Radian measure, arc length and sector areaEdexcel International A Level Maths: Subtopic test

1. 1
   A sector $OAB$ of a circle with centre $O$ and radius $6$ cm has angle $\frac{2\pi}{3}$ radians at $O$.

   (a)

   Find the length of the arc $AB$.

   [1 mark]

   • A$4\pi$ cm
   • B$12\pi$ cm
   • C$2\pi$ cm
   • D$8\pi$ cm

   (b)

   Find the area of the sector $OAB$.

   [1 mark]

   • A$24\pi$ cm$^2$
   • B$12\pi$ cm$^2$
   • C$2\pi$ cm$^2$
   • D$4\pi$ cm$^2$

   (c)

   Find the perimeter of the sector $OAB$, giving your answer in the form $a+b\pi$.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A circle has radius $8$ cm. A sector of this circle has an arc of length $10$ cm.

   (a)

   Find the angle of the sector, in radians.

   [1 mark]

   • A$80$
   • B$0.8$
   • C$1.25$
   • D$1.25\pi$

   (b)

   Find the area of the sector.

   [1 mark]

   • A$80$ cm$^2$
   • B$64$ cm$^2$
   • C$50$ cm$^2$
   • D$40$ cm$^2$

   (c)

   Give the angle of the sector in degrees, correct to 1 decimal place.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A sector $OPQ$ of a circle with centre $O$ and radius $9$ cm has area $36$ cm$^2$.

   (a)

   Find the angle $POQ$ in radians.

   [3 marks]

   (b)

   Find the perimeter of the sector.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The points $A$ and $B$ lie on a circle with centre $O$ and radius $10$ cm, and angle $AOB=1.2$ radians. The minor segment is the region between the chord $AB$ and the minor arc $AB$.

   (a)

   (i) Find the length of the minor arc $AB$.
   (ii) Find the area of the minor segment.

   [6 marks]

   (b)

   (i) Show that $AB=20\sin0.6$.
   (ii) Find the perimeter of the minor segment.
   (iii) Find the area of the minor segment as a percentage of the area of the circle, giving your answer to 2 significant figures.

   [6 marks]

   Total for question 4: 12 marks

End of questions