| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Single binomial expansion |
| Difficulty | Moderate -0.8 Part (a) is a straightforward binomial expansion requiring direct application of the binomial theorem to find coefficients—pure recall with minimal calculation. Part (b) requires identifying which term gives x^0, involving slightly more thought but still a standard textbook exercise. The 5 total marks reflect routine application rather than problem-solving or insight. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n1.04c Extend binomial expansion: rational n, |x|<1 |
| Answer | Marks |
|---|---|
| 4(a) | Express at least one term |
| Answer | Marks | Guidance |
|---|---|---|
| Condone sign error for –3 | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| may be unsimplified | 1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| show the required result | 2.1 | R1 |
| Subtotal | 3 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 4(b) | Deduces the constant term |
| Answer | Marks | Guidance |
|---|---|---|
| PI by (…x)5 (…x)-5 | 2.2a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| Obtains –1959552 | 1.1b | A1 |
| Subtotal | 2 | |
| Question Total | 5 | |
| Q | Marking instructions | AO |
Question 4:
--- 4(a) ---
4(a) | Express at least one term
correctly using binomial
expansion
PI by correct value of p or q or
expression for x8 and x9
Condone sign error for –3 | 1.1a | M1 | (2x)10+10C (2x)9(−3)+10C (2x)8(−3)2
1 2
1024x10 −15360x9 +103680x8
Obtains correct value of p or q
PI in the expression
may be unsimplified | 1.1a | M1
Completes argument with
correct values of p and q to
show the required result | 2.1 | R1
Subtotal | 3
Q | Marking instructions | AO | Marks | Typical solution
--- 4(b) ---
4(b) | Deduces the constant term
5
3
comes from ( 2x )5 ±
x
PI by (…x)5 (…x)-5 | 2.2a | M1 | 10C ×25×(−3)5 =−1959552
5
Obtains –1959552 | 1.1b | A1
Subtotal | 2
Question Total | 5
Q | Marking instructions | AO | Marks | Typical solution\begin{enumerate}[label=(\alph*)]
\item Show that the first three terms, in descending powers of $x$, of the expansion of
$$(2x - 3)^{10}$$
are given by
$$1024x^{10} + px^9 + qx^8$$
where $p$ and $q$ are integers to be found.
[3 marks]
\item Find the constant term in the expansion of
$$\left(2x - \frac{3}{x}\right)^{10}$$
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 2021 Q4 [5]}}