Numeracy Higher June 2024 Unit 2 Q2
2.
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
Remember:
1 kilowatt (kW) = 1000 watts (W)
There are 8 street lights in Ffordd Alwyn.
Each light is fitted with an 80 watt light bulb.
Each of the 8 street lights is usually on from 6 p.m. to 6 a.m.
It costs 32.4p per hour for each kilowatt of electricity used.
How much would be saved per week if the 8 street lights were only on from 7 p.m. to 5 a.m.?
Give your answer in pounds, correct to the nearest penny.
You must show all your working. [5 + 2 OCW]
A lamp post is vertical and stands on horizontal ground.
The angle of elevation of the top of the lamp post is 68° when measured from a point 3·3 m from the centre of the base of the lamp post.
Diagram not drawn to scale
Calculate the height of the lamp post. [3]
| Scheme | Mark | Comments |
|---|---|---|
| 2(a) Method not directly working with a stated or omitted number of hours difference | Methods may be shown in stages or be embedded Use this method if 2 separate numbers of hours are used, which may not be correct, i.e. ≠12 and ≠10, with or without indication of subtraction Penalise every additional spurious term by reducing the count of correct terms by 1* | |
| 0.324 × 8 × (10 or 12) × 7 × 80 ÷ 1000 | M3 | Allow ‘× 32.4’ for ‘× 0.324’ M2 for any 4 or 5 correct terms* M1 for any 3 correct terms* |
| 0.324 × 8 × (12 or 10) × 7 × 80 ÷ 1000 with the intention to subtract | m1 | Must be an indication of the intention to subtract, in either order FT from 5 (or 6) consistent correct terms for use of
|
| (Saving is 17.418… – 14.515…=) (£) 2.90 | A1 | CAO All working must be checked, do not award 5 marks for £2.90 from incorrect working. |
Alternative
2(a) Alternative method:
Method directly working with a stated or omitted number of hours difference
| Scheme | Mark | Comments |
|---|---|---|
| Methods may be shown in stages or be embedded Use this method if a single number of hours is used, which may not be correct, i.e. ≠2, or if the number of hours is omitted Do not allow 2 hours as a correct term from incorrect working, e.g. 13 – 11 = 2 Penalise every additional spurious term by reducing the count of correct terms by 1* | ||
| 0.324 × 8 × 2 × 7 × 80 ÷ 1000 | M4 | Allow ‘× 32.4’ for ‘× 0.324’ M3 for any 5 correct terms* M2 for any 4 correct terms* M1 for any 3 correct terms* |
| (Saving is) (£) 2.90 | A1 | CAO All working must be checked, do not award 5 marks for £2.90 from incorrect working. |
Organisation and communication
| Scheme | Mark | Comments |
|---|---|---|
| Organisation and communication Organised to include labels, e.g. Number of hours Total number of kWh Cost per day Cost per week | 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 Units to include, e.g. kW kWh £ | 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. |
| Scheme | Mark | Comments |
|---|---|---|
| Height = tan68° × 3.3 or height = \(\dfrac{\sin 68^\circ \times 3.3}{\sin(90 - 68)^\circ}\) | M2 | Or alternative correct full method, isolating height M1 for tan68° = height / 3.3 or \(\dfrac{\text{height}}{\sin 68^\circ}\) = \(\dfrac{3.3}{\sin(90 - 68)^\circ}\) or equivalent |
| 8.167… (m) or 8.17 (m) or 8.2 (m) | A1 | Allow 8(m), 8.1(m) 8.16(m) from correct working |