Numeracy Intermediate November 2022 Unit 1 Q1
1. Rosie is printing two different rectangular pictures of her dog.
The small picture has a height of 10 cm and a width of 5 cm.
The large picture has a height of 40 cm and a width of 15 cm.
(a)
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The small picture costs £2 to print.
Each 1 cm2 of the small picture costs the same to print as each 1 cm2 of the large picture.
Calculate the cost of printing the large picture.
You must show all your working. [6 + 2 OCW]
(b) To make a frame, it costs 40p for each centimetre of the total distance around the outside of the picture.
Calculate the cost of making a frame for the small picture. [3]
Cost of making a frame for the small picture is ……………
| Scheme | Marks | Comments |
|---|---|---|
| (Area of the small picture is) 10 × 5 OR (Area of the large picture is) 40 × 15 | M1 | |
| (Area of the small picture is) 50 (cm2) (Area of the large picture is) 600 (cm2) | A1 A1 | May be implied in further working May be implied in further working |
| (Cost to print large picture is) \(\frac{600}{50}\) × 2(.00) OR For a full proportion method calculated correctly or or with working shown, e.g. 50cm2 is (£)2, 100cm2 is 2 × 2 (=£4), 150cm2 is 2 + 2 × 2 and 600cm2 is 4 × (2 + 2 × 2) | M2 | May be seen in stages FT ‘their 10 × 5’ and FT ‘their 40 × 15’ M1 for any one of the following:
|
| (£)24 or 2400(p) | A1 | Only FT from previous M2 If units are given they must be correct |
| 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. |
1(a) Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| (To find the number of small pictures to cover area of the large picture) 40 ÷ 10 AND 15 ÷ 5 | M1 | Allow 40 ÷ 5 AND 15 ÷ 10 |
| 4 (up) and 3 (across) | A2 | May be shown on a diagram Allow 8 and 1.5 (from 40 ÷ 5 = 8 and 15 ÷ 10= 1.5) A1 for any one of the 4 possible divisions accurately evaluated |
| (Cost to print the large picture) 4 × 3 × (£) 2 or equivalent | M2 | FT ‘their 4 across and 3 up’ provided 2 different values ≠ 1 Allow 8 × 1.5 × (£)2 M1 for appropriate sight of 4 × 3 or 8 × 1.5 including if embedded in other working |
| (Cost to print large picture) (£)24 or 2400(p) | A1 | FT from M2 only If units are given they must be correct |
The alternative method is printed in italics in the original.
| Scheme | Marks | Comments |
|---|---|---|
| (10 + 5 + 10 + 5) × (0.)40 or 30 × (0.)40 or 10 × (0.)40 + 5 × (0.)40 + 10 × (0.)40 + 5 × (0.)40 or 4 + 2 + 4 + 2 or 400 + 200 + 400 + 200 | M2 | M1 for sight of any one of the following:
|
| (£)12 or 1200(p) | A1 | CAO. If units are given they must be correct If no marks, award SC1 for an answer of (£)44 or 4400(p) (working with the larger picture) |