Foundation November 2018 Paper 1 Q18
18.
(a)
(i) Write down the value of \(\sqrt[3]{8}\). [1]
(ii) Simplify \(\sqrt{5} \times \sqrt{5}\). [1]
(b)
(i) Work out the value of \((2 \times 10^4) \times (4 \times 10^3)\).
Give your answer in standard form. [2]
Give your answer in standard form. [2]
(ii)
Light travels at \(3 \times 10^5\) kilometres per second.
The circumference of the Earth at the equator is 40 000 km.
Show that, in theory, a beam of light could circle the Earth at the equator more than 7 times in 1 second. [2]
| Scheme | Marks | Comments |
|---|---|---|
| (i) 2 | B1 | |
| (ii) 5 | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| (i) \(8 \times 10^7\) | B2 | B1 for \(\ldots \times 10^7\) or for 80 000 000 |
| (ii) (\(3 \times 10^5\) =) 300 000 or (40 000 = ) \(4 \times 10^4\) | B1 | |
| \(\frac{3 \times 10^5}{4 \times 10^4}\) or \(\frac{300\,000}{40\,000}\) = 7.5 (so more than 7) | B1 | |
| (6) |
Alternative
Alternative method 1
| Scheme | Marks | Comments |
|---|---|---|
| 7 × 40000 = 280 000 | B1 | |
| (\(3 \times 10^5\) =) 300 000 (so more than 7) | B1 |
Alternative method 2
| Scheme | Marks | Comments |
|---|---|---|
| \(\frac{7 \times 40\,000}{300\,000}\) | M1 | |
| \(\frac{280\,000}{300\,000}\) (which is less than 1) | A1 |