| Exam Board | OCR MEI |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2008 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Theorem (positive integer n) |
| Type | Standard binomial expansion coefficient |
| Difficulty | Easy -1.3 This is a straightforward C1 binomial theorem question requiring direct application of the combination formula and binomial coefficient formula. Part (i) is pure recall/calculation of 8C3, and part (ii) is a standard textbook exercise applying the binomial expansion formula with a simple substitution. No problem-solving or insight required—just mechanical application of learned formulas. |
| Spec | 1.04a Binomial expansion: (a+b)^n for positive integer n |
| Answer | Marks | Guidance |
|---|---|---|
| (i) 56 | Marks: 2 | Guidance: M1 for \(\frac{8 \times 7 \times 6}{3 \times 2 \times 1}\) or more simplified |
| (ii) \(-7\) or ft from \(-\)their (i)/8 | Marks: 2 | Guidance: M1 for 7 or ft their (i)/8 or for \(56 \times (-\frac{1}{2})^3\) o.e. or ft: condone \(x^2\) in answer or in M1 expression; 0 in qn for just Pascal's triangle seen |
**(i)** 56 | **Marks:** 2 | **Guidance:** M1 for $\frac{8 \times 7 \times 6}{3 \times 2 \times 1}$ or more simplified | **Total:** 2
**(ii)** $-7$ or ft from $-$their (i)/8 | **Marks:** 2 | **Guidance:** M1 for 7 or ft their (i)/8 or for $56 \times (-\frac{1}{2})^3$ o.e. or ft: condone $x^2$ in answer or in M1 expression; 0 in qn for just Pascal's triangle seen | **Total:** 2
**Total for Question 7:** 47 (i) Find the value of ${ } ^ { 8 } \mathrm { C } _ { 3 }$.\\
(ii) Find the coefficient of $x ^ { 3 }$ in the binomial expansion of $\left( 1 - \frac { 1 } { 2 } x \right) ^ { 8 }$.
\hfill \mbox{\textit{OCR MEI C1 2008 Q7 [4]}}