Polar Coordinates

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A2 Further Maths – Core – Polar Coordinates and Equations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5A Slides (Courtesy of Owen134866)

Polar Coordinates 1 • Converting from Polar/Cartesian Coordinates • CP2 Ex5A • 🎯

Polar Coordinates 2 • Converting from Polar to Cartesian Equations • CP2 Ex5A • 🎯

Polar Coordinates 3 • Converting from Cartesian to Polar Equations • CP2 Ex5A • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 1-8

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

• 729a: Convert from Cartesian coordinates to polar coordinates.
• 729b: Convert from polar coordinates to Cartesian coordinates. (not yet active)
• 729c: Convert an equation of a curve from polar form to Cartesian/rectangular form. (not yet active)
• 729d: Convert an equation of a curve from Cartesian/rectangular form to polar form. (not yet active)
• 729e: Convert a straight line equation of a curve from Cartesian/rectangular form to polar form and simplify to a single trigonometric function. (not yet active)
• 729: Exam Practice: Conversion between polar and Cartesian coordinates

3Blue1Brown Linear transformations and matrices | Chapter 3, Essence of linear algebra

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 2×2 transformations and questions

A2 Further Maths – Core – Polar Graphs

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5B Slides (Courtesy of Owen134866)

Polar Coordinates 4 • Sketching simple equations • CP2 Ex5B • 🎯

Polar Coordinates 5 • Polar Roses, negative r values • CP2 Ex5B • 🎯

Polar Coordinates 6 • Egg vs Dimple • CP2 Ex5B • 🎯

Polar Coordinates 7 • Summary of Graph Types • CP2 Ex5B • 🎯

Polar Coordinates 8 • Loci in Argand Diagrams to Polar Form • CP2 Ex5B • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 9-19

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

• 730a: Recognise common polar graphs including r = a, θ = alpha, r = 2a cos θ and r = kθ (not yet active)
• 730b: Sketch a cardioid r = a(1 + cosθ) (not yet active)
• 730c: Sketch a polar rose r = sin kθ (not yet active)
• 730d: Sketch a polar equation given in the form r = p sec(alpha – θ) (not yet active)
• 730e: Sketch a polar equation given in the form r = a secθ (not yet active)
• 730f: Sketch a lemniscate r2 = a² cos 2θ (not yet active)
• 730g: Distinguish between variants of the generalisation of a cardioid r = a(p + qcos θ) (limaçons). (not yet active)
• 730: Exam Practice: Sketching polar curves with r given as a function of θ

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• IXL Match Polar Equations and Graphs (Max 10 per day)
• Quizizz by Lyn Hearty G11 Polar Graphs and Equations
• Ben Sparks (GeoGebra)
  • Polar Sketcher Demo: GeoGebra

A2 Further Maths – Core – Integrating Polar Curves

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5C Slides (Courtesy of Owen134866)

Polar Coordinates 9 • How does polar integration work? • CP2 Ex5C • 🎯

Polar Coordinates 10 • Polar integration preparation • CP2 Ex5C • 🎯

Polar Coordinates 11 • Area enclosed by simple curves • CP2 Ex5C • 🎯

Polar Coordinates 12 • Areas on Argand Diagrams • CP2 Ex5C • 🎯

Polar Coordinates 13 • Intersecting/Complicated Areas • CP2 Ex5C • 🎯

Polar Coordinates 14 • Strategies for Harder Areas (Spirals) • CP2 Ex5C • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 20-30

Extra Questions

• Dr Frost Questions (very short)

Key Skills

Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost

• 731a: Determine the full area under a polar curve. (not yet active)
• 731b: Determine the area under a polar curve between two half lines. (not yet active)
• 731c: Determine an unknown constant in a polar equation given the area under the curve. (not yet active)
• 731d: Determine the area between two polar curves. (not yet active)
• 731e: Determine the area between a polar curve and vertical or horizontal line. (not yet active)
• 731f: Determine the area of a polar curve extracted from another region. (not yet active)
• 731g: Use the area under a polar curve in a modelled context. (not yet active)
• 731h: Determine an area on an Argand diagram using polar coordinates. (not yet active)
• 731: Exam Practice: Determining the area enclosed by a polar curve

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 3×3 transformations and questions

A2 Further Maths – Core – Tangents to Polar Curves

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5D Slides (Courtesy of Owen134866)

Polar Coordinates 17 • Vertical and Horizontal Tangents • CP2 Ex5D • 🎯

Polar Coordinates 18 • Challenging Tangents example • CP2 Ex5D • 🎯

Polar Coordinates 19 • Proof: Dimple vs Egg • CP2 Ex5D • 🎯

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

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• Dr Frost Slides 31-37

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

• 732a: Determine the polar coordinates where the tangent is parallel to the initial line. (not yet active)
• 732b: Determine the polar coordinates where the tangent is perpendicular to the initial line. (not yet active)
• 732c: Determine the polar equation of the tangent of a polar curve parallel to the initial line. (not yet active)
• 732d: Determine the polar equation of the tangent of a polar curve perpendicular to the initial line. (not yet active)
• 732: Exam Practice: Tangents and normals to polar curves (not yet active)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Online Platform

• Bossmaths interactive 2×2 transformations and questions

Worksheet & Activities

• MEI activities from old FP1

Whole Topic Videos

Polar Coordinates 15 • Area Exam Questions: Part 1 • CP2 Ex5C Exam Qs • 🎯

Polar Coordinates 16 • Area Exam Questions: Part 2 • CP2 Ex5C Exam Qs • 🎯

Bicen Maths Exam Questions

External Whole Topic Past Paper Style Questions

• WW Dr Frost Style QQQs Word Doc, PDF (Q’s Only) or PDF (Q’s & Sol.)

Activities

• Math = Love (Sarah Carter)
  • Polar Functions activities
• NRICH (student problems)
  • Polar Coordinates (Further)

Worksheets

• Jethwa Maths
  • 10 Minute Starters: Polar Coordinates
• Physics & Maths Tutor
  • CP2 Ch.5 Polar Coordinates: Questions by topic
• MadAsMaths (T. Madas)
  • Polar Coordinates Exam Questions Standard Questions Q3, 10, 11, 15, 17, 21, 23, 24; Hard Questions Q2, 3, 8; Enrichment Questions Q2, 3, 6–10 (difficulty 3–5 of 5)
• Dr Austin Maths
  • Curves Match-Up (Word | PDF | Answers)
  • More Curves Match-Up (Word | PDF | Answers)
  • Cartesian Conversions Fill in the Blanks (Word | PDF | Answers)