| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Single coefficient given directly |
| Difficulty | Moderate -0.8 This is a straightforward application of the binomial theorem requiring only recall of the formula and basic algebraic manipulation. Part (i) involves a simple equation to solve for k, part (ii) is verification using the same formula, and part (iii) requires multiplying two polynomials—all routine C2-level techniques with no problem-solving insight needed. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
4. The coefficient of $x ^ { 2 }$ in the binomial expansion of $( 1 + k x ) ^ { 7 }$, where $k$ is a positive constant, is 525.\\
(i) Find the value of $k$.
Using this value of $k$,\\
(ii) show that the coefficient of $x ^ { 3 }$ in the expansion is 4375 ,\\
(iii) find the first three terms in the expansion in ascending powers of $x$ of
$$( 2 - x ) ( 1 + k x ) ^ { 7 }$$
\hfill \mbox{\textit{OCR C2 Q4 [8]}}