EDEXCEL 4MA1: Circle Sectors Progressive Test
Topic 4.9.2 | 15 Questions | Foundation → Higher → Grade 9
Calculate the circumference of a full circle with radius 5 cm.
Hint: Use the formula C = 2πr
What fraction of a full circle is a sector with angle 90°?
Hint: Compare the sector angle to 360°
Calculate the arc length of a semi-circle with radius 10 cm.
Hint: Semi-circle means angle = 180°
Find the area of a sector with angle 60° and radius 6 cm.
Hint: Area of sector = (θ/360) × πr²
Calculate the perimeter of a quadrant (quarter circle) with radius 4 cm.
EXAMINER TRAP: TRAP: Students forget to add the two radii! Common error: giving just the arc length.
Hint: TRAP ALERT: Perimeter includes the arc AND the two radii!
A sector has area 10π cm² and radius 6 cm. Find the angle θ.
Hint: Rearrange: θ = (Area × 360)/(πr²)
An arc has length 12 cm and the sector angle is 45°. Find the radius.
Hint: Rearrange arc formula: r = (Arc × 360)/(2π × θ)
The perimeter of a semi-circle is 20 cm. Find the radius.
EXAMINER TRAP: TRAP: Common error is forgetting the diameter! Students write πr = 20.
Hint: TRAP ALERT: Perimeter = πr + 2r (curved part + diameter)
A sector has area 50 cm² and angle 100°. Find the arc length.
Hint: Two steps: (1) Find radius from area, (2) Calculate arc length
A minor sector has angle 120° and radius 8 cm. Find the area of the MAJOR sector.
Hint: Major sector angle = 360° - 120°
A segment is formed by a sector with angle 60° and radius 10 cm. Find the area of the segment.
Hint: Segment Area = Sector Area - Triangle Area. Use Area = (1/2)ab sin C
A sector with radius 12 cm and angle 120° is folded to make a cone. Find the radius of the cone's base.
Hint: Arc length of sector = Circumference of cone base
Three circles of radius 4 cm touch each other externally. Find the area of the curved triangular gap between them.
Hint: Gap = Equilateral triangle - Three sectors (each 60°)
A rectangle measures 12 cm by 8 cm. A quadrant of radius 4 cm is cut from each corner. Find the shaded area.
Hint: Shaded = Rectangle - 4 quadrants
A sector has a fixed perimeter of 40 cm. Find the angle θ that maximizes the area.
Hint: Express area in terms of θ using perimeter constraint, then differentiate
Grade Boundaries (Indicative):
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