CAIE IGCSE Additional Math Combinatorics Series and Vectors Questions

n=7 soi
$5\times\frac{7\times6}{2}\times2^5\times a^2=30240$ oe
$5\times7\times2^6\times a=b^2$a=3 only, nfww
$b=\pm\sqrt{6720}$ oe, isw, nfww
If first B1 only scored then SC1 for $a=3\sqrt5$ or $\sqrt{45}$ or 6.71 or 6.708... only, and SC1 for $b=\pm\sqrt{1344\sqrt5}$ or $\pm54.8...$.

$$\frac{(n-4)(n+1)!}{(n-4)!5!}=\frac{(n+2)!}{(n-5)!7!}$$

leading to
$$\times 6=n+2$$ B1 for $7 \times 6$ or 42 seen as a result of simplification of the numerical factorials

B1 for n+2 seen as a result of simplification of the algebraic factorials
n=40 B1

$$2^{10}+10\times2^9\times\frac{3}{x^2}+45\times2^8\times\left(\frac{3}{x^2}\right)^2\ \text{oe, soi}$$
and
$$1-8x^2+16x^4\ \text{soi}$$
B2 for the first expansion;
B1 for two correct terms in the first expansion;
B1 for $1-8x^2+16x^4$.
$2^{10}+$ their $15360\times$ their (-8)+ their $103680\times$ their 16
M2 FT expansions;
M1 FT for any two correct terms in this sum.
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