1. 1
   A ship sails from port A on a bearing of $072°$ to reach point B, then returns from B back to A.

   (a)

   What bearing is due north measured clockwise as, at the very start of the journey?

   [1 mark]

   • A$000°$
   • B$090°$
   • C$180°$
   • D$360°$ only

   (b)

   Find the bearing of A from B (the return journey), given the ship sailed from A to B on a bearing of $072°$.

   [1 mark]

   • A$072°$
   • B$252°$
   • C$108°$
   • D$180°$

   (c)

   A bearing must always be written using how many figures?

   [1 mark]

   • AFour figures
   • BTwo figures
   • CThree figures
   • DAny number of figures

   Total for question 1: 3 marks

2. 2
   A cartographer is producing a map of a region using a scale of 1 : 25000.

   (a)

   A map uses a scale of 1 : 25000. Two towns are 8 cm apart on the map. Find the actual distance between them in kilometres.

   [2 marks]

   (b)

   A national park is 15 km wide in reality. Find the width it should be drawn on this map, giving your answer in centimetres.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   An engineer is constructing a triangular support bracket ABC with AB = 7 cm, BC = 9 cm and AC = 11 cm, using a ruler and pair of compasses only.

   (a)

   A triangular support bracket ABC is to be constructed with AB = 7 cm, BC = 9 cm and AC = 11 cm using only a ruler and pair of compasses. Describe the first two steps of the construction, before the final point C is located.

   [3 marks]

   (b)

   Explain why construction arcs must be clearly shown as part of the completed construction, rather than erased, and state what would happen if only a ruler (with no compasses) were used to attempt this construction.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A packaging designer folds a cardboard net into a closed cuboid box with length 12 cm, width 8 cm and height 5 cm.

   (a)

   A cardboard net is folded to form a closed cuboid box with length 12 cm, width 8 cm and height 5 cm. Using the net's face measurements, calculate the total surface area of the box.

   [4 marks]

   (b)

   Using the same net measurements, calculate the volume of the box.

   [4 marks]

   (c)

   The box has line symmetry properties when viewed from certain faces, and as a 3D solid it has rotational symmetry about certain axes. Describe the order of rotational symmetry of the cuboid about the vertical axis through the centres of its top and bottom faces (assuming the base is a rectangle, not a square), and explain your reasoning.

   [5 marks]

   Total for question 4: 13 marks

End of questions