1. 1
   A polygon has 6 equal sides and 6 equal interior angles.

   (a)

   What is the correct name for this shape?

   [1 mark]

   • APentagon
   • BHexagon
   • CHeptagon
   • DOctagon

   (b)

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

   [1 mark]

   • A$540°$
   • B$600°$
   • C$720°$
   • D$900°$

   (c)

   What is the order of rotational symmetry of this shape?

   [1 mark]

   • A3
   • B4
   • C5
   • D6

   Total for question 1: 3 marks

2. 2
   Quadrilateral WXYZ has two pairs of adjacent sides equal in length (WX = XY and YZ = ZW), but only one pair of opposite angles is equal.

   (a)

   State the mathematical name of quadrilateral WXYZ, and explain why it cannot be a rhombus.

   [2 marks]

   (b)

   The equal pair of opposite angles in WXYZ (angle W and angle Y) are each $116°$. The other two angles, angle X and angle Z, are equal to each other. Calculate the size of angle X.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Parallelogram EFGH has $EF = 9$ cm, $FG = 6$ cm, and angle $EFG = 70°$.

   (a)

   Show that parallelogram EFGH has rotational symmetry of order 2 but has no lines of symmetry.

   [3 marks]

   (b)

   Calculate the size of angle FGH and angle GHE, stating the geometric property you use for each.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A circular garden has centre O and radius $10$ m. A straight path forms a chord AB across the garden, and the perpendicular distance from O to AB is $6$ m. Bilal wants to fence the minor arc between A and B and plant flowers in the minor segment enclosed.

   (a)

   Calculate the length of the chord AB.

   [4 marks]

   (b)

   Calculate the size of angle AOB (the angle at the centre subtended by chord AB), giving your answer to 1 decimal place.

   [4 marks]

   (c)

   Using angle $AOB = 106.26°$ (unrounded), calculate the area of the minor segment enclosed by chord AB and the minor arc, giving your answer to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions