| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Radians, Arc Length and Sector Area |
| Type | Logo and design problems |
| Difficulty | Standard +0.3 This is a straightforward C2 geometry question involving basic trigonometry and circle properties. Part (i) requires finding a length using Pythagoras or trigonometry and calculating an area. Part (ii) involves standard tangent properties (angle = 90°, using right-angled triangle) and sector area/arc length formulas with radians. While multi-step, all techniques are routine applications of C2 content with no novel problem-solving required, making it slightly easier than average. |
| Spec | 1.05b Sine and cosine rules: including ambiguous case1.05c Area of triangle: using 1/2 ab sin(C)1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
| Answer | Marks |
|---|---|
| 4 | i |
| ii | AB = 7.8(0), 7.798 to 7.799 seen |
| Answer | Marks |
|---|---|
| perimeter = 55.3 to 55.4 | 2 |
| Answer | Marks |
|---|---|
| A1 | M1 for correct use of sine rule |
| Answer | Marks |
|---|---|
| oe using degrees | 4 |
Question 4:
4 | i
ii | AB = 7.8(0), 7.798 to 7.799 seen
area = 52.2 to 52.3
tan 0.91 = ST/12.6
ST = 12.6 × tan 0.91 and
completion (16.208...)
area OSTR = [2×][0.5 ×]12.6 ×
their(16.2) nb 204. ….
area of sector = 0.5 × 12.62 × 1.82
=144.47…
Logo = 59.6 to 60.0
arc = 12.6 × 1.82 [=22.9...]
perimeter = 55.3 to 55.4 | 2
2
M1
E1
M1
M1
A1
A1
M1
A1 | M1 for correct use of sine rule
For long methods M1A1 for art 7.8
M1 for [2×][0.5 ×] their AB × 11.4 ×
sin 36°
Accept 16.2 if ST is explicit but for
long methods with pa check that their
explicit expression = 16.2
oe using degrees
soi by correct ans Accept 144, 144.5
oe using degrees | 4
8\emph{Arrowline Enterprises} is considering two possible logos:
\includegraphics{figure_6}
\begin{enumerate}[label=(\roman*)]
\item Fig. 10.1 shows the first logo ABCD. It is symmetrical about AC.
Find the length of AB and hence find the area of this logo. [4]
\item Fig. 10.2 shows a circle with centre O and radius 12.6 cm. ST and RT are tangents to the circle and angle SOR is 1.82 radians. The shaded region shows the second logo.
Show that ST = 16.2 cm to 3 significant figures.
Find the area and perimeter of this logo. [8]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 Q4 [12]}}