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GCSE: Circles

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 = 4 π. ?. Perimeter = 8 + 2 π. ?. Area = 18 π. ?. Perimeter = 12 + 6 π.

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GCSE: Circles

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  1. GCSE: Circles Dr J Frost (jfrost@tiffin.kingston.sch.uk) Last modified: 6th October 2013

  2. Starter Give your answers in terms of π 4 Area of shaded region = 4 – π ? 12 Area = 4π ? Perimeter = 8 + 2π ? Area = 18π ? Perimeter = 12 + 6π ? 4

  3. Typical GCSE example Edexcel March 2012 What is the perimeter of the shape? P = 3x + pi x / 2 ?

  4. 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 2x 2x 5 3x 2x Perimeter: Area: ? Perimeter: Area: ? ? ? 4 5 2 Perimeter: Area: ? Perimeter: Area: 8 ? ? ? 6 2 Perimeter: Area: ? ?

  5. Arcs and Sectors Arc Area of circle: = πr2 ? Circumference of circle: = 2πr ? θ r Proportion of circle shaded: = _θ_ 360 ? Sector (Write down) _θ_ 360 _θ_ 360 ? ? Area of sector = πr2× Length of arc = 2πr ×

  6. Practice Questions Sector area = 10.91 ? Area = 20 50° Arc length = 4.36 ? 5 135° (Hint: Plug values into your formula and rearrange) Sector area = 4.04cm2 ? 105° Radius = 4.12 ? ? Arc length = 3.85cm 2.1cm

  7. A* GCSE questions Helpful formula: Area of triangle = ½ ab sin C ? Area of triangle = 3√27 Area of sector = 1.5π ? Area of shaded region = 3√27 - 1.5π = 10.9cm2 ?

  8. Difficult A* Style Question The shape PQR is a minor sector. The area of a sector is 100cm2. The length of the arc QR is 20cm. Determine the length PQ.Answer: 10cm Determine the angle QPRAnswer: 114.6° Q P ? 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? ?

  9. Exercises Rayner GCSE Pg 191 Exercise 17C: Q2, 3, 10, 11, 12 Exercise 18C: Q9, 10, 13, 17, 19, 22

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