| Exam Board | Edexcel |
|---|---|
| Module | PMT Mocks (PMT Mocks) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Ratio of coefficients condition |
| Difficulty | Standard +0.3 This is a straightforward binomial theorem problem requiring students to write out two coefficient expressions, set up an equation from the given ratio, and solve for k. While it involves multiple steps (finding two coefficients, forming an equation, simplifying), each step uses standard techniques with no novel insight required. Slightly easier than average due to the mechanical nature of the solution. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| Find the value of \(k\) in binomial expansion of \((2 - kx)^{10}\) | (3) | M1 For attempt at correct coefficient of \(x^4\) and \(x^6\); dM1 For \(^{10}C_4 2^6(-k)^4 = 256 \times ^{10}C_6 2^4(-k)^6\) and attempt to find \(k\); A1 \(k = \frac{1}{8}\) and no other values |
Find the value of $k$ in binomial expansion of $(2 - kx)^{10}$ | (3) | M1 For attempt at correct coefficient of $x^4$ and $x^6$; dM1 For $^{10}C_4 2^6(-k)^4 = 256 \times ^{10}C_6 2^4(-k)^6$ and attempt to find $k$; A1 $k = \frac{1}{8}$ and no other values
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\item In the binomial expansion of $( 2 - k x ) ^ { 10 }$ where $k$ is a non-zero positive constant.
\end{enumerate}
The coefficient of $x ^ { 4 }$ is 256 times the coefficient of $x ^ { 6 }$.\\
Find the value of $k$.\\
\hfill \mbox{\textit{Edexcel PMT Mocks Q4 [3]}}