||
| 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 17 | 18 | 19 | 20 | 21 | 22 | 23 |
| 24 | 25 | 26 | 27 | 28 | 29 | 30 |
| 31 | ||||||
What is the latest possible date in December that Luca could have his eye test? [2]
The latest date that Luca could have his eye test is …………………… December
Luca last had his eyes tested in 2021.
In 2021, Luca was given the strength of his left eye and the strength of his right eye.
He compares these strengths with those from 2019.
| Left eye strength | Right eye strength | |
|---|---|---|
| 2019 | +0·75 | +1·50 |
| 2021 | +1·25 | +2·25 |
Which eye changed the most between 2019 and 2021?
You must show working to support your answer. [2]
Left ☐ Right ☐
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
These are the costs of Luca’s eye test and glasses:
- £32 for the eye test
- £84 for the frames
- £39 for the lenses.
The optician gave Luca a discount voucher.
With the voucher, Luca gets:
- 25% off the cost of the eye test
- \(\dfrac{1}{3}\) off the cost of the frames.
Calculate the total amount that Luca has to pay.
You must show all your working. [6 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| (Thursday) 28th (December) | B2 | Answer space takes precedence Award B1 for any one of the following (for missing one criteria):
|
| Scheme | Marks | Comments |
|---|---|---|
| (left eye) 1.25 – 0.75 or 0.25 + 0.25 OR (right eye) 2.25 – 1.50 or 0.5 + 0.25 | M1 | Check table for workings. Allow embedded values e.g. 0.75 + 0.5(0) = 1.25 OR 1.50 + 0.75 = 2.25 Allow place value errors e.g. 125 - 75 |
| Right indicated AND 0.5 AND 0.75 seen | A1 | Allow M1A1 if right is indicated and 50 and 75 seen (consistent use of non-decimals). If no marks awarded, award SC2 for right indicated and saying has increased by 0.25 or 25 more (than the left one) |
| Scheme | Marks | Comments |
|---|---|---|
| (Cost of eye test) 32 – 0.25 × 32 or equivalent | M1 | |
| (£)24 | A1 | If M0A0 award SC1 for (£)8 |
| (Cost of frames) 84 – 1/3 × 84 or equivalent | M1 | |
| (£) 56 | A1 | If M0A0 award SC1 for (£)28 |
| (Total cost =) 24 + 56 + 39 | M1 | FT ‘their derived 24’ and ‘their derived 56’ including the use of (£)8 and (£)28 |
| (£)119 | A1 | Award final A1 only if at least one M1 or SC1 has been awarded and there are derived values for both eye test and frames. e.g 8 + 56 + 39 = 103 award M0A0SC1M1A1M1A1. Use of (£)8 and (£)28: 8 + 28 + 39 (=£75) award SC1 SC1 M1 A1 If M0A0 awarded for the last 2 marks, award SC1 for an answer of (£)80 (cost of lenses not included) |
| 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 explanations and working in a way that is clear and logical • write a conclusion that draws together their results and explains what their answer means |
| 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. |