Higher November 2020 Paper 1 Q14
14.
(a) Simplify \(\dfrac{x^2\times x^7}{x^3}\). [2]
(b)
(i) Find the positive value of \(16^{\frac{1}{4}}\). [1]
(ii) Find the value of \(27^{\frac{4}{3}}\). [2]
(c) Estimate the value of \(\left(3{\cdot}9\times10^6\right)^3\).
Give your answer in standard form. [3]
Give your answer in standard form. [3]
(d) Write \(\dfrac{42}{\sqrt{6}}\) in the form \(a\sqrt{6}\) where \(a\) is an integer. [2]
| Scheme | Marks | Comments |
|---|---|---|
| \(x^6\) | B2 | B1 for sight of \(\dfrac{x^9}{x^3}\) or \(x^{2+7-3}\) attempted, may be in stages |
| Scheme | Marks | Comments |
|---|---|---|
| (i) 2 | B1 | Not from wrong working |
| (ii) 81 | B2 | B1 for sight of \(3^4\) oe or \(\left(\sqrt[3]{27}\right)^4\) or \(\sqrt[3]{\left(27^4\right)}\) |
| Scheme | Marks | Comments |
|---|---|---|
| \(4^3\times10^{6\times3}\) | M1 | Allow dot for multiplication Allow for \(4\,000\,000^3\) |
| \(64\times10^{18}\) | A1 | implies M1; allow for 64 000 000 000 000 000 000 |
| \(6.4\times10^{19}\) | B1 | FT ‘their \(64\times10^{18}\)’ converted to standard form, provided of equivalent difficulty |
| Scheme | Marks | Comments |
|---|---|---|
| \(7\sqrt{6}\) | B2 | B1 for \(\dfrac{42}{\sqrt{6}}\times\dfrac{\sqrt{6}}{\sqrt{6}}\) oe seen |
| (10) |