Numeracy Intermediate November 2018 Unit 1 Q9
9.
(a) Jade is planning a weekend break to celebrate her 21st birthday.
The weekend break costs £350.
Jade’s father says,
The weekend break costs £350.
Jade’s father says,
‘If you save 21% of your earnings each week for the next 20 weeks, I will give you the rest of the money you need.’
Jade earns £72 per week.
How much is Jade’s father offering to pay towards her weekend break?
You must show all your working. [4]
(b)
(i) Jade has bought a new suitcase that can hold 65 litres.
What is 65 litres in cm\(^3\)?
Circle your answer. [1]
What is 65 litres in cm\(^3\)?
Circle your answer. [1]
65 cm\(^3\) 650 cm\(^3\) 6 500 cm\(^3\) 65 000 cm\(^3\) 650 000 cm\(^3\)
(ii) Jade’s new suitcase weighs 3 kg.
When it is packed, her suitcase must not weigh more than 25 kg altogether.
What percentage of the 25 kg does Jade have left for packing? [2]
When it is packed, her suitcase must not weigh more than 25 kg altogether.
What percentage of the 25 kg does Jade have left for packing? [2]
(iii) Which one of the following formulae could be used to work out the volume of Jade’s new suitcase?
\(a\), \(b\) and \(c\) are measurements of the 3 dimensions of the suitcase.
Circle your answer. [1]
\(a\), \(b\) and \(c\) are measurements of the 3 dimensions of the suitcase.
Circle your answer. [1]
\(a + b^2 + c\) \(2a^2c - 4\pi b^2\) \(abc + \pi a^2c\) \(a^3 - b^2 + c\) \(a + b^3 + c\)
(c) Jade needs a new passport photograph.
A passport photograph must be 45 mm high by 35 mm wide.
A passport photograph must be 45 mm high by 35 mm wide.
Jade has a mathematically similar photograph that she could reduce in size to use as her new passport photograph.
The height of this photograph is 9 cm.
Calculate the width of this photograph. [2]
| Scheme | Marks | Comments |
|---|---|---|
| (Jade saves each week) 72 × 0.21 or 7.2(0) + 7.2(0) + 0.72 (= £ 15.12) | M1 | Do not accept ‘1512’ without indication of pence, unless used correctly in working |
| (Total savings 15.12) × 20 | M1 | These 2 M marks can be awarded in either order, i.e. 72 × 20 (=1440), followed by × 0.21 |
| (£) 302.4(0) | A1 | CAO |
| (Jade’s father pays £350 – 302.40 =) (£) 47.6(0) | B1 | FT ‘their £302.40’ provided
|
| Scheme | Marks | Comments |
|---|---|---|
| (i) 65 000 cm\(^3\) | B1 | |
| (ii) \(100 - \dfrac{3}{25} \times 100\) or \(\dfrac{(25 - 3)}{25} \times 100\) | M1 | Or equivalent Allow M1 for 88/100 |
| 88(%) | A1 | If no marks, award SC1 for an answer of or sight of 12(%) provided it is not from incorrect working |
| (iii) abc + πa\(^2\)c | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| 35 × 9 ÷ 45 or 35 ÷ 5 or equivalent | M1 | Allow with incorrect place value from conversion of units |
| 7 (cm) or 70 mm | A1 | CAO. Do not accept an answer of:
|