1. 1
   A regular polygon has 15 sides.

   (a)

   What is the sum of the interior angles of this polygon?

   [1 mark]

   • A$2340°$
   • B$2700°$
   • C$2160°$
   • D$1800°$

   (b)

   What is the size of each interior angle of this polygon?

   [1 mark]

   • A$166°$
   • B$156°$
   • C$150°$
   • D$144°$

   (c)

   What is the size of each exterior angle of this polygon?

   [1 mark]

   • A$36°$
   • B$12°$
   • C$24°$
   • D$30°$

   Total for question 1: 3 marks

2. 2
   A trapezium-shaped garden bed has parallel sides of length 6 m and 10 m, and a perpendicular height of 4 m. A triangular flower bed is attached to one side, with base 5 m and perpendicular height 6 m.

   (a)

   Calculate the area of the trapezium-shaped garden bed.

   [2 marks]

   (b)

   Calculate the total area of the garden bed and the triangular flower bed together.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Triangle $ABC$ has a right angle at $B$, with $AB=9$ cm and angle $BAC=37°$.

   (a)

   Calculate the length of $BC$, giving your answer to 3 significant figures.

   [3 marks]

   (b)

   Calculate the length of $AC$, giving your answer to 3 significant figures.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A metal cylinder has radius 5 cm and height 12 cm. Use $\pi=3.14$ throughout.

   (a)

   Calculate the volume of the cylinder, giving your answer to 3 significant figures.

   [4 marks]

   (b)

   Calculate the total surface area of the cylinder, giving your answer to 3 significant figures.

   [4 marks]

   (c)

   The cylinder is made of a metal with density 7.8 g/cm$^3$. Using your volume from part (a), calculate the mass of the cylinder in kilograms, giving your answer to 3 significant figures. (Density = mass ÷ volume; 1 kg = 1000 g)

   [5 marks]

   Total for question 4: 13 marks

5. 5
   A sector of a circle has radius 9 cm and an angle of 80 degrees at the centre.

   (a)

   Find the arc length of the sector, in terms of $\pi$.

   [1 mark]

   • A$18\pi$ cm
   • B$8\pi$ cm
   • C$2\pi$ cm
   • D$4\pi$ cm

   (b)

   Find the area of the sector, in terms of $\pi$.

   [1 mark]

   • A$18\pi$ cm$^2$
   • B$81\pi$ cm$^2$
   • C$9\pi$ cm$^2$
   • D$4\pi$ cm$^2$

   (c)

   Find the perimeter of the sector, in terms of $\pi$.

   [1 mark]

   • A$4\pi$ cm
   • B$4\pi+18$ cm
   • C$18\pi+18$ cm
   • D$4\pi+9$ cm

   Total for question 5: 3 marks

6. 6
   Point $Y$ is on a bearing of $048°$ from point $X$, at a distance of 14 km.

   (a)

   State the bearing of $X$ from $Y$.

   [2 marks]

   (b)

   On a map with scale 1 : 200 000, calculate the distance between $X$ and $Y$ on the map, in centimetres.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   $A$, $B$, $C$ and $D$ lie on a circle, in that order, so that $ABCD$ is a cyclic quadrilateral. Angle $BAD=110°$. The tangent to the circle at $C$ makes an angle of $65°$ with the chord $CD$.

   (a)

   Prove that angle $BCD=70°$, stating the circle theorem you use.

   [3 marks]

   (b)

   Use the alternate segment theorem to find angle $CBD$, the angle subtended by chord $CD$ at point $B$.

   [3 marks]

   Total for question 7: 6 marks

8. 8
   Triangle $PQR$ has $PQ=13$ cm, $QR=17$ cm and angle $PQR=58°$.

   (a)

   Calculate the length of $PR$, giving your answer to 3 significant figures.

   [4 marks]

   (b)

   Calculate the area of triangle $PQR$, giving your answer to 3 significant figures.

   [4 marks]

   (c)

   Triangle $PQR$ forms the horizontal base of a pyramid with apex $V$ vertically above $P$, where $PV=9$ cm. Using your value of $PR^2$ from part (a), calculate the length $VR$, giving your answer to 3 significant figures.

   [5 marks]

   Total for question 8: 13 marks

End of questions