| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Binomial times linear coefficient |
| Difficulty | Moderate -0.8 This is a straightforward binomial expansion question requiring direct application of the binomial theorem formula to find specific coefficients. Part (i) is routine calculation, and part (ii) adds one simple multiplication step. The question involves no problem-solving or insight beyond applying a standard formula, making it easier than average but not trivial since it requires careful arithmetic with signs and coefficients. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks |
|---|---|
| (ii) | (2−x)6 |
| Answer | Marks |
|---|---|
| → 720 – 160 = 560 | B1 |
| Answer | Marks |
|---|---|
| [2] | co |
Question 3:
--- 3 (i)
(ii) ---
3 (i)
(ii) | (2−x)6
Coeff of x² is 240
Coeff of x³ is − 20 × 8 = −160
(3x+1)(2−x)6
Product needs exactly 2 terms
→ 720 – 160 = 560 | B1
B2,1
[3]
M1
A1
[2] | co
B1 for +160
3 × their 240 + their -160
for candidate’s answers.\begin{enumerate}[label=(\roman*)]
\item Find the coefficients of $x^2$ and $x^3$ in the expansion of $(2 - x)^6$. [3]
\item Find the coefficient of $x^3$ in the expansion of $(3x + 1)(2 - x)^6$. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE P1 2015 Q3 [5]}}