| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Binomial with reciprocal terms coefficient |
| Difficulty | Moderate -0.8 This is a straightforward binomial expansion question requiring routine application of the binomial theorem formula. Part (i) involves calculating three more terms using the given pattern, and part (ii) is a simple multiplication to find one coefficient. The question is more mechanical than conceptual, with no problem-solving insight required, making it easier than average. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks |
|---|---|
| 2(i) | −5 5 1 5 1 |
| Answer | Marks | Guidance |
|---|---|---|
| x 8x3 32x5 8 32 | B1B1B1 | B1 for each correct term |
| Answer | Marks | Guidance |
|---|---|---|
| 2(ii) | 1×20+4×their ( −5 ) = 0 | M1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 2:
--- 2(i) ---
2(i) | −5 5 1 5 1
+ − (or −5x−1+ x−3 − x−5)
x 8x3 32x5 8 32 | B1B1B1 | B1 for each correct term
+5 +1
SCB1 for both &
x 32x5
3
--- 2(ii) ---
2(ii) | 1×20+4×their ( −5 ) = 0 | M1A1 | Must be from exactly 2 terms
SCB1 for 20 + 20 = 40
2
Question | Answer | Marks | Guidance\begin{enumerate}[label=(\roman*)]
\item In the binomial expansion of $\left(2x - \frac{1}{2x}\right)^5$, the first three terms are $32x^5 - 40x^3 + 20x$. Find the remaining three terms of the expansion. [3]
\item Hence find the coefficient of $x$ in the expansion of $(1 + 4x^2)\left(2x - \frac{1}{2x}\right)^5$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2019 Q2 [5]}}