| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2016 |
| Session | March |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Coefficient zero after multiplying binomial |
| Difficulty | Moderate -0.8 This is a straightforward binomial theorem application requiring students to find specific coefficients using the standard formula, then solve a simple linear equation when one coefficient equals zero. The mechanics are routine with no conceptual challenges beyond basic binomial expansion and algebraic manipulation. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(80(x^4)\), \(-32(x^5)\) | B1B1 [2] | Fully simplified |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((-32 + 80p)(x^5) = 0\) | M1 | Attempt to multiply relevant terms & put \(= 0\) |
| \(p = 2/5\) or \(32/80\) | A1\(\checkmark\) [2] |
## Question 1:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $80(x^4)$, $-32(x^5)$ | B1B1 [2] | Fully simplified |
### Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(-32 + 80p)(x^5) = 0$ | M1 | Attempt to multiply relevant terms & put $= 0$ |
| $p = 2/5$ or $32/80$ | A1$\checkmark$ [2] | |
---1 (i) Find the coefficients of $x ^ { 4 }$ and $x ^ { 5 }$ in the expansion of $( 1 - 2 x ) ^ { 5 }$.\\
(ii) It is given that, when $( 1 + p x ) ( 1 - 2 x ) ^ { 5 }$ is expanded, there is no term in $x ^ { 5 }$. Find the value of the constant $p$.
\hfill \mbox{\textit{CAIE P1 2016 Q1 [4]}}