Numeracy Intermediate June 2017 Unit 1 Q12
12.
(a) A standard piece of A4 paper is usually 0·08 mm thick.
What is 0·08 mm written in metres in standard form?
Circle your answer. [1]
What is 0·08 mm written in metres in standard form?
Circle your answer. [1]
\(8 \times 10^{4}\) \(8 \times 10^{-4}\) \(8 \times 10^{-3}\) \(8 \times 10^{3}\) \(8 \times 10^{-5}\)
(b) A piece of card is 1 mm thick.
A stack of these pieces of card is \(3 \times 10^{-2}\) metres high.
A stack of these pieces of card is \(3 \times 10^{-2}\) metres high.
(i) Calculate how many pieces of card there are in the stack. [2]
(ii) What assumption have you made in answering (b)(i)? [1]
(c) In 2012 it was recorded that
- the total mass of the paper used for printing newspapers, in the world, was \(2{\cdot}88 \times 10^{7}\) tonnes,
- the world population was approximately \(7{\cdot}2 \times 10^{9}\) people.
Use this information to calculate the mass of paper per person used to print newspapers in 2012.
Give your answer in kg per person. [4]
Mass of paper: …………… kg per person
| Scheme | Marks | Comments |
|---|---|---|
| 8 × 10-5 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 30 (pieces of card) | B2 | If working is shown, it needs to be correct for the award of B2 Do not accept final answer of 30mm for B2 B1 for: 3 × 10-2 written as 0.03 (metres) or 3 cm or (0.03m =) 30mm OR for a calculation that could lead to a correct response, e.g. 3 × 10-2 ÷ 0.001 or (3 × 10-2) ÷ (1×10-3) or 3 × 10-2 ×1000 (Watch for compensating errors such as 3 × 10-2 = 0.003, 0.003 × 1000 = 30, this is awarded B1 for intention of 3 × 10-2 ×1000) |
| (ii) Assumption, e.g. ‘no gaps between pieces of card’, ‘all pieces of card completely touch’, ‘all pieces of card are (exactly) 1 mm thick’ | E1 | Allow e.g. ‘the thickness of each piece of card is the same’, ‘none of them are folded’ |
| Scheme | Marks | Comments |
|---|---|---|
| Use of 1 tonne = 1000 kg | B1 | |
| 1000 × 2.88 × 107 ÷ (7.2 × 109) or 1000 × 28 800 000 ÷ 7 200 000 000 or equivalent | M2 | For M2 any calculations used by the candidate (which may be seen in stages) need to be correct, unless replaced with a correct calculation, perhaps e.g. reverting back to correct standard form FT ‘their 1000’, provided a power of 10 and ≠ 1 M1 for (2.88 × 107 (tonnes)) ÷ (7.2 × 109), or 28 800 000 ÷ 7 200 000 000, including no attempt to change tonnes to kg or possible place value errors in converting from standard form, this could be implied within working |
| 4 (kg per person) | A1 | CAO |