1. 1
   A cuboid ABCDEFGH has base ABCD with AB = 6 cm and BC = 8 cm. The vertical edges (including CG) have length 10 cm, with EFGH directly above ABCD.

   (a)

   What is the length of the diagonal AC of the base ABCD?

   [1 mark]

   • A10 cm
   • B14 cm
   • C48 cm
   • D6.5 cm

   (b)

   What is the length of the space diagonal AG, to 3 significant figures?

   [1 mark]

   • A20.0 cm
   • B10.0 cm
   • C18.0 cm
   • D14.1 cm

   (c)

   Which right-angled triangle should be used to calculate the length of AG?

   [1 mark]

   • ATriangle ABG, right-angled at B
   • BTriangle ACG, right-angled at C
   • CTriangle ABC, right-angled at B
   • DTriangle CDG, right-angled at D

   Total for question 1: 3 marks

2. 2
   A right pyramid VABCD has a square base ABCD with side length 12 cm. The apex V is directly above the centre of the base, and the vertical height of the pyramid is 8 cm.

   (a)

   Find the length of the diagonal AC of the square base, giving your answer to 3 significant figures.

   [2 marks]

   (b)

   Find the length of the sloping edge VA, giving your answer to 3 significant figures.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cuboid-shaped box ABCDEFGH has a rectangular base ABCD with AB = 9 cm and BC = 12 cm, and vertical height AE = 5 cm (E is directly above A, F above B, G above C, H above D).

   (a)

   Find the length of the diagonal BD of the base ABCD, showing your full method.

   [3 marks]

   (b)

   Find the angle between the space diagonal BH and the base ABCD, giving your answer to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A vertical mast stands at corner A of a horizontal rectangular field ABCD, where AB = 40 m and AD = 30 m. The top of the mast, T, is joined by straight cables to points B, C and D. The mast has height AT = 24 m.

   (a)

   Find the length of the cable TC, giving your answer to 3 significant figures.

   [4 marks]

   (b)

   Find the length of the cable TB, giving your answer to 3 significant figures.

   [4 marks]

   (c)

   Find the angle of elevation of T from B, giving your answer to 1 decimal place.

   [5 marks]

   Total for question 4: 13 marks

End of questions