| Exam Board | OCR MEI |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Exact form answers |
| Difficulty | Challenging +1.2 This question requires understanding of inscribed/escribed polygons and their relationship to π, applying trigonometry (sin or tan of 15°) to find perimeters, and expressing answers in surd form. While it involves multiple steps and surd manipulation, the approach is relatively standard for A-level: divide the circle into 12 equal sectors, find one side length using basic trigonometry, multiply by 12, and simplify. The conceptual demand is moderate but the execution is methodical rather than requiring novel insight. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Lower bound: \(3(\sqrt{6}-\sqrt{2})\) | B1 | Half perimeter (from text) |
| Upper bound: \(24-12\sqrt{3}\) | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(= 3.11\) and \(3.22\) | B1 | Both as decimals |
# Question 16:
## Part (i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Lower bound: $3(\sqrt{6}-\sqrt{2})$ | B1 | Half perimeter (from text) |
| Upper bound: $24-12\sqrt{3}$ | B1 | |
## Part (ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $= 3.11$ and $3.22$ | B1 | Both as decimals |16 On a unit circle, the inscribed regular polygon with 12 edges gives a lower bound for $\pi$, and the escribed regular polygon with 12 edges gives an upper bound for $\pi$.
Calculate the values of these bounds for $\pi$, giving your answers:\\
(i) in surd form\\
(ii) correct to 2 decimal places.
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\hfill \mbox{\textit{OCR MEI Paper 3 Q16 [3]}}