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Radian measure, arc length and sector areaAQA A-Level Maths: Mind map

Radian measure
Arc length
Sector area

Radians

arcs and sectors

s=rθs=r\thetaA=12r2θA=\frac12r^2\thetaradians
Segments
Problem solving
Exam tips

Exam questions on Radian measure, arc length and sector area

  1. A sector OABOAB has centre OO, radius 55 cm and AO^B=1.2A\hat{O}B=1.2 radians.
    Convert 1.21.2 radians to degrees, giving your answer to 1 decimal place.2 marks
  2. A sector of a circle has arc length 88 cm and area 2424 cm2^2.
    Find the perimeter of the sector.2 marks
  3. A circle has centre OO and radius 1010 cm. The chord ABAB subtends an angle of π3\frac{\pi}{3} radians at OO. The minor segment is the region between the chord ABAB and the minor arc ABAB.
    Find the exact perimeter of the minor segment.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).