Moderate -0.5 This is a straightforward binomial coefficient problem requiring application of the binomial theorem formula twice and solving a simple equation. It's slightly easier than average because it's purely mechanical with no conceptual challenges—students just need to recall the formula and perform basic algebra.
The coefficient of \(x^2\) in the expansion of \((1-4x)^6\) is 12 times the coefficient of \(x^2\) in the expansion of \((2+ax)^5\).
Find the value of the positive constant \(a\). [3]
Question 1:
1 | 240x2 or 80a2[x2]
| B1 | May be seen in an expansion.
2401280a2 | M1 | Their 240 equated to 12 × their 80a2 which must
contain a2.
0.5 | A1 | OE
Condone ± 0.5
3
Question | Answer | Marks | Guidance
The coefficient of $x^2$ in the expansion of $(1-4x)^6$ is 12 times the coefficient of $x^2$ in the expansion of $(2+ax)^5$.
Find the value of the positive constant $a$. [3]
\hfill \mbox{\textit{CAIE P1 2024 Q1 [3]}}