1. 1
   Triangle XYZ has a right angle at Y. XY = 9 cm and YZ = 12 cm.

   (a)

   What is the length of XZ?

   [1 mark]

   • A15 cm
   • B21 cm
   • C3 cm
   • D225 cm

   (b)

   What is the value of $\sin(XZY)$?

   [1 mark]

   • A0.75
   • B0.6
   • C1.33
   • D0.8

   (c)

   What is the value of $\tan(XZY)$?

   [1 mark]

   • A1.5
   • B0.6
   • C1.33
   • D0.75

   Total for question 1: 3 marks

2. 2
   In triangle LMN, angle M = 90°, angle L = 30°, and LM = 8 cm.

   (a)

   Using the exact value $\tan(30°) = \frac{1}{\sqrt{3}}$, find the length of MN.

   [2 marks]

   (b)

   Using the exact value $\cos(30°) = \frac{\sqrt{3}}{2}$, find the length of LN.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A cuboid box has length 6 cm, width 8 cm and height 10 cm.

   (a)

   Find the length of the diagonal of the base of the box (the face with length 6 cm and width 8 cm).

   [3 marks]

   (b)

   Find the length of the space diagonal of the cuboid (from one corner to the opposite corner), giving your answer to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A triangular field has sides PQ = 70 m, QR = 50 m, and angle PQR = 60°.

   (a)

   Use the cosine rule to find the length of PR, giving your answer to 3 significant figures.

   [4 marks]

   (b)

   Use the sine rule and your answer to part (a) to find angle QPR, giving your answer to 3 significant figures.

   [4 marks]

   (c)

   Calculate the area of the field using $\text{Area} = \frac{1}{2}ab\sin C$, then convert your answer to hectares (1 hectare = 10 000 m²), giving your final answer to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions