June 2017 Paper 2 Q13
13 Simplify fully \(\qquad \dfrac{8a}{3a + 6} \times \dfrac{5a + 10}{3a^2} \div \dfrac{4}{15a^3}\) [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| Single correct fraction with terms processed | M1 | eg1 \(\dfrac{600a^5 + 1200a^4}{36a^3 + 72a^2}\) eg2 \(\dfrac{50a^3 + 100a^2}{3a + 6}\) Only bracket allowed is \((a + 2)\) eg \(\dfrac{50a^4(a + 2)}{3a^3 + 6a^2}\) (scores M2) |
| Factorises correctly using \((a + 2)\) | M1 | Only needs to be seen once eg1 \(\dfrac{8a}{3a + 6} \times \dfrac{5(a + 2)}{3a^2} \div \dfrac{4}{15a^3}\) eg2 \(\dfrac{8a}{3(a + 2)} \times \dfrac{5a + 10}{3a^2} \times \dfrac{15a^3}{4}\) Award M2 for fully correct unprocessed expression with full cancelling seen eg \(\dfrac{{}^{2}\cancel{8}a}{3\cancel{(a + 2)}} \times \dfrac{5\cancel{(a + 2)}}{\cancel{3}\,\cancel{a^2}} \times \dfrac{{}^{5}\cancel{15}a^{\cancel{3}\,1}}{\cancel{4}}\) or \(\dfrac{2a}{3} \times 5 \times 5a\) oe |
| \(\dfrac{50a^2}{3}\) or \(16\dfrac{2}{3}a^2\) or \(16.\dot{6}a^2\) | A1 |
Additional guidance
| \(\dfrac{50 \times a \times a}{3}\) | M2A0 |
| A correct single fraction with \((a + 2)\) cancelled will be M2 eg1 \(\dfrac{250a^2}{15} \qquad\) eg2 \(\dfrac{50a^4}{3a^2}\) | M2A0 |
| \(\dfrac{8a}{3} \times \dfrac{5(a + 2)}{3a^2} \times \dfrac{15a^3}{4}\) | M0M1A0 |
| \(3a + 6 = 3(a + 2)\) with no other valid working | M0M1A0 |
| Brackets other than \((a + 2)\) may be seen \(\quad \dfrac{10a^2(5a + 10)}{3a + 6}\) | M0M0 |
| Correct answer followed by incorrect further work | M2A0 |
| Allow one miscopy for up to M2A0 |