4MA0 Higher June 2015 Paper 3 Q10
10 The table shows some information about the five Great Lakes in North America.
| Name | Surface area (m2) | Volume of water (m3) |
|---|---|---|
| Lake Erie | \(2.57 \times 10^{10}\) | \(4.80 \times 10^{11}\) |
| Lake Huron | \(6.01 \times 10^{10}\) | \(3.52 \times 10^{12}\) |
| Lake Michigan | \(5.80 \times 10^{10}\) | \(4.87 \times 10^{12}\) |
| Lake Ontario | \(1.91 \times 10^{10}\) | \(1.64 \times 10^{12}\) |
| Lake Superior | \(8.21 \times 10^{10}\) | \(1.22 \times 10^{13}\) |
(a) Work out the total surface area of the five Great Lakes.
Give your answer in standard form. (2)
Give your answer in standard form. (2)
Loch Ness is the largest lake in Scotland.
The lake has a volume of water of \(7.45 \times 10^9\) m3
The volume of water in Lake Superior is \(k\) times the volume of water in Loch Ness.
(b) Work out the value of \(k\).
Give your answer correct to 3 significant figures. (2)
Give your answer correct to 3 significant figures. (2)
| Scheme | Marks |
|---|---|
| \(2.57 \times 10^{10} + 6.01 \times 10^{10} + 5.80 \times 10^{10} + 1.91 \times 10^{10} + 8.21 \times 10^{10}\) or 2.57 + 6.01 + 5.8 + 1.91 + 8.21 or 245 000 000 000 oe or digits 245 | M1 |
| \(2.45 \times 10^{11}\) | A1 |
| (2) |
Notes
M1: for clear intention to add all surface areas
A1: cao
| Scheme | Marks |
|---|---|
| \((1.22 \times 10^{13}) \div (7.45 \times 10^9)\) or 1637(.58…) or digits 1637(58…) | M1 |
| 1640 | A1 |
| (2) |
Notes
M1: condone missing brackets
A1: accept 1637 – 1640 (may be in standard form)