Numeracy Intermediate June 2024 Unit 2 Q9
9.
A volcano is an opening in the Earth’s crust, through which molten lava, hot ash and gases escape into the air.
An estimated 500 000 000 people live near active volcanoes.
What is 500 000 000 written in standard form? [1]
The teragram is a unit of mass.
1 teragram = \(10^9\) kg
Last year, a volcano released a total of 140 teragrams of carbon dioxide in 300 days.
Calculate the average number of kilograms of carbon dioxide that were released by this volcano per hour.
Give your answer correct to 3 significant figures.
You must show all your working. [5]
The planet Venus orbits the Sun.
Its orbit can be considered to be circular.
The distance between Venus and the Sun is \(1.08 \times 10^8\) km.
Venus orbits the Sun once every 224.7 days.
Calculate the distance Venus travels in 1 day.
Give your answer in standard form. [4]
The surface area of Venus is 460 234 320 km\(^{2}\).
The surface of Venus is wrinkled-volcanic, smooth-volcanic or non-volcanic.
The areas of these three different types of surface are in the ratio 7 : 1 : 2.
| Wrinkled-volcanic : Smooth-volcanic : Non-volcanic = 7 : 1 : 2 |
Calculate the total surface area of Venus that is volcanic.
You must show all your working. [3]
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(5 \times 10^8\) or \(5.0 \times 10^8\) | B1 | |
| (ii) 140 | Method marks can be awarded in any order but the operation must be unique (not contradicted or repeated in the working) | |
| × \(10^9\) | M1 | |
| ÷ 300 | M1 | |
| ÷ 24 | M1 | ‘÷ 7200’ implies final M1 M1 Award M3 for sight of \(\dfrac{140 \times 10^9}{300 \times 24}\) or \(\dfrac{1.4 \times 10^{11}}{7.2 \times 10^3}\) or equivalent |
| 19 400 000 (kg per hour) | A2 | ISW, accept 19.4 million or \(1.94 \times 10^7\) or equivalent A1 for sight of 19 444 444(.44…) or for incorrect rounding or truncation of this answer FT, for A1, from M1 M0 M1 or M1 M1 M0, including if an incorrect 3rd term is included, for correct evaluation of ‘their calculation’ and expressing ‘their final answer’ correct to 3 significant figures provided rounding is required, e.g.
140 × \(10^9\) ÷ 24 × 300 = 1 750 000 000 000, no rounding required, hence A0) FT, for A1, from M0 M1 M1 for an answer of 194 000, 1 940 000, 194 000 000, or 1 940 000 000, provided it is from a correct evaluation of ‘their calculation’ If no marks, award SC1 for equivalent operations used without 140, i.e. \(\dfrac{10^9}{300 \times 24}\) or \(10^9\) ÷ 300 ÷ 24 or equivalent |
| Scheme | Marks | Comments |
|---|---|---|
| (i) (Venus orbit) 2 × π × \(1.08 \times 10^8\) or 678 000 000 to 680 000 000 or \(6.78 \times 10^8\) to \(6.8 \times 10^8\) | M1 | |
| (To find distance travelled in one day) ÷ 224.7 | M1 | FT ‘their derived orbit’ provided π is involved in ‘their calculation of Venus orbit’ |
| (Distance in one day) 3.(0....) × \(10^6\) | A2 | CAO A1 for any one of the following answers:
4.8(0…) × \(10^5\) (from \(1.08 \times 10^8\) ÷ 224.7) or 9.6(1…) × \(10^5\) (from 2 × \(1.08 \times 10^8\) ÷ 224.7) |
| (ii) 368 187 456 (km\(^{2}\)) | B3 | ISW Allow appropriate rounding from correct working, such as 368 187 500 or 368 000 000 or 370 000 000 B2 for any one of the following:
|