Defining the radian, converting between degrees and radians, and using l = rθ, A = ½r²θ and the segment area formula.
5 narrated scenes. Press play, listen and read along — the points appear as they are explained. Use ‹ Prev / Next › or the scene bar to jump to any scene.
Degrees are a human invention. Radians come from the circle itself — and they make the formulas for arc length and area wonderfully simple.
Narration uses your device’s built-in voice. No sound? Switch to “Captions only” — the captions advance on their own.
Change the angle and the radius.
Copy these into your notebook in your own words — that is how they stick.
Angle subtended by an arc equal to the radius. π rad = 180°.
Degrees → radians × π/180; radians → degrees × 180/π.
l = rθ.
A = ½r²θ.
2r + rθ.
Area = ½r²(θ − sin θ); chord = 2r sin(θ/2).
Switch the calculator to RAD for sin, cos, tan of radian angles.
Leave answers in terms of π when asked.
3 quick games on this lesson. Earn XP and badges as you play — your best score for each game is saved. Games are for practice and do not change your exam readiness. More games in the Additional Mathematics Arcade.
8 items modelled on real CSEC Paper 1 questions. Choose one answer for each, then check. Aim for 80% or better. Work each item on paper first.
Write full answers, then reveal the mark scheme and tick the points you earned (23 marks in total). Show all your working — method marks count. Your answers are saved on this device.
Question 1 [11 marks]
A sector of a circle has radius 8 cm and angle 1.2 radians.
(a) Calculate the arc length. [2]
(b) Calculate the area of the sector. [2]
(c) Calculate the perimeter of the sector. [2]
(d) Calculate the area of the segment cut off by the chord joining the ends of the arc. [3]
(e) Express the angle 1.2 radians in degrees, to 1 decimal place. [2]
Question 2 [12 marks]
A wire of length 40 cm is bent to form the boundary of a sector of a circle of radius 10 cm.
(a) Find the arc length of the sector. [2]
(b) Show that the angle of the sector is 2 radians. [2]
(c) Calculate the area enclosed by the wire. [2]
(d) Calculate the area of the segment, to 1 decimal place. [3]
(e) Calculate the length of the chord joining the ends of the arc. [3]
Find these in your own past-paper booklets for extra timed practice. Items above are written in the style of these papers; any adapted from a specific question say so.