| Exam Board | SPS |
|---|---|
| Module | SPS SM (SPS SM) |
| Year | 2020 |
| Session | June |
| Marks | 4 |
| Topic | Binomial Theorem (positive integer n) |
| Type | Expansion up to x^3 term |
| Difficulty | Easy -1.2 This is a straightforward application of the binomial theorem with a positive integer exponent. Students need only substitute into the formula (1+x)^n = 1 + nx + n(n-1)x²/2! + ... with x replaced by (3/4)x, requiring basic arithmetic and coefficient simplification but no problem-solving or conceptual insight. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
Use the binomial expansion to find, in ascending powers of $x$, the first four terms in the expansion of
$$\left(1 + \frac{3}{4}x\right)^6$$
simplifying each term. [4]
\hfill \mbox{\textit{SPS SPS SM 2020 Q5 [4]}}