Numeracy Higher November 2023 Unit 2 Q3
3. Jac is planning to visit the Empire State Building in New York.
Planners had an original budget of $60 million to construct the Empire State Building.
It actually cost $41 000 000 to construct.
Complete the following statement.
Give your answer correct to 2 decimal places. [3]
Constructing the Empire State Building cost …………… % less than the original budget.
More than 4 million people visit the Empire State Building each year.
What is 4 million written in standard form?
Circle your answer. [1]
\(4 \times 10^{-5}\) \(0{\cdot}4 \times 10^{5}\) \(4 \times 10^{5}\) \(4 \times 10^{6}\) \(4 \times 10^{7}\)
In this part of the question, you will be assessed on the quality of your organisation, communication and accuracy in writing.
The conversion rate at the exchange shop is £1 = $1.25.
The exchange shop only has $10 notes and $50 notes.
Jac has exactly £350.
He wants to exchange as close to £350 as possible for US dollars ($).
He asks for as few notes as possible.
Calculate:
- how many $10 notes and how many $50 notes Jac gets
- how much he pays for his currency.
You must show all your working. [6 + 2 OCW]
| Scheme | Marks | Comments |
|---|---|---|
| (Difference 60 million – 41 000 000 =) 19 000 000 or 19 million | B1 | May be implied in further working Allow 19 m(il) |
| (Underspend) \(\dfrac{19\,000\,000}{60\,000\,000}\) (× 100) or equivalent | M1 | FT ‘their 60 million – 41 000 000’ including if a place value error made |
| 31.67(%) | A1 | CAO (must be 2 d.p.) Answer space takes precedence |
Alternative
3(a) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Underspend) (100 -) \(\dfrac{41\,000\,000}{60\,000\,000}\) (× 100) or equivalent | M1 | Allow place value error |
| 31.67(%) | A2 | CAO (must be 2 d.p.) Answer space takes precedence A1 for 31.6(6…%), 31.7(%), 32(%) or 68.33(%) |
| Scheme | Marks | Comments |
|---|---|---|
| \(4 \times 10^{6}\) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (Change to $) 350 × 1.25 ($)437.5(0) | M1 A1 | Do not penalise slips in giving incorrect use of £ for $ |
| (Only $10 and $50 notes available so he can buy) ($)430 | A1 | FT ‘their ($)437.5(0)’ (provided not a multiple of 10) rounded down to nearest multiple of 10 Accept stated or implied as ($)7.50 can’t be converted ($)430 implies previous M1 A1, provided not from incorrect working |
| (Fewest number of notes making up $430) 8 $50 (notes) and 3 $10 (notes) | A1 | FT ‘their $430’ provided it is a multiple of 10 (and provided M1 previously awarded) Must be fewest number of notes, that may be listed Sight of correct number of notes with no incorrect working implies previous A1, unless contradicted |
| (Cost in £ to buy $430 is) 430 ÷ 1.25 or 350 – 7.5(0) ÷ 1.25 (= 350 – 6) | M1 | FT ‘their whole number multiple of $10’ ÷ 1.25 Ignore attempt at any further calculation if 430 ÷ 1.25 seen |
| (£)344 | A1 | Must be <(£)350 and depends on M1 M1 previously awarded Mark final answer If final M0 A0, then award SC1 for (£) 6 (left) or similar on FT, provided not from incorrect or inappropriate working |
Alternative
3(c) Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| £40 = $50 and £8 = $10 8 $50 notes, 3 $10 notes | M1 A3 | A2 for 8 $50 notes and sight of 350 – 8 × 40 or equivalent OR A1 for 8 $50 notes |
| (Cost to buy £350 is) 8 × 40 + 3 × 8 (£)344 | M1 A1 |
| Scheme | Marks | Comments |
|---|---|---|
| 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. |