1 / 9

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.

oakes
Download Presentation

GCSE: Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related