Moderate -0.5 This is a straightforward binomial expansion question requiring students to identify the correct term, apply the binomial coefficient formula, set up an equation with the given coefficient value, and solve a simple quadratic. While it involves multiple steps, each step is routine and the question follows a standard textbook pattern with no novel insight required.
1 The coefficient of \(x ^ { 3 }\) in the expansion of \(\left( p + \frac { 1 } { p } x \right) ^ { 4 }\) is 144 .
Find the possible values of the constant \(p\).
OE; correct with correct power of \(p\) and only one \(p\) term
\(p = \pm\frac{1}{6}\)
B1 B1
OE \(\pm\frac{2}{12}\) etc. Allow \(\pm 0.167\) for B1 B1; SC B1 for \(\pm\sqrt{\frac{1}{36}}\) B1 only
4
## Question 1:
| Answer | Marks | Guidance |
|--------|-------|----------|
| $4C1 \times p \times \frac{1}{p^3}x^3$ | **B1** | OE; soi can be seen in an expansion |
| $\frac{4}{p^2} = 144$ | **B1** | OE; correct with correct power of $p$ and only one $p$ term |
| $p = \pm\frac{1}{6}$ | **B1 B1** | OE $\pm\frac{2}{12}$ etc. Allow $\pm 0.167$ for B1 B1; **SC B1** for $\pm\sqrt{\frac{1}{36}}$ B1 only |
| | **4** | |
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1 The coefficient of $x ^ { 3 }$ in the expansion of $\left( p + \frac { 1 } { p } x \right) ^ { 4 }$ is 144 .\\
Find the possible values of the constant $p$.\\
\hfill \mbox{\textit{CAIE P1 2022 Q1 [4]}}