GCSE: Circles Dr J Frost ([email protected]) Last modified: 6th October 2013 Starter Give your answers in terms of 4 Area of shaded region = 4 ? 12 Area = 4 ? Perimeter = 8 +?2 4

Area = 18 ? Perimeter = 12 +? 6 Typical GCSE example Edexcel March 2012 What is the perimeter of the shape? P = 3x +? 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

2x 2x 5 3x 2x ? ? Perimeter: Area: 4 Perimeter: Area: ? ? 5

2 Perimeter: Area: 8 6 Perimeter: Area: ? ? 2 ? ? Perimeter: Area: ? ?

Arcs and Sectors Arc Area of circle: = r2 ? Circumference of circle: = 2r ? r (Write down) Proportion of circle shaded: __ = ?

360 Sector __ Area of sector = r ? 360 2 __ Length of arc = 2r ? 360 Practice Questions Sector area = 10.91 ? 50 Area = 20 5

Arc length = 4.36 ? Sector area = 4.04cm ? 2 105 2.1cm ? Arc length = 3.85cm 135 (Hint: Plug values into your formula and rearrange) Radius = 4.12 ? A* GCSE questions ?

Area of triangle = 327 Area of sector = 1.5 ? Area of shaded region = 327 - 1.5 ? = 10.9cm2 Helpful formula: Area of triangle = ab sin C 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. Q a) Determine the length PQ. P ? Answer: 10cm R

b) Determine the angle QPR Answer: 114.6 ? Bonus super hard question: Can you produce an inequality that relates the area A of a sector to its arc length L? L < ?4AA Hint: Find an expression for . What constraint is on this variable? Exercises Rayner GCSE Pg 191 Exercise 17C: Q2, 3, 10, 11, 12 Exercise 18C: Q9, 10, 13, 17, 19, 22

Recently Viewed Presentations

• Comparing Biblical Faith and Scientific "Faith" Both types of "faith" are based on experience. As we find that the Bible or science is reliable in points we can confirm, we are inclined to trust them in areas we cannot confirm.
• American Asian Supply Chain. By: Christopher Gorski, Nikola . ... In regards to the Flying Geese Model/Race-to-the-Bottom, is there an end? Future. Challenge of the lifestyle . the supply chain provides. mass consumption, constant technological updates.
• City of Boca Raton 1998 Burlington Industries, Inc. v. Ellerth 1998 Quid Pro Quo Hostile Work Environment Quid Pro Quo sexual harassment occurs when: Employment decisions or expectations-hiring decisions, promotions, salary increases, work assignments or performance evaluations are based on...
• * Time windows logistics Many exceptions Logistics between 7-12 AM and 6-8 PM (shopping nights 9-10 PM) Residents Entrepeneurs (if needed) Utility traffic Fresh goods 'City distributor (60 addresses, 20 addresses per ride) Taxi's Buses (P+R and 220Xpress) Insufficient enforcement...
• 51 RCACS parent briefing Topics Camp Overview Selection Process Allergies Courses Expectations What to bring Daily routine CF-51 Contact Camp Overview The opportunity to further training is provided to cadets to attend summer training Cadet Summer Training Centers (CSTC) are...
• TMSI - GSM 03.20 TMSI: temporary local ID: protected identifying method is normally used instead of the IMSI on the radio path; and IMSI is not normally used as addressing means on the radio path (see GSM 02.09); when the...
• Biblical Allusions. Stephen's name is an allusion to St. Stephen, the first Christian martyr. Like St. Stephen, Stephen Dedalus has conflicts with the established religion of his day. St. Stephen was one of the seven deacons appointed by the apostles.
• Number of supply sources exceeds number of demand depots. The matrix formed is not square. We make it square by adding a row or column. By convention the row or column added is filled with the largest number in the...