Numeracy Higher November 2024 Unit 2 Q2
2.
A small packet contains four Caru chocolate cakes.
The four cakes have a total mass of 84 g.
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The following information is written on the packet:
‘Caru chocolate cakes contain 600 calories per 100 g.’
Simon aims for a calorie intake of 2400 calories per day.
Today Simon eats one Caru chocolate cake.
What percentage of his daily calorie intake is this cake?
You must show all your working. [5 + 2 OCW]
Caru chocolate cakes contain only fat, carbohydrate, protein and salt.
The ratio of the masses is
fat : carbohydrate : protein : salt = 1360 : 2725 : 515 : 4
How many grams of protein are there in an 84 g packet of four cakes?
Give your answer correct to 2 significant figures. [3]
Cheryl keeps fit by running every day.
Cheryl burns 690 calories per hour when she runs.
Eating a banana gives Cheryl 92 calories of energy.
Cheryl wants to burn off the energy in this banana.
For how many minutes would she need to run?
You must show all your working. [3]
…………… minutes
Cheryl runs at an average speed of 9 km per hour.
Yesterday morning she ran for 38 minutes.
Calculate the distance Cheryl ran yesterday morning. [3]
…………… km
| Scheme | Marks | Comments |
|---|---|---|
| (i) (Calories in cake(s)) 84 × 600 ÷ 100 (÷ 4) OR (Mass per cake) 84 ÷ 4 (= 21)g AND (Calories per 1g of cake) 600 ÷ 100 (= 6 calories) | M1 | |
| (Calories in 1 cake 21 × 6 =) 126 (calories) | A2 | A1 for any one of the following:
|
| (% of required calories) \(\dfrac{126}{2400}\) (× 100) or 0.0525 (× 100) or \(\dfrac{5.25}{100}\) | M1 | FT ‘their derived calories’ provided
|
| 5.25(%) | A1 | ISW further rounding or truncation Allow 5(%), 5.2(%) or 5.3(%) from correct working If no marks, award SC1 for (600 × 84 ÷ 4 =) 12 600 |
| 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. |
| (ii) 84 × 515 ÷ (1360 + 2725 + 515 + 4) or 84 × 515 ÷ 4604 | M1 | |
| 9.4 (g) | A2 | A1 for 9.3(96... g) not from premature approximation or \(\dfrac{10815}{1151}\) or 9.40 (g) |
Alternative
(a)(i) Alternative method only when working is seen as a single calculation
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{600}{2400}\) × \(\dfrac{84}{100}\) × \(\dfrac{1}{4}\) (× 100) or equivalent | M3 | M2 for \(\dfrac{600}{2400}\) × \(\dfrac{84}{100}\) (× 100) or equivalent |
| Two correct stages of simplifying or calculation | A1 | FT from M2 |
| 5.25 (%) | A1 | FT from M2 for an answer of 21(%)) |
| Scheme | Marks | Comments |
|---|---|---|
| (i) Any one of the following complete methods for the number of minutes to burn off energy in 1 banana:
| M2 | May be seen in stages M1 for any one of the following:
|
| 8 (minutes) | A1 | CAO. Answer space takes precedence |
| (ii) 9 × 38 ÷ 60 | M2 | M1 for sight of any one of the following:
|
| 5.7 (km) | A1 | CAO, allow 5700m Answer space takes precedence Do not accept 5700 (km) in the answer space |