| Date | May 2017 | Marks available | 6 | Reference code | 17M.2.hl.TZ1.3 |
| Level | HL only | Paper | 2 | Time zone | TZ1 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
The coefficient of \({x^2}\) in the expansion of \({\left( {\frac{1}{x} + 5x} \right)^8}\) is equal to the coefficient of \({x^4}\) in the expansion of \({\left( {a + 5x} \right)^7},{\text{ }}a \in \mathbb{R}\). Find the value of \(a\).
Markscheme
METHOD 1
\(^8{C_r}{\left( {\frac{1}{x}} \right)^{8 - r}}{(5x)^r} = {}^8Cr{\left( 5 \right)^r}{x^{2r - 8}}\) (M1)
\(r = 5\) (A1)
\(^8{C_5} \times {5^5}{ = ^7}{C_4}{a^3} \times {5^4}\) M1A1
\(56 \times 5 = 35{a^3}\)
\({a^3} = 8\) (A1)
\(a = 2\) A1
METHOD 2
attempt to expand both binomials M1
\(175000{x^2}\) A1
\(21875{a^3}{x^4}\) A1
\(175000 = 21875{a^3}\) M1
\({a^3} = 8\) (A1)
\(a = 2\) A1
[6 marks]
Examiners report
[N/A]
