| Exam Board | AQA |
|---|---|
| Module | AS Paper 1 (AS Paper 1) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Numerical approximation using expansion |
| Difficulty | Moderate -0.8 Part (a) is direct application of the binomial expansion formula requiring only substitution and basic arithmetic. Part (b) requires recognizing that 0.998 = 1 - 2(0.001) and evaluating the approximation, which is a standard textbook application. The question tests routine binomial expansion skills with minimal problem-solving, making it easier than average for A-level. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks |
|---|---|
| 8(a) | Uses binomial theorem to expand |
| Answer | Marks | Guidance |
|---|---|---|
| expression but condone sign error | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| both correct | AO1.1b | A1 |
| Obtains correct x2 term | AO1.1b | A1 |
| (b) | Selects x = 0.001 | AO3.1a |
| Answer | Marks | Guidance |
|---|---|---|
| obtain a 5 decimal place value | AO1.1a | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| found by using the expansion | AO2.4 | A1 |
| Total | 6 | |
| Q | Marking Instructions | AO |
Question 8:
--- 8(a) ---
8(a) | Uses binomial theorem to expand
bracket – correct unsimplified
expression but condone sign error | AO1.1a | M1 | 10 10
1 (2x)1 (2x)2
1 2
120x180x2...
Obtains constant term and x term,
both correct | AO1.1b | A1
Obtains correct x2 term | AO1.1b | A1
(b) | Selects x = 0.001 | AO3.1a | B1 | Substituting x = 0.001
1 – 0.020 + 0.000180 = 0.98018
0.99810 = 0.980179… = 0.98018 to 5
dp, which matches Carly’s value.
Substitutes ‘their’ chosen value of x
into ‘their’ expansion from part (a) to
obtain a 5 decimal place value | AO1.1a | M1
Gives a correct explanation to confirm
that the value found from the
calculator is 0.98018 to 5 decimal
places which is the same as the value
found by using the expansion | AO2.4 | A1
Total | 6
Q | Marking Instructions | AO | Marks | Typical Solution\begin{enumerate}[label=(\alph*)]
\item Find the first three terms, in ascending powers of $x$, of the expansion of $(1 - 2x)^{10}$ [3 marks]
\item Carly has lost her calculator. She uses the first three terms, in ascending powers of $x$, of the expansion of $(1 - 2x)^{10}$ to evaluate $0.998^{10}$
Find Carly's value for $0.998^{10}$ and show that it is correct to five decimal places.
[3 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 1 Q8 [6]}}