June 2024 Paper 2 Q16
16 Simplify \(\quad \dfrac{\sqrt{x^3}\left(\sqrt{x^3} + x^3\right)}{\sqrt{x}}\)
Give your answer in the form \(\quad x^{\frac{a}{b}} + x^c \quad\) where \(a\), \(b\) and \(c\) are integers. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(x^{\frac{5}{2}} + x^4\) | B3 | B2 \(x^{\frac{5}{2}}\ (+ \ldots)\) or \((\ldots +)\ x^4\) B1 correct expansion of numerator eg \(\sqrt{x^3} \times \sqrt{x^3} + \sqrt{x^3} \times x^3\) or \(x^3 + x^{\frac{9}{2}}\) or correct expression with fraction eliminated eg \(\sqrt{x^2}\left(\sqrt{x^3} + x^3\right)\) or \(x\left(\sqrt{x^3} + x^3\right)\) or \(\sqrt{x^3}\left(\sqrt{x^2} + x^{\frac{5}{2}}\right)\) |
Additional guidance
| B1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| B1 may be awarded after multiplication by \(\dfrac{\sqrt{x}}{\sqrt{x}}\) eg \(\dfrac{\sqrt{x^3}\left(\sqrt{x^3} + x^3\right)}{\sqrt{x}} \times \dfrac{\sqrt{x}}{\sqrt{x}} = \dfrac{\sqrt{x^4}\left(\sqrt{x^3} + x^3\right)}{x}\) \(\dfrac{\sqrt{x^7} + x^3\sqrt{x^4}}{x}\) (B1 at this stage for correct expansion of numerator) | B1 |
| Check the answer line and award B3 or B2 if possible Otherwise check the working for B2 or B1 | |
| Condone \(x^4 + x^{\frac{5}{2}}\) | B3 |
| Accept oe values for fractional powers for up to B2 | |
| Accept eg \(x^{\frac{10}{4}} + x^4\) | B3 |