GCSE Circles Dr J Frost jfrosttiffin kingston sch
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GCSE: Circles Dr J Frost (jfrost@tiffin. kingston. sch. uk) Last modified: 6 th October 2013
Starter Give your answers in terms of π 4 Area of shaded region = 4 –? π 12 Area = 4π ? Perimeter = 8 +? 2π 4 Area = 18π ? Perimeter = 12 +? 6π
Typical GCSE example Edexcel March 2012 What is the perimeter of the shape? P = 3 x +? pi x / 2
Exercises Find the perimeter and area of the following shapes in terms of the given variable(s) and in terms of . (Copy the diagram first) 3 2 1 2 x 2 x 5 3 x 2 x ? ? 4 ? ? 5 2 8 6 ? ? 2 ? ?
Arcs and Sectors Arc Area of circle: Circumference of circle: = 2πr? θ r (Write down) Area of sector = = πr 2? πr 2 Proportion of circle shaded: _θ_ = ? 360 Sector _θ_ ×? 360 _θ_ Length of arc = 2πr ×? 360
Practice Questions Sector area = 10. 91 ? 50° 5 105° 2. 1 cm Arc length = 4. 36 ? Sector area = 4. 04 cm ? 2 ? Arc length = 3. 85 cm Area = 20 135° (Hint: Plug values into your formula and rearrange) Radius = 4. 12 ?
A* GCSE questions ? Area of triangle = 3√ 27 Area of sector = 1. 5π ? Area of shaded region = 3√ 27 - 1. 5π ? = 10. 9 cm 2 Helpful formula: Area of triangle = ½ ab sin C
Difficult A* Style Question The shape PQR is a minor sector. The area of a sector is 100 cm 2. The length of the arc QR is 20 cm. Q a) Determine the length PQ. P ? Answer: 10 cm b) Determine the angle QPR Answer: 114. 6° ? R Bonus super hard question: Can you produce an inequality that relates the area A of a sector to its arc length L? L < ? 4πA Hint: Find an expression for θ. What constraint is on this variable?
Exercises Rayner GCSE Pg 191 Exercise 17 C: Q 2, 3, 10, 11, 12 Exercise 18 C: Q 9, 10, 13, 17, 19, 22
