| Exam Board | AQA |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2020 |
| Session | June |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Generalised Binomial Theorem |
| Type | State validity only |
| Difficulty | Easy -1.2 This is a straightforward recall question about the validity condition for binomial expansion. Students need only remember that |x/9| < 1 for the expansion of (9+2x)^(1/2) = 9^(1/2)(1+2x/9)^(1/2), giving |x| < 9/2. Part (b) is trivial (a=3). No problem-solving or calculation required, just pattern recognition. |
| Spec | 1.04c Extend binomial expansion: rational n, |x|<11.04d Binomial expansion validity: convergence conditions |
| Answer | Marks | Guidance |
|---|---|---|
| \(8\) | \(3\) | \(8 > 3\) |
| \(1\) | \(1.9459\) |
Question 1:
$8$ | $3$ | $8 > 3$
$1$ | $1.9459$
M1: Award for correct comparison showing $8 > 3$
A1: Award for correct numerical value $1.9459$1 The first three terms, in ascending powers of $x$, of the binomial expansion of $( 9 + 2 x ) ^ { \frac { 1 } { 2 } }$ are given by
$$( 9 + 2 x ) ^ { \frac { 1 } { 2 } } \approx a + \frac { x } { 3 } - \frac { x ^ { 2 } } { 54 }$$
where $a$ is a constant.
1
\begin{enumerate}[label=(\alph*)]
\item State the range of values of $x$ for which this expansion is valid.\\
Circle your answer.\\
$| x | < \frac { 2 } { 9 }$\\
$| x | < \frac { 2 } { 3 }$\\
$| x | < 1$\\
$| x | < \frac { 9 } { 2 }$
1
\item Find the value of $a$.\\
Circle your answer.\\[0pt]
[1 mark]\\
1239
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 1 2020 Q1 [2]}}