June 2019 Paper 2 Q5
5
(a) Write \(\quad \sqrt[4]{a \times a^{-9}} \quad\) as an integer power of \(a\). [2 marks]
(b) Simplify fully \(\quad \dfrac{(4cd^2)^3}{2cd^4}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(a^{-2}\) | B2 | B1 applies an index law or changes fourth root to fractional or decimal power in a correct expression eg \(\sqrt[4]{a^{-8}}\) or \((a^{-8})^{\frac{1}{4}}\) or \((a^8)^{-\frac{1}{4}}\) or \(a^{-\frac{8}{4}}\) or \(\dfrac{1}{a^{\frac{8}{4}}}\) or \(\dfrac{1}{a^2}\) or \(a^{\frac{1}{4}} \times a^{-\frac{9}{4}}\) or \(a^{\frac{1}{4}} \times \dfrac{1}{a^{\frac{9}{4}}}\) or \(\left(\dfrac{1}{a^8}\right)^{\frac{1}{4}}\) or \(\sqrt[4]{\dfrac{1}{a^8}}\) or \(\sqrt[4]{a \times \dfrac{1}{a^9}}\) or \((a \times a^{-9})^{\frac{1}{4}}\) or \(\left(a \times \dfrac{1}{a^9}\right)^{\frac{1}{4}}\) |
Additional guidance
| \(a^{\frac{-8}{4}}\) or \(a^{\frac{8}{-4}}\) | B1 |
| \(a^{-2}\) in working with \(-2\) on answer line | B1 |
| \(a^{-2}\) in working with \(\dfrac{1}{a^2}\) on answer line | B1 |
| B1 response followed by further work is still awarded B1 | |
| Allow 0.25 for \(\dfrac{1}{4}\) etc | |
| Allow recovery of missing brackets |
| Answer | Mark | Comments |
|---|---|---|
| \(32c^2d^2\) or \(32(cd)^2\) | B3 | B2 (numerator \(=\)) \(64c^3d^6\) or single term answer with two of 32, \(c^2\) and \(d^2\) (not in a denominator) B1 single term answer with one of 32, \(c^2\) and \(d^2\) (not in a denominator) SC2 factorised correct expression eg \(16cd(2cd)\) |
Additional guidance
| \(2c^2d^2\) or \(32c^2d\) or \(32c^2\) or \(\dfrac{32d^2}{c^3}\) or \(\dfrac{c^2d^2}{32}\) or \(64(cd)^2\) etc | B2 |
| \(32c^3d\) or \(c^2\) or \(\dfrac{d^2}{c}\) or \(\dfrac{c^2d}{32}\) or \(\dfrac{32}{c^2}\) etc | B1 |
| \(\dfrac{32c^2d^2}{1}\) or \(\dfrac{32(cd)^2}{1}\) | B2 |
| Allow denominator of 1 in a B2 or B1 answer eg \(\dfrac{32c^2d}{1}\) | B2 |
| Multiplication signs in a correct expression eg \(32 \times c^2 \times d^2\) | B2 |
| Allow multiplication signs in a B2, SC2 or B1 answer eg \(32 \times c^3 \times d\) | B1 |
| Do not accept \(2^5\) for 32 eg \(2^5c^2d\) | B1 |
| If answer line scores B1 or B0 check working lines for possible response for up to 2 marks | |
| \(32c^2d^2\) in working with different answer on answer line | B2 |