Higher November 2021 Paper 2 Q9
9 A rainwater tank contains \(2.4 \times 10^7\) raindrops.
The rainwater tank also contains \(1.75 \times 10^6\) bacteria.
(a) Work out the number of bacteria per raindrop in the tank.
Give your answer in standard form correct to 2 significant figures. (3)
Give your answer in standard form correct to 2 significant figures. (3)
A drop of rainwater contains \(5.01 \times 10^{21}\) atoms.
In a drop of rainwater the number of atoms is 3 times the number of molecules.
(b) Work out the number of molecules in the rainwater tank.
Give your answer in standard form correct to one significant figure. (2)
Give your answer in standard form correct to one significant figure. (2)
| Scheme | Marks |
|---|---|
\(1.75 \times 10^6 \div 2.4 \times 10^7\) or 1 750 000 ÷ 24 000 000 oe eg \(\dfrac{1.75}{24}\) | M1 |
0.0729(16…) or 0.072 or 0.073 or for \(\dfrac{7}{96}\) or 7.29(16…)% or 7.2% or 7.3% | A1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(7.3 \times 10^{-2}\) | A1 |
| (3) |
Notes
A1: accept \(7.3 \times 10^{-2}\) or better \((7.29(16\ldots) \times 10^{-2})\)
| Scheme | Marks |
|---|---|
| \(2.4 \times 10^7 \times 5.01 \times 10^{21} \div 3\) oe | M1 |
| Correct answer scores full marks (unless from obvious incorrect working) Answer: \(4 \times 10^{28}\) | A1 |
| (2) | |
| (5 marks) |
Notes
A1: accept \(4 \times 10^{28}\), \(4.0 \times 10^{28}\), \(4.01 \times 10^{28}\), \(4.008 \times 10^{28}\)