| Exam Board | CAIE |
|---|---|
| Module | P1 (Pure Mathematics 1) |
| Year | 2004 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Binomial times linear coefficient |
| Difficulty | Moderate -0.8 Part (i) is a direct application of the binomial theorem requiring only substitution into the formula. Part (ii) adds one extra step of multiplying by (1-3x) and collecting terms, but remains a routine textbook exercise with no problem-solving required. Both parts are more straightforward than average A-level questions. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks |
|---|---|
| B1 B1 B1 [3] | B1 for 6C3; B1 for \(2^3\); B1 for 160 |
| Answer | Marks |
|---|---|
| B1 M1 A1 [3] | B1 for 60 (could be given in (i)); Needs to consider 2 terms; coefficient |
**(i)** Coeff of $x^3 = 6C3 \times 2^3 = 160$
| B1 B1 B1 [3] | B1 for 6C3; B1 for $2^3$; B1 for 160 |
**(ii)** Term in $x^2 = 6C2 \times 2^2 = 60$ reqd coeff = $1 \times (i) - 3 \times 60$ → $-20$
| B1 M1 A1 [3] | B1 for 60 (could be given in (i)); Needs to consider 2 terms; coefficient |
---4 Find the coefficient of $x ^ { 3 }$ in the expansion of\\
(i) $( 1 + 2 x ) ^ { 6 }$,\\
(ii) $( 1 - 3 x ) ( 1 + 2 x ) ^ { 6 }$.
\hfill \mbox{\textit{CAIE P1 2004 Q4 [6]}}