1. 1
   A cyclist rides from village A on a bearing of $063^\circ$ to village B. At B, she turns and rides on a bearing of $154^\circ$ to village C.

   (a)

   Work out the bearing of A from B.

   [1 mark]

   • A$117^\circ$
   • B$207^\circ$
   • C$243^\circ$
   • D$063^\circ$

   (b)

   Using your answer to part (a), work out the size of angle ABC (the interior angle of the triangle at village B, between BA and BC).

   [1 mark]

   • A$89^\circ$
   • B$91^\circ$
   • C$111^\circ$
   • D$69^\circ$

   (c)

   The bearing of C from B is $154^\circ$. Which compass direction is this closest to?

   [1 mark]

   • ANorth-East
   • BNorth-West
   • CSouth-West
   • DSouth-East

   Total for question 1: 3 marks

2. 2
   A garden is in the shape of a rectangle measuring 12 m by 7 m. A semicircular flower bed with a diameter of 7 m is cut out of one of the 7 m sides, so that side of the rectangle is replaced by the curved edge of the semicircle.

   (a)

   Work out the perimeter of the garden. Give your answer correct to 1 decimal place.

   [2 marks]

   (b)

   Work out the area of the garden that remains once the semicircular flower bed has been removed. Give your answer correct to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A solid metal cylinder has a radius of 4 cm and a height of 10 cm. The cylinder is melted down completely and recast, with no loss of metal, into a solid sphere.

   (a)

   Work out the volume of the cylinder. Give your answer correct to 3 significant figures.

   [3 marks]

   (b)

   The cylinder from part (a) is melted down completely and recast, with no loss of metal, into a solid sphere. Work out the radius of the sphere. Give your answer correct to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A water tank is made from a cylinder of radius 5 cm and height 20 cm, with a hemisphere of the same radius fixed on top like a dome.

   (a)

   Work out the total volume of the tank. Give your answer correct to 3 significant figures.

   [4 marks]

   (b)

   The tank is filled with water at a constant rate of 25 cm$^3$ per minute, starting empty. Using your answer to part (a), work out the time taken to fill the tank completely. Give your answer to the nearest minute.

   [4 marks]

   (c)

   The tank stands on the ground and only the curved outer surfaces (the curved surface of the cylinder and the curved surface of the hemisphere) need to be painted; the circular base is not painted. Work out the total area to be painted. Give your answer correct to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions