Prior Content: 2D Area & Perimeter, Constructions, Fractions, Using a Calculator/ BIDMAS, Advanced Trigonometry
Possible Next Steps: Prisms, Volume & Surface Area, Circle Theorems, Advanced Trigonometry, Drawing & Using Graphs
Contents
- 1.1 Labelling a Circle
- 1.2 Area & Circumference of a Circle
- 1.3 Semi-Circles & Compound Shapes
- 2.1 Area of a Sector & Segment
- 2.2 Perimeter of a Sector
- Whole Topic Summary Resources (Including Past Paper Questions)
1.1 Labelling a Circle
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Parts of a Circle
Online Platforms (with Videos & Exercises)
- Khan Academy
- Circle basics: Videos & practice
Activities & Resources
- Pixi Maths
- Transum
- Go Teach Maths
- BossMaths
Worksheets
- Corbettmaths
- Parts of a Circle Practice Questions & Solutions
- Parts of a Circle Worksheet & Solutions
- Maths 4 Everyone
- CIMT MEP (online self-checking)
- Physics & Maths Tutor
- Mr Morley Maths
- Parts of a Circle: Notes jotter/worksheet
Dr Frost Resources
Dr Frost Video
K295: Know Key Terms in Relation to Circles.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 317a: Identify tangents, chords, arcs, sectors and segments of a circle.
- 317: Exam Practice: Further terms in relation to circles, including chord and segment
Further Practice
- Practise Questions
Extension Materials
Worksheet
1.2 Area & Circumference of a Circle
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Area of a Circle
Corbett Maths Circumference
Online Platforms (with Videos & Exercises)
- Khan Academy
- Area & circumference of circles: Videos & practice
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Math = Love (Sarah Carter)
- Don Steward
- The Chalkface
- Tolstoy and Circles: PDF
- Penny Farthing: PDF
- Crop Circles: PowerPoint
- Ben Sparks (GeoGebra)
- Archimedes’ Approximation of Pi: GeoGebra
- Transum
- Interactive Maths
- Circles: Discovering Pi | Circumference | Area of a Circle
- Goal Free Problems
- Go Teach Maths
- GeoGebra
- Jo Morgan
- Rhymes for the area and circumference of a circle✦ (by Jo Morgan)
- Ticktock Maths
- CP3 Maths (cparkinson3)
- Mr Thompson Maths
- BossMaths
- Pondering Planning in Mathematics (Paul Rowlandson)
- Thinking About Calculating Areas of Circles✦ (blog post) · slides
- NCETM
- NCETM Key Idea: The area of a circle (PowerPoint)
Worksheets
- Dr Austin Maths
- Investigating Activity (Word | PDF)
- Practice Strips (Word | PDF | Answers)
- Match-Up (Word | PDF | Answers)
- Practice Strips (Word | PDF | Answers)
- Match-Up (Word | PDF | Answers)
- Problems in Reverse Practice Strips (Word | PDF | Answers)
- Fill in the Blanks (Word | PDF | Answers)
- Crack the Code (Word | PDF | Answers)
- Name the Film (Word | PDF | Answers)
- Practice Grid (Word | PDF | Answers)
- Practice Grid (Word | PDF | Answers))
- Practice Grid (Word | PDF | Answers)
- Corbettmaths
- Area of a Circle Practice Questions & Solutions
- Area of a Circle Worksheet & Solutions
- Circumference Practice Questions & Solutions
- Circumference Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
- CIMT MEP (online self-checking)
- Maths Genie
- Area and Circumference of Circles: Booklet · Worksheet · Solutions · Lesson · Topic page
- Kuta Software
- Access Maths
- MME
- Jo Morgan
- Frank Tapson
- @taylorda01
- Starting Points Maths
- Circles: Circumference/Perimeter (by Kyle Gillies) · PDF
- Mr Morley Maths
- Area and Circumference of Circles: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (@_rhi_rhi)
- Circumference and Area of Circles (@_rhi_rhi, pdf)
- Pret Homework (@missnmaths)
- Area of a Circle (@missnmaths, pptx)
Dr Frost Resources
Dr Frost Video
K287: Find the Circumference of a Full Circle Given its Radius.
K288: Find the Circumference of a Full Circle Given its Diameter.
K289: Find the Radius of a Circle Given its Circumference.
K290: Find the Area of a Full Circle Given its Radius.
K291: Find the Area of a Full Circle Given its Diameter.
K292: Find the Radius of a Circle Given its Area.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 209a: Calculate the circumference of a full circle given its radius.
- 209b: Calculate the circumference of a full circle given its diameter.
- 209c: Calculate the exact circumference of a full circle.
- 209d: Determine the radius or diameter of a full circle given its circumference.
- 209e: Determine a cost involving the circumference of a full circle.
- 209f: Determine the circumference of a full circle given the area or perimeter of a square it is inscribed in.
- 209g: Determine the number of revolutions of a wheel across a given distance.
- 210a: Calculate the area of a full circle given its radius.
- 210b: Calculate the area of a full circle given its diameter.
- 210c: Calculate the exact area of a full circle.
- 210d: Determine the radius of a circle given its area.
- 210e: Determine the area of a circle given its circumference. (not yet active)
- 210f: Determine the circumference of a circle given its area. (not yet active)
- 210g: Determine unknown lengths in a circle or a rectangle with related areas.
- 210h: Determine unknown lengths in a circle or a triangle with related areas.
- 209: Exam Practice: Circumference of a full circle
- 210: Exam Practice: Area of a full circle
Further Practice
- Practise Questions
Extension Materials
Enrichment Video
Veritasium: The SAT Question Everyone Got Wrong
Worksheet
1.3 Semi-Circles & Compound Shapes
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Area of a Semi-Circle
Corbett Maths Perimeter of a Semi-Circle
Online Platforms (with Videos & Exercises)
- Khan Academy
- Area & perimeter of parts of circles: Videos & practice
Activities & Resources
- Maths 4 Everyone
- Don Steward
- Interactive Maths
- Circle Problems: Running Tracks | Circle Area Problem | Circles & Squares
- Goal Free Problems
- Go Teach Maths
- Owen134866
- mrwhy1089
- Ticktock Maths
Worksheets
- Corbettmaths
- Area of a Circle (Some Compound Shapes Towards the End) Practice Questions & Solutions
- Area of a Circle (Some Compound Shapes Towards the End) Worksheet & Solutions
- Circumference (Some Semi-Circles Towards the End) Practice Questions & Solutions
- Area of a Semi-Circle Practice Questions & Solutions
- Area of a Semi-Circle Worksheet & Solutions
- Semi-Circle Perimeter Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
- Dr Austin Maths
- CIMT MEP (online self-checking)
- Miss Konstantine (MathsHKO)
- Access Maths
- Circle Crossover Problem: Problem | Accompany Sheet
- Starting Points Maths
Dr Frost Resources
Dr Frost Video
K293: Find the Perimeter of a Simple Fraction of a Circle.
K294: Find the Area of a Simple Fraction of a Circle.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 211a: Calculate the area of a simple fraction of a circle.
- 211b: Determine the perimeter of a simple fraction of a circle.
- 211c: Calculate the exact area of a simple fraction of a circle.
- 211d: Determine the exact perimeter of a simple fraction of a circle.
- 211e: Solve problems involving the cost of covering a fraction of a circle or the quantity of materials needed.
- 211f: Equate the area of fractions of circles or full circles to determine a length.
- 211g: Determine the shaded area where a semicircle is enclosed in a rectangle.
- 212a: Determine the perimeter of a standard running track.
- 212b: Determine the perimeter of a compound shape involving a rectangle and a fraction of a circle.
- 213a: Determine the area of an annulus/ring.
- 213b: Determine the area of a fraction of an annulus/ring.
- 213c: Determine the shaded area where a circle is enclosed in a square.
- 213d: Determine the shaded area where one or more circles is enclosed in a rectangle.
- 213e: Determine the exact shaded area where one or more circles is enclosed in a rectangle.
- 213f: Determine the remaining area where a semicircle is cut from a quarter circle.
- 213g: Determine the area of a polygon joined to a fraction of a circle.
- 213h: Determine the area of a segment formed within a quarter circle.
- 213i: Solve problems involving cost and a composite shape with curved areas.
- 211: Exam Practice: Area or perimeter of simple fractions of circles
- 212: Exam Practice: Perimeter of compound shapes that includes curved edges
- 213: Exam Practice: Area of composite shapes involving circles
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.1 Area of a Sector & Segment
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Area of a Sector
Corbett Maths Area of a Segment
Online Platforms (with Videos & Exercises)
- Khan Academy
- Area of a sector: Videos & practice
Activities & Resources
- Pixi Maths
- Andy Lutwyche
- Don Steward
- Goal Free Problems
- Mr Draper Maths Maths You Can Redraft
- Go Teach Maths
- Desmos
- Sector Area (official Desmos activity from Amplify’s UK GCSE collection: link sector angle, sector area and circle area)
- Jo Morgan
- Miss Konstantine (MathsHKO)
- Middleton Maths
- BossMaths
- CP3 Maths (cparkinson3)
Worksheets
- Dr Austin Maths
- Corbettmaths
- Area of a Sector Practice Questions & Solutions
- Area of a Sector Worksheet & Solutions
- Area of a Segment Practice Questions & Solutions
- Area of a Segment Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
- Mathshelper (Jon Stone)
- Maths Genie
- Sector Areas and Arc Lengths: Booklet · Worksheet · Solutions · Lesson · Topic page
- Mathsaurus (Kevin Olding)
- Naiker Maths
- Sectors & Arcs: Worksheet
- Physics & Maths Tutor
- Access Maths
- MME
- @taylorda01
- Starting Points Maths
- Mr Morley Maths
- Arc Length and Area of a Sector: Notes jotter/worksheet · How-to sheet · Exam questions · Mark scheme
- Pret Homework (Diane Cooley)
- Area of Circles and Sectors (Diane Cooley, docx)
Dr Frost Resources
Dr Frost Video
K501: Find the Area of the Sector of a Circle.
K502: Find the Radius of a Sector Given its Area and Angle.
K503: Find the Angle of a Sector Given its Area and Radius.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 319a: Calculate the area of the sector of a circle.
- 319b: Determine the angle of a sector given its area and radius.
- 319c: Determine the radius of a sector given its area and angle.
- 319d: Determine the area of a portion of an annulus given the area of a sector.
- 319e: Determine the area of a sector given its arc length.
- 319f: Determine the perimeter or arc length of a sector given its area.
- 467i: Calculate the area of a segment of a circle, given the radius of the circle and the angle.
- 467j: Calculate the area of a segment of a circle, given the radius of the circle and chord length.
- 467k: Calculate the length of an arc given the area of the segment.
- 467m: Determine the area of a compound shape consisting of a triangle and sector.
- 467r: Determine the shaded area in overlapping circles.
- 319: Exam Practice: Area of more general sectors
- 467: Exam Practice: Area of a triangle using two lengths and the angle between them
Further Practice
- Practise Questions
Extension Materials
Worksheet
2.2 Perimeter of a Sector
Teaching Videos, Exercises & Activities
Tutorial Videos
Corbett Maths Arc Length
Online Platforms (with Videos & Exercises)
- Khan Academy
- Arc length (degrees): Videos & practice
Activities & Resources
- Pixi Maths
- Don Steward
- Go Teach Maths
- BossMaths
Worksheets
- Dr Austin Maths
- Corbettmaths
- Arc Length Practice Questions & Solutions
- Arc Length Worksheet & Solutions
- Maths 4 Everyone
- Pixi Maths
Dr Frost Resources
Dr Frost Video
K498: Find the Perimeter of a Sector of a Circle.
K499: Find the Radius of a Sector Given its Arc Length and Angle.
K500: Find the Angle of a Sector Given its Arc Length and Radius.
Dr Frost Slides & Activities
- All in one summary sheet
Topic Tests
- Standard Test
- Advanced Test
Extra Questions
- Dr Frost Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 318a: Calculate the arc length of a sector of a circle.
- 318b: Calculate the perimeter of a sector of a circle.
- 318c: Determine the angle of a sector given its arc length and radius.
- 318d: Determine the radius of a sector given its arc length and angle.
- 318e: Determine the perimeter of a portion of an annulus.
- 466b: Determine the perimeter of a segment or a compound shape consisting of a sector and a triangle.
- 318: Exam Practice: Arc length of more general sectors
- 466: Exam Practice: Cosine rule (Law of Cosines)
Further Practice
- Practise Questions
Extension Materials
Worksheet
Whole Topic Summary Resources (Including Past Paper Questions)
Download Circles & Sectors PPQs as WW Powerpoint for Edexcel IGCSE, AQA GCSE, Edexcel GCSE or OCR GCSE (or all GCSE together)
Other Whole Topic Resources
Acute Learning Problem Pairs
- Circle area/circumference as PowerPoint or PDF
Worksheets
- Dr Austin Maths
- Maths 4 Everyone
- MathedUp
- Circumference & Area of Circles: Worksheet · Practice · Quiz · Question Gallery
- Arc Length & Sector Area: Worksheet · Practice · Quiz · Question Gallery
- Access Maths
- Problem Pentagons: Functional Circles | Functional Circle Area
- Formula Tetrahedron: Circles
Activities
- NRICH (student problems)
- Don Steward
- The Chalkface
- Polygon Pi: PDF
- @drpas1001
- Mathigon
- Henk Reuling
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.