Explain — 2 marks
A satellite orbits Earth in a circular path. Engineers need to understand the geometry of the orbit to calculate safe distances and predict the satellite's position at any time.
-
The satellite completes one full orbit. Explain why the angle subtended at the centre of Earth during one complete orbit is 360°.
[1 mark]
-
The satellite travels along an arc that subtends an angle of 90° at Earth's centre. Explain what fraction of the total orbital circumference the satellite has travelled.
[1 mark]
Show mark scheme
State — 4 marks
A circular running track has a radius of 50 m. Athletes train on this track, and coaches need to understand the geometric properties of the circular path to plan training routes and measure distances accurately.
-
State the name of the line segment that connects the centre of the circle to any point on the circumference.
[1 mark]
-
State what the diameter of the running track is, given that the radius is 50 m.
[1 mark]
-
State the relationship between the radius and the diameter of a circle.
[1 mark]
-
State the name of the curved line that forms the outer edge of the circular running track.
[1 mark]
Show mark scheme
Compare — 3 marks
A designer is creating two circular logos for a company. Logo A has a radius of 5 cm. Logo B has a diameter of 8 cm. Both logos will be printed on promotional materials.
-
Compare the radii of Logo A and Logo B.
[1 mark]
-
Compare the circumferences of the two logos. Show your working.
[1 mark]
-
Compare the areas of Logo A and Logo B. Which logo has the greater area and by how much? Show your working.
[1 mark]
Show mark scheme
Calculate — 2 marks
A gardener is designing a circular pond for a park. The pond has a diameter of 4 metres.
-
(01.1) Calculate the circumference of the pond. Give your answer in terms of π.
[1 mark]
-
(01.2) The gardener wants to place decorative stones around the edge of the pond, leaving a 1 metre wide border. Calculate the area of the border.
[1 mark]
Show mark scheme
- (01.1) 4π (m) or equivalent
- (01.2) π × 3² − π × 2² or 9π − 4π or equivalent method
- (01.2) 5π (m²) or 15.7 (m²) or 15.71 (m²)
Describe — 3 marks
The diagram shows a circle with centre O. Points A, B and C lie on the circumference of the circle. Angle AOC = 124° where AOC is the angle at the centre subtended by the minor arc AC. Point B is on the major arc AC.
-
(01.1) Describe the relationship between the angle at the centre and the angle at the circumference when both angles are subtended by the same arc.
[1 mark]
-
(01.2) Given that angle AOC = 124°, describe how to calculate the size of angle ABC, and state the value of angle ABC.
[2 marks]
Show mark scheme
- (01.1) Angle at centre is twice angle at circumference (or equivalent)
- (01.2) Divide 124 by 2 (or half the angle at centre)
- (01.2) 62°
GCSE Perfect