| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Product with reciprocal term binomial |
| Difficulty | Moderate -0.3 This is a straightforward binomial expansion question requiring standard application of the binomial theorem with a two-term expression containing x and 1/x. Part (i) is routine calculation, and part (ii) requires identifying which terms from the product yield x, which is a common exam technique but requires minimal problem-solving beyond pattern recognition. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| \(32x^5 - 240x^3 + 720x\) | \(3 \times\) B1 [3] | co. SC B2 for other 3 terms (i.e. ascending) |
| Answer | Marks | Guidance |
|---|---|---|
| Coeff of \(x\): \((1 \times 720) + (2 \times -240) \rightarrow 240\) | M1, A1\(\sqrt{}\) [2] | Looks at exactly 2 terms. co from his answer to (i) |
## Question 2:
**Part (i):**
$32x^5 - 240x^3 + 720x$ | $3 \times$ B1 [3] | co. SC B2 for other 3 terms (i.e. ascending)
**Part (ii):**
$\left(1 + \frac{2}{x^2}\right)(32x^5 - 240x^3 + 720x)$
Coeff of $x$: $(1 \times 720) + (2 \times -240) \rightarrow 240$ | M1, A1$\sqrt{}$ [2] | Looks at exactly 2 terms. co from his answer to (i)
---2 (i) Find the first 3 terms in the expansion of $\left( 2 x - \frac { 3 } { x } \right) ^ { 5 }$ in descending powers of $x$.\\
(ii) Hence find the coefficient of $x$ in the expansion of $\left( 1 + \frac { 2 } { x ^ { 2 } } \right) \left( 2 x - \frac { 3 } { x } \right) ^ { 5 }$.
\hfill \mbox{\textit{CAIE P1 2010 Q2 [5]}}