| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Numerical approximation using expansion |
| Difficulty | Easy -1.2 This is a straightforward application of binomial expansion with small n=4, followed by a routine substitution (x=0.002) to evaluate 1002^4 = (1000(1+0.002))^4. Requires only basic recall of the binomial theorem and arithmetic, with no problem-solving insight needed. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(1 + 4x + 6x^2 + 4x^3 + x^4\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \((1+0.002)^4 =\) \(1 + 0.008 + 0.000024 + 0.000000032 + 1.6\times10^{-11}\) | M1 | Attempt subst \(x=0.002\) in their expansion |
| \(= 1.008024032016\) | A1 | Correct values for all terms, not just correct expressions |
| \(1002^4 = 1\,008\,024\,032\,016\) | A1 | cao. No working, or inadequate working, no marks |
| or \(1.008\,024\,032\,016 \times 10^{12}\) | A1 | \((1000+2)^4\) scores no marks. \((1001+1)^4\) unless a complete solution is seen to an exact answer |
## Question 4:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $1 + 4x + 6x^2 + 4x^3 + x^4$ | B1 | |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $(1+0.002)^4 =$ $1 + 0.008 + 0.000024 + 0.000000032 + 1.6\times10^{-11}$ | M1 | Attempt subst $x=0.002$ in their expansion |
| $= 1.008024032016$ | A1 | Correct values for all terms, not just correct expressions |
| $1002^4 = 1\,008\,024\,032\,016$ | A1 | cao. No working, or inadequate working, no marks |
| or $1.008\,024\,032\,016 \times 10^{12}$ | A1 | $(1000+2)^4$ scores no marks. $(1001+1)^4$ unless a complete solution is seen to an exact answer |
---4
\begin{enumerate}[label=(\alph*)]
\item Expand $( 1 + x ) ^ { 4 }$.
\item Use your expansion to determine the exact value of $1002 ^ { 4 }$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q4 [5]}}