Radians

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Word Doc

PDF

A2 Maths – Pure – Intro to Radians

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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5A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Radians 1 • What are radians? • P2 Ex5A/B • 💡

Radians 2 • Converting between Degrees and Radians • P2 Ex5A/B • 💡

Radians 3 • Graphs and Trig Functions • P2 Ex5A/B • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (Part 3 up to 2:36 only)

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 1-9✦

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

• 584a: Understand the definition of radians and convert between degrees and radians.
• 584: Exam Practice: Using radians for arc lengths and areas of sectors, and lengths, angles and areas of triangles

Other Videos & Multimedia

Radians

Courtesy of Maths Genie (Up to 2:07)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• risps.co.uk Radians RISP (& Teacher Notes)
• MEI Radians Activities✦ (Activity 1)
• Math = Love (Sarah Carter)
  • Radians & Degrees activities
  • Radians to Degrees Search Puzzle
  • Degrees & Radians Tarsia
  • Printable Radian Sectors
  • Radian arts & crafts activity
  • Radians & Degrees War
  • Radians & Degrees Foldable
  • What is a Radian? Hands-On
• Interactive Maths
  • Radian & Degree Conversions: QQI | 10QQI | Count Down | Relay | Bingo
  • Radian & Degree Conversions: Worksheets

Worksheets

• Solomon C2 Worksheet B and Solutions B (Q1-4 only)
• Starting Points Maths
  • Radian Measure: Intro

A2 Maths – Pure – Trigonometry in Radians

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Download Slides

5B Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Radians 3 • Graphs and Trig Functions • P2 Ex5A/B • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths (From 2:36)

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 10-11✦

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

• 585a: Determine the period (in radians) of a sinusoidal graph given two points on the graph. (not yet active)
• 585b: Determine the period (in radians) of a sinusoidal function given in the form y = a sin (bx + c) (not yet active)
• 585c: Determine the equation of the midline of a sinusoidal function given in the form y = a sin (bx + c) + d (not yet active)
• 585d: Determine the amplitude of a sinusoidal function given in the form y = a sin (bx + c) + d (not yet active)
• 585: Exam Practice: Properties of sinusoidal graphs (in radians) and sinusoidal modelling

Other Videos

Radians

Courtesy of Maths Genie (From 2:07 to 2:27)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• MEI Radians Activities✦ (Activity 2)
• Andy Lutwyche
  • Exact Trigonometric Codebreakers (Involving Degrees)
• Transum
  • Common Trig Ratios Radians
• Underground Mathematics
  • Trig tables✦
  • Can you find… trigonometry edition✦
  • Muddled Trig✦

Worksheets

• Solomon C2 Worksheet D and Solutions D (Q4 & 12)

A2 Maths – Pure – Arc Length using Radians

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

5C Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Radians 4 • Arc Length • P2 Ex5C • 💡

Radians 5 • Arc Lengths tricky questions • P2 Ex5C • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost slides 12-16✦

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

• 584b: Determine the length of an arc of a sector where the angle is in radians. (not yet active)
• 584c: Determine the radius or angle subtended by the arc given the arc length or perimeter. (not yet active)
• 584d: Determine the perimeter of a portion of an annulus where the angle is in radians. (not yet active)
• 584: Exam Practice: Using radians for arc lengths and areas of sectors, and lengths, angles and areas of triangles

Other Videos

Radians

Courtesy of Maths Genie (From 4:10)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions (Only First Two on Arc Length)
• Goal Free Problems
  • A-Level Trigonometry set Q11

Worksheets

• Solomon C2 Worksheet B and Solutions B (Q5-8 Only)
• Physics & Maths Tutor
  • Arc Length and Sector Area: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q6, 38, 58, 92, 95 (difficulty 2–4 of 5)

A2 Maths – Pure – Sector Area in Radians

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

5D Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Radians 6 • Sector and Segment Areas • P2 Ex5D • 💡

Radians 7 • Sector Exam Question • P2 Ex5D • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 17-22✦

Exam Practice

• Exam Practice

Extra Questions

• Dr Frost Questions (Big)

Key Skills

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

• 584e: Determine the area of a sector where the angle is in radians. (not yet active)
• 584f: Use basic trigonometry and sine/cosine rules (Laws of Sines/Cosines) when the angles are in radians. (not yet active)
• 584g: Use the area of a triangle formula where the angle is in radians. (not yet active)
• 584h: Determine the perimeter of a segment where the angle is in radians. (not yet active)
• 584i: Determine the area of a segment where the angle is in radians. (not yet active)
• 584j: Determine the perimeter of a region obtained by removing a triangle from a sector. (not yet active)
• 584k: Determine the area of a region obtained by removing a triangle from a sector. (not yet active)
• 584l: Determine the area of a sector where the angle is obtained using trigonometry. (not yet active)
• 584m: Determine the perimeter of a composite shape involving a sector. (not yet active)
• 584n: Determine the area of a shape involving subtraction of a sector. (not yet active)
• 584o: Determine the angle or radius of a sector given an area involving subtraction of the sector. (not yet active)
• 584p: Solve problems involving area or perimeter of a sector with algebraic lengths/angles. (not yet active)
• 584q: Determine the angle and radius of a sector given its perimeter and area. (not yet active)
• 584: Exam Practice: Using radians for arc lengths and areas of sectors, and lengths, angles and areas of triangles

Further Practice

• Practise Questions

Other Videos

Radians

Courtesy of Maths Genie (From 2:27 to 4:10)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions 1 · 2
• MEI
  • Fill in the Blanks✦
  • Radians Activities✦ (Activity 4, Similar to Above)
• Goal Free Problems
  • A-Level Algebra & Coordinate Geometry set Q13 | A-Level Trigonometry set Q1, Q2, Q4, Q5, Q6, Q7, Q16, Q17, Q19, Q22, Q23, Q24, Q25
• Mathematics Assessment Project
  • Sectors of Circles✦
• SRWhitehouse
  • Radians, arcs and sectors✦
• Underground Mathematics
  • Sector spirals✦

Worksheets

• Jethwamaths Starters
• Solomon C2 Worksheet B and Solutions B (Q9-13 only)
• Solomon C2 Worksheet C and Solutions C
• MathedUp
  • Triangles & sectors: Questions · Challenge · Answers
• MadAsMaths (T. Madas)
  • Geometric Mensuration Q1–3, 5, 7–8, 13–16, 18–31, 35–36, 39–44, 47, 49–50, 53, 55–57, 59–61, 63–65, 69–70, 72–74, 76, 78–79, 81–83, 85–86, 88–89, 91, 93–94, 104, 106–107, 111–112, 117 (difficulty 2–5 of 5)
  • Advanced Mensuration Q6 (difficulty 5 of 5)

Exam Practice

• WW PPQ Section on Radians – Go to Old Spec Questions for Numerous PPQs on this.

A2 Maths – Pure – Solving Trig Equations in Radians Mode

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

5E Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Radians 8 • Solving Equations • P2 Ex5E • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 23-24✦

Extra Questions

• Dr Frost Questions (limited)

Key Skills

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

• 587a: Solve a trigonometric equation given in the form sin ≤ft(axright) = k where x is in radians.
• 587b: Determine the minimum or maximum point(s) of a trigonometric graph, in radians. (not yet active)
• 587c: Determine the roots, in radians, of a trigonometric graph y = a + b sin(cx) (not yet active)
• 587d: Solve an equation, in radians, given in the form sin(kx) = a cos(kx) (not yet active)
• 587e: Determine the points of intersection of two trigonometric graphs, in radians. (not yet active)
• 587g: Solve a trigonometric inequality given in the form sin(kx) < a in radians. (not yet active)
• 587h: Solve a trigonometric equation, in radians, which can be written as a mixture of sin and cos where one is squared. (not yet active)
• 587: Exam Practice: Solving trigonometric equations, involving sin, cos and tan, in an interval in radians

Other Videos

Solving Trigonometric Equations

Courtesy of Maths Genie (From 7:55 to 12:54)

Solving Quadratic Trigonometric Equations

Courtesy of Maths Genie (From 2:52 to 7:08)

Also See AS Trigonometry Course Support

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activity

• MEI Radians Activities✦ (Activity 3)

Worksheets

• Solomon C2 Worksheet E and Solutions E (Q4 & 7)
• Solomon C2 Worksheet F and Solutions F (Q4)
• Naiker Maths
  • Solving Trigonometric Equations in Radians: Exam Qs 2005–11✦ · Mark scheme✦ · Exam Qs 2012–17 · Mark scheme
• MadAsMaths (T. Madas)
  • Trigonometric Equations Introduction Q7, 9–13, 16–17, 29–32, 35–36
  • Trigonometry Introduction Exam Equations Q4, 10, 15–16, 18, 21, 26, 28–29, 31, 36, 40, 42–43, 50, 52, 55–56, 59–61, 63, 65, 67, 74 (difficulty 2–5 of 5)

A2 Maths – Pure – Small Angle Approximations

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

Download Blank Notes

Download Slides

5F Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Radians 9 • Small Angle Approximations • P2 Ex5F • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

Download Blank Notes

(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 25-28✦

Exam Practice

• Exam Practice

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

• 586a: Simplify expressions involving sin or tan using small angle approximations. (not yet active)
• 586b: Simplify expressions involving cos using small angle approximations. (not yet active)
• 586c: Simplify expressions involving cos of angles kθ using small angle approximations. (not yet active)
• 586d: Approximate the solution of an equation using small angle approximations. (not yet active)
• 586e: Determine a small angle approximation for a root of cos x by use of a binomial expansion. (not yet active)
• 586: Exam Practice: Small angle approximations for sin, cos and tan when in radians

Further Practice

• Practise Questions

Other Videos

Small Angle Approximations

Courtesy of Maths Genie

A-Level Maths E2-01 Small-Angle Approximation: Geometrical Derivation

TLMaths Deriving the formulae (requires knowledge of double angle formulae for cos)

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• Berwick Maths Diagnostic Questions
• NRICH
  • What do functions do for tiny x?✦

Worksheets

• Jethwamaths Worksheet (p11-12) and Topic Test (p1-2)
• Physics & Maths Tutor
  • Small Angle Approximation: Questions 2021–24 · Mark scheme · Model answers · Questions 2018–21 (with MS) · Model answers
• MME
  • Small Angle Approximations: Questions | Answers
• MadAsMaths (T. Madas)
  • Trigonometry Exam Questions Standard Questions Q60–61, 78, 80, 94, 108 (difficulty 3–4 of 5)

External Whole Topic Past Paper Style Questions

• Dr Frost Topic Tests✦ (Teacher Login Required)
• NaikerMaths Arc length and Sector Area Exam Questions✦ (Solutions)✦
• PMT
  • Edexcel
    • Arc Length and Sector Area
  • OCR
    • Radians
    • Small Angle Approximations
  • OCR MEI
    • Radian Exam Questions 1 QP✦ (MS✦)
    • Radian Exam Questions 2 QP✦ (MS✦)
    • Radian Exam Questions 3 QP✦ (MS✦)
    • Radians
  • Cheat Sheet

Worksheets

• Maths Genie
  • Radians: Questions · Solutions · Lesson · Topic page
• Jethwa Maths
  • Year 2 Trigonometry: Worksheets · Unit Test
• Mathsaurus (Kevin Olding)
  • Trigonometry: radians (exam questions)
• Dr Austin Maths
  • Degrees Conversions Fill in the Blanks (Word | PDF | Answers)
  • Arc Length and Perimeter Match-Up (Word | PDF | Answers)

Activities

• MEI
  • MEI teaching notes, misconceptions & prompts: Trigonometry✦
• Andy Lutwyche
  • Erica’s Errors