| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | June |
| Marks | 5 |
| Topic | Radians, Arc Length and Sector Area |
| Type | Chord and sector relationship |
| Difficulty | Moderate -0.8 This is a straightforward application of basic radian geometry formulas. Part (i) requires the cosine rule to find chord length PQ, and part (ii) adds arc length to complete the perimeter. Both are standard textbook exercises with no problem-solving insight required, making this easier than average but not trivial since it involves two steps and the cosine rule. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
**(i)** Attempt correct cosine or sine rule — M1 [3]
Obtain unsimplified form $PQ^2 = 7^2 + 7^2 - 2(7)(7)\cos 1.7$ — A1
Obtain 10.5 — A1
**(ii)** Use $7\theta$ — M1 [2]
Obtain 22.4 — A1 **[5]**3 A sector, $P O Q$, of a circle centre $O$ has radius 7 cm and angle 1.7 radians (see diagram).\\
\includegraphics[max width=\textwidth, alt={}, center]{41d9ff74-82de-4ac5-928f-f6ab008319d2-2_469_723_662_712}\\
(i) Find the length of the line $P Q$.\\
(ii) Hence find the perimeter of the shaded area.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q3 [5]}}