1. 1
   A cuboid storage box ABCD.EFGH has base length AB = 12 cm, base width BC = 5 cm, and height 4 cm, with EFGH directly above ABCD.

   (a)

   Find the length of the diagonal AC of the base.

   [1 mark]

   • A13 cm
   • B17 cm
   • C9 cm
   • D14 cm

   (b)

   Using your answer to part (a), find the length of the space diagonal AG, correct to 1 decimal place.

   [1 mark]

   • A12.6 cm
   • B17.0 cm
   • C13.6 cm
   • D14.6 cm

   (c)

   Find the angle between AG and the base plane ABCD (angle GAC), correct to 1 decimal place.

   [1 mark]

   • A27.1 degrees
   • B22.1 degrees
   • C13.1 degrees
   • D17.1 degrees

   Total for question 1: 3 marks

2. 2
   A right pyramid VABCD has a square base ABCD of side 10 m, with vertex V directly above the centre O of the base at a height of 12 m.

   (a)

   Find the length OA, the distance from the centre of the base to a corner, correct to 2 decimal places.

   [2 marks]

   (b)

   Using your answer to part (a), find the length of the sloping edge VA, correct to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A rectangular room ABCD (floor) has EFGH directly above it (ceiling), with AB = 8 m, BC = 6 m and height 3 m. An electrician runs a cable from corner A on the floor to the diagonally opposite corner G on the ceiling.

   (a)

   Find the length of the cable AG, correct to 1 decimal place.

   [3 marks]

   (b)

   Find the angle that the cable AG makes with the floor of the room, correct to 1 decimal place.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A surveyor is measuring a rectangular warehouse ABCD (base) with EFGH directly above it (roof), where AB = 12 m, BC = 5 m, and the height AE = 6 m. A support cable runs from corner A (floor) to the diagonally opposite corner G (roof).

   (a)

   Find the length of the base diagonal AC, and hence find the length of the cable AG, giving both answers to 1 decimal place.

   [4 marks]

   (b)

   Find the angle that the cable AG makes with the base of the warehouse (angle GAC), correct to 1 decimal place.

   [4 marks]

   (c)

   Find the angle that the cable AG makes with the vertical edge AE (angle EAG), correct to 1 decimal place.

   [5 marks]

   Total for question 4: 13 marks

End of questions