$\frac{x - 3}{x + 2}$ or $1 - \frac{5}{x + 2}$ as final answer www | 3 | B2 for correct answer seen and then spoilt; M1 for $(x + 3)(x - 3)$ and M1 for $(x + 2)(x + 3)$
| [3] |

# Question 5(i):

30 | 3 | M1 for $(\sqrt{6})^6 = 6\sqrt{6}$ soi and M1 for $\sqrt{24} = 2\sqrt{6}$ soi or allow SC2 for final answer of $5(\sqrt{6})^2$ or $5\sqrt{36}$ or $10\sqrt{9}$ etc | M0 for $6000\sqrt{6}$ ie cubing 10 as well; for those using indices: M1 for both $10 \times 6^{1/2}$ and $2 \times 6^{1/2}$ oe then M1 for $5 \times 6$ oe; award SC2 for similar correct answer with no denominator
| [3] |

# Question 5(ii):

$\frac{8}{11}$ | 2 | M1 for common denominator $(4 + \sqrt{5})(4 - \sqrt{5})$ soi - may be in separate fractions or for a final answer with denominator 11, even if worked with only one fraction | condone lack of brackets
| [2] |

# Question 6(i):

10 cao | [1] |

# Question 6(ii):

$-720[x^3]$ | 4 | B3 for $720[x^3]$ or for $10 \times 9 \times -8[x^3]$ or M2 for $10 \times 3^2 \times (-2)^r$ oe or ft from (i) or M1 for two of these three elements correct or ft; condone $x$ still included | condone $-720 x$ etc; allow equivalent marks for the $x^3$ term as part of a longer expansion eg M2 for $3^r\ldots 10 \times \left(\frac{-2}{3}\right)^r\ldots$ or M1 for $10 \times \left(\frac{-2}{3}\right)^r$ etc
| [4] |