OCR MEI C2 (Core Mathematics 2)

Fig. 11.1 shows a village green which is bordered by 3 straight roads AB, BC and CA. The road AC runs due North and the measurements shown are in metres. \includegraphics{figure_1}

1. Calculate the bearing of B from C, giving your answer to the nearest 0.1°. [4]
2. Calculate the area of the village green. [2]

The road AB is replaced by a new road, as shown in Fig. 11.2. The village green is extended up to the new road. \includegraphics{figure_2} The new road is an arc of a circle with centre O and radius 130 m.

1. (A) Show that angle AOB is 1.63 radians, correct to 3 significant figures. [2] (B) Show that the area of land added to the village green is 5300 m² correct to 2 significant figures. [4]

\includegraphics{figure_3} For triangle ABC shown in Fig. 4, calculate

1. the length of BC, [3]
2. the area of triangle ABC. [2]

1. A boat travels from P to Q and then to R. As shown in Fig. 11.1, Q is 10.6 km from P on a bearing of 045°. R is 9.2 km from P on a bearing of 113°, so that angle QPR is 68°. \includegraphics{figure_4} Calculate the distance and bearing of R from Q. [5]
2. Fig. 11.2 shows the cross-section, EBC, of the rudder of a boat. \includegraphics{figure_5} BC is an arc of a circle with centre A and radius 80 cm. Angle CAB = \(\frac{2\pi}{3}\) radians. EC is an arc of a circle with centre D and radius \(r\) cm. Angle CDE is a right angle.
   1. Calculate the area of sector ABC. [2]
   2. Show that \(r = 40\sqrt{3}\) and calculate the area of triangle CDA. [3]
   3. Hence calculate the area of cross-section of the rudder. [3]

\emph{Arrowline Enterprises} is considering two possible logos: \includegraphics{figure_6}

1. 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]
2. 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]

1. The course for a yacht race is a triangle, as shown in Fig. 11.1. The yachts start at A, then travel to B, then to C and finally back to A. \includegraphics{figure_7}
   1. Calculate the total length of the course for this race. [4]
   2. Given that the bearing of the first stage, AB, is 175°, calculate the bearing of the second stage, BC. [4]
2. Fig. 11.2 shows the course of another yacht race. The course follows the arc of a circle from P to Q, then a straight line back to P. The circle has radius 120 m and centre O; angle POQ = 136°. \includegraphics{figure_8} Calculate the total length of the course for this race. [4]