Numeracy Higher November 2019 Unit 2 Q4
4. Finbar’s skateboard is shown below.
(a) The diameter of each wheel on Finbar’s skateboard is 6·4 cm.
He uses his skateboard to go to visit his friend Sab.
Sab lives 2340 metres from Finbar.
He uses his skateboard to go to visit his friend Sab.
Sab lives 2340 metres from Finbar.
(i) In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
When Finbar visits Sab, how many times will each wheel on Finbar’s skateboard rotate? [4 + 2 OCW]
(ii) What assumption did you make in answering (a)(i)? [1]
(b) A skateboard deck is usually made from one of maple wood, fibreglass or plastic.
The density of these materials is given in the following table.
The density of these materials is given in the following table.
| Skateboard deck material | Density (g/cm3) |
|---|---|
| Maple wood | 0·7 |
| Fibreglass | 2·6 |
| Plastic | 1·8 |
Finbar and Sab compare their skateboards.
| Finbar’s skateboard | Sab’s skateboard | |
|---|---|---|
| Area of the skateboard deck | 1800 cm2 | 1600 cm2 |
| Thickness of the skateboard deck | 1·2 cm | 1·4 cm |
| Material used to make the deck | Fibreglass | Maple wood |
The wheels and the fittings on both their skateboards are identical.
How much heavier is Finbar’s skateboard than Sab’s skateboard?
Give your answer in grams.
You must show all your working. [5]
| Scheme | Marks | Comments |
|---|---|---|
| (i) (Circumference of a wheel) π × 6.4 or π × 0.064 | M1 | Ignore inclusion of ‘×4’ (for 4 wheels) for M1 M2 (A0) |
| (Number of revolutions is) 2340 × 100 ÷ (π × 6.4) or 2340 ÷ (π × 0.064) or equivalent | M2 | FT ‘their circumference’ provided ‘their calculation of circumference’ includes π in the calculation (with consistent place value for M2, with inconsistent place value for M1) M1 for appropriate calculation but containing a place value error, e.g. 2340 ÷ (π × 6.4) or 234000 ÷ (π × 0.064) or 2340 ÷ (π × 0.64) |
| (Number of revolutions is) Answer in the range 11636(.69...) to 11644(.1083) | A1 | CAO, except allow an answer of 11700 (from premature approximation of circumference to 20cm) Mark final answer (Do not ignore further work such as ÷ 4) |
| 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) Assumption, e.g. ‘rode all the way’, ‘didn’t carry the skateboard’, ‘was able to use his skateboard’ ‘skated in a straight line’, ‘each wheel rotates the same number of times’ ‘wheels perfectly circular’, ‘no wear on the wheels’, ‘the wheels are all on the ground throughout’ | E1 | Allow, e.g ‘went directly to Sab’s house’ Do not accept, e.g. ‘2340m is not exact’, ‘he doesn’t stop on his journey’, ‘constant speed’ |
| Scheme | Marks | Comments |
|---|---|---|
| (Mass of Finbar’s skateboard deck) 2.6 × 1800 × 1.2 AND (Mass of Sab’s skateboard deck) 0.7 × 1600 × 1.4 | M3 | Accept shown in stages but not if embedded within incorrect working M2 for one of the following provided not embedded within incorrect working, may be shown in stages: (Mass of Finbar’s skateboard deck) 2.6 × 1800 × 1.2 OR (Mass of Sab’s skateboard deck) 0.7 × 1600 × 1.4 M1 for any one of the following, including embedded within incorrect working, may be shown in stages:
|
| (Mass of Finbar’s skateboard deck) 5616 (g) AND (Mass of Sab’s skateboard deck) 1568 (g) | A1 | CAO |
| (Difference is) 4048 (g) | A1 | Answer must be in grams FT ‘their 5616’ – ‘their 1568’ provided M2 previously awarded |