Moderate -0.3 This is a straightforward application of the binomial theorem requiring students to set up the general term, identify which term contains x^8, equate the coefficient to the given value, and solve for k. While it involves some algebraic manipulation and calculation, it's a standard textbook-style question with a clear method and no conceptual challenges beyond direct application of the formula.
7 The coefficient of \(x ^ { 8 }\) in the expansion of \(( 2 x + k ) ^ { 12 }\), where \(k\) is a positive integer, is 79200000.
Determine the value of \(k\).
allow M1 for \(495 \times 2 \times k^4 = 79\,200\,000\) oe; "\(= 79\,200\,000\)" may be implied by \(k=5\)
\(k = 5\) cao isw
A1 (3.2a)
not from wrong working; but allow recovery from \(x^8\) on one side of equation only; allow SC2 for \(k=5\) unsupported
## Question 7:
$(2x)^8$ soi | M1 (3.1a) | allow recovery from bracket error; may be implied by award of second M1
$^{12}C_8$ or $^{12}C_4$ or $495$ seen | B1 (1.1) |
$495 \times 256 \times k^4\ [x^8] = 79\,200\,000\ [x^8]$ oe | M1 (1.1) | allow M1 for $495 \times 2 \times k^4 = 79\,200\,000$ oe; "$= 79\,200\,000$" may be implied by $k=5$
$k = 5$ cao isw | A1 (3.2a) | not from wrong working; but allow recovery from $x^8$ on one side of equation only; allow SC2 for $k=5$ unsupported
7 The coefficient of $x ^ { 8 }$ in the expansion of $( 2 x + k ) ^ { 12 }$, where $k$ is a positive integer, is 79200000.\\
Determine the value of $k$.
\hfill \mbox{\textit{OCR MEI Paper 2 2023 Q7 [4]}}