1. 1
   A circle has radius 7 cm.

   (a)

   Using $\pi = \frac{22}{7}$, what is the circumference of the circle?

   [1 mark]

   • A$44$ cm
   • B$22$ cm
   • C$154$ cm
   • D$14$ cm

   (b)

   Using $\pi = \frac{22}{7}$, what is the area of the circle?

   [1 mark]

   • A$44\ \text{cm}^2$
   • B$49\ \text{cm}^2$
   • C$154\ \text{cm}^2$
   • D$308\ \text{cm}^2$

   (c)

   Using $\pi = \frac{22}{7}$, what is the perimeter of a semicircle with this radius (the curved arc plus the diameter)?

   [1 mark]

   • A$22$ cm
   • B$36$ cm
   • C$44$ cm
   • D$58$ cm

   Total for question 1: 3 marks

2. 2
   From an external point P, two tangents PA and PB touch a circle with centre O and radius 3 cm, at points A and B respectively. The length PA = 4 cm.

   (a)

   State the length of PB, giving a reason.

   [2 marks]

   (b)

   Given that the tangent at A is perpendicular to the radius OA, use Pythagoras' theorem to find the length OP.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A chord AB of a circle with centre O has length 16 cm. The perpendicular distance from O to the chord is 6 cm.

   (a)

   Using the property that the perpendicular from the centre to a chord bisects the chord, find the radius of the circle.

   [3 marks]

   (b)

   A different chord in the same circle (radius 10 cm, from part (a)) has length 12 cm. Find the perpendicular distance from the centre to this chord.

   [3 marks]

   Total for question 3: 6 marks

4. 4
   A sector of a circle has radius 12 cm and an angle of 60 degrees at the centre.

   (a)

   Find the arc length of the sector, giving your answer in terms of $\pi$ and also correct to 3 significant figures.

   [4 marks]

   (b)

   Find the area of the sector, giving your answer in terms of $\pi$ and also correct to 3 significant figures.

   [4 marks]

   (c)

   The chord joining the two ends of the arc is drawn, forming a triangle with the two radii. Explain why this triangle is equilateral, state the length of the chord, and hence find the perimeter of the sector (arc length plus the two radii), correct to 3 significant figures.

   [5 marks]

   Total for question 4: 13 marks

End of questions