Year 10 GCSE Higher Tier

CIRCLES TEST

You have 1 hour 30 minutes for this test. TOTAL Marks = 75

Section A:Perimeter and Area problems: (32 marks)

1 / The diagram shows a semi-circle.
The diameter of the semi-circle is 15 cm.
Calculate the area of the semi-circle.
Give your answer correct to 3 significant figures.(4) /
2 / a) Find the perimeter (3)b) Find the area (4)

3 / A bicycle wheel has a diameter of 65cm.
How many times does the wheel rotate in a journey of distance 100m? (3)
4 / The diagram shows a sector of a circle, centre O.
The radius of the circle is 9 cm.
The angle at the centre of the sector is 40°.
a) Find the perimeter of the sector.
b) Find the area of the sector.(6) /
5 / The arc length of a sector of a circle is 15 cm.
The radius of the circle is 12 cm.
Work out size of the angle, °, of the sector.(3) /
6 / RST is a circular arc with centre P and radius 18 cm. Angle RPT = 40.
(a)Calculate the length of the circular arc RST.
Give your answer correct to 3 significant figures. (2)
PQR is a semicircle with centre O.
(b)Calculate the total area of the shape PQRST. Give your answer correct to 3 significant figures. (3) /
7 / Find the shaded area. (4) /

Section B:Circle Theorems: (43 marks)

1. / In the diagram, A, B and C are points on the circle, centre O.
Angle BCE = 63°.
FE is a tangent to the circle at point C.
(i) Calculate the size of angle ACB.
Give reasons for your answer.(2)
(ii) Calculate the size of angle BAC.
Give reasons for your answer. (2) /
2 / A,B,C and D are points on a circle, centre O.
Angle BOD = 116°
(a) Calculate the size of angle BAD.(1)
BC = CD.
(b) Calculate the size of angle DBC.(2) /
3 / P, Q and R are points on a circle, centre O.
POQ is a straight line.
TQ and TR are tangents to the circle.
Angle TQR = 56°.
(a) Explain why angle PQR = 34°. (1)
(b) Calculate the size of angle PRT.
Give reasons for your answer. (3) /
4 / A, B and C are points on the circumference of a circle, with centre O.
(i) Find angle AOC. (1)
(ii) Give a reason for your answer.(3) /
5 / A and B are points on the circumference of the circle, centre O.
PA and PB are tangents to the circle.
Angle APB = 56o.
Calculate the size of angle AOP.
Give a reason for each stage in your working.
(3) /
6 / B and C are points on the circle, centre O.
AB and AC are tangents to the circle.
Angle BAC = 48
(a) Find the size of angle ABO.
Give a reason for your answer. (2)
(b) Find the size of angle BOC.
Give reasons for your answer. (2) /
7 / A, B, C and D are points on a circle.
AB is equal in length and parallel to CD.
Lines AD and BC intersect at E.
Angle EDC = 35°.
(a) Write down the size of angle ABE.
Give a reason for your answer. [1]
(b) (i) Find the size of angle AEC.
Show all your working clearly. [2]
(ii) What does this tell you about point E? Give a reason for your answer. [2] /
8 / CP and CQ are tangents to the circle with centre O.
a) Explain why triangles CPO and CQO are congruent (exactly the same).(3)
b) Given that angle PCQ = 74°, calculate the reflex angle POQ.(2) /
9 / A, B, C and D are points on the circumference of a circle centre O.
A tangent is drawn from E to touch the circle at C.
Angle AEC = 36°
EAO is a straight line.
(a)Calculate the size of angle ABC.
Give reasons for your answer. (4)(4 marks)
(b)Calculate the size of angle ADC.
Give a reason for your answer. (2) /
10 / Points A, B and C lie on the circumference of a circle with centre O.
DA is the tangent to the circle at A.
BCD is a straight line.
OC and AB intersect at E.
Angle BOC = 80°
Angle CAD = 38°.
(a)Calculate the size of angle BAC. (1)
(b)Calculate the size of angle OBA. (3)
(c)Give a reason why it is not possible to draw a circle with diameter ED through the point A.(1) /