Numeracy Foundation November 2022 Unit 1 Q4
4. A jewellery designer makes brooches.
Each brooch consists of a number of identical pieces of metal.
These brooches come in different designs.
These designs follow a simple pattern.
The first three designs are shown below.
Design 1 consists of 3 pieces of metal.
How many pieces of metal will be used to make the brooch in Design 5? [1]
Which design uses 11 pieces of metal? [1]
A customer says,
“To find how many pieces of metal are used in every design, you multiply the design number by 3, because Design 1 has three pieces of metal.”
Is the customer correct for every design?
Yes ☐ No ☐
Give a reason for your answer. [1]
One customer decides to order a special brooch with a horizontal bar at the top.
The designer knows two of the angles. These are shown in the diagram below.
Diagram not drawn to scale
Calculate the size of angle \(x\). [2]
\(x =\) …………………… °
The designer uses the following formula to calculate how much he will charge for a brooch.
Charge for a brooch (in £) = 2 × cost of materials + 14
A customer spends £30 on a brooch for a friend.
Calculate the cost of the materials for this brooch. [2]
Cost of materials is £ ……………………
| Scheme | Marks | Comments |
|---|---|---|
| 7 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| 9 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| No and valid reason given e.g. ‘No because you add two onto each of the design numbers’ ‘No because it is the design + 2’ ‘No because that rule doesn’t work for Design 2’ ‘No because Design 2 uses 4 pieces (not 6)’ ‘No, because for design 2, 2 × 3 = 6, design 3, 3×3 = 9 and both totals are not correct’ ‘No, because design 3 has 5 pieces of metal which shows it is not multiplied by 3’ ‘No because design 3 would be 9 and not 5’ ‘No because the rule is n + 2 not n × 3’ | E1 | Ignore any further spurious comments. Do not accept ‘No, because the designs add one more piece of metal each time’ ‘No because you add on 1 each time’ Do not accept values from incorrect number work e.g. ‘No because design 3 would be 6 and not 5’ |
| Scheme | Marks | Comments |
|---|---|---|
| 180 – (55 + 90) or 90 - 55 | M1 | |
| 35(°) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| (30 – 14) ÷ 2 | M1 | May be seen in stages Allow sight of embedded 8 for M1, e.g.
2 × 6 + 14 = 26 AND 2 × 7 + 14 = 28 |
| (£)8 | A1 | Answer line takes precedence – do not award A1 if answer line states £30 If answer line is blank, accept embedded answers provided that it is not contradicted (e.g. if they say cost of materials is 30) |