Proof

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A2 Maths – Proof by Contradiction

Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.

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Download Slides

1A Slides (Courtesy of Owen134866)

Bicen Maths Live Lesson

Proof 1 • Proof by Contradiction • P2 Ex1A • 💡

Proof 2 • Contradiction with Rational and Irrational Numbers • P2 Ex1A • 💡

Proof 3 • 'Infinitely many primes' proof • P2 Ex1A • 💡

Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths

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(Courtesy of King’s Chester Maths Department)

Download Slides

• Dr Frost Slides 1-11✦
• Dr Frost Algebraic Methods Section

Key Skills

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

• 562a: Write the negation of a statement, including conditional statements. (not yet active)
• 562b: Prove by contradiction that there is no greatest number with some property. (not yet active)
• 562c: Prove by contradiction some statement about the evenness/oddness of squares or cubes. (not yet active)
• 562d: Prove by contradiction that the arithmetic combination of some pair of irrational/rational numbers is irrational. (not yet active)
• 562e: Prove by contradiction that there are infinitely many prime numbers. (not yet active)
• 562f: Prove by contradiction that a surd is irrational. (not yet active)
• 562: Exam Practice: Proof by contradiction

Other Videos

Root 2 – Numberphile

Numberphile Proof of root 2 & Pythagoras the murderer?

Vihart Alternative root 2 approach & was Pythagoras a murderer?

Note this Simon Gregg article defending Pythagoras

Proof by Contradiction

Courtesy of Maths Genie

Legally Blonde (11/11) Movie CLIP – Elle Wins! (2001) HD

Legally Blonde Court Room Scene Proof by Contradiction

Enrichment Video

Infinite Primes – Numberphile

Numberphile: Infinite Primes

Alternative Handouts

• Acute Learning Problem Pairs as PowerPoint or PDF

Activities

• MEI √2 Proof Sort✦ (Including 2 Proofs and One Mistake to Find)
• undergroundmaths √2 Proof Sort✦
• The Chalk Face Primes True or False to Lead in to Infinite Primes Proof by Contradiction
• Ticktock Maths
  • Proof by Contradiction lesson (slides)

Worksheets

• Jethwamaths Starter Activity (p1-2)
• Maths Made Easy Questions & Solutions
• advancedhighermaths.co.uk Ex 5, Ex 5 Typed Solns, Ex 5 Handwritten Solns
• Mathshelper (Jon Stone)
  • Proof That Root 2 Is Irrational
• Naiker Maths
  • Proof by Contradiction: Extra practice · Solutions
• MME
  • Proof by Contradiction 2: Questions | Answers
• MadAsMaths (T. Madas)
  • Number Theory Q16 (difficulty 3 of 5)
  • Proof (General) Q6, 7, 9, 14, 15, 17, 22, 23, 26, 27, 42, 45 (difficulty 2–5 of 5)

External Whole Topic Past Paper Style Questions (Covering All Proof)

• CrashMaths Proof Worksheet✦ (Solutions✦)
• Jethwamaths Worksheet & Topic Test
• Solomon C3 Proof Worksheet A (Answers), Worksheet B (Answers)
• phildb Proof Worksheet✦ (TES Account Required)
• Dr Frost Topic Test✦ (Teacher Login Required)
• PMT
  • OCR Proof
  • OCR MEI Proof (Yr. 2)
  • Cheat Sheet (First Column Only)

Activities

• NRICH (student problems)
  • Reasoning, Justifying & Proof (Advanced)
• MEI
  • MEI teaching notes, misconceptions & prompts: Proof✦

Worksheets

• Mathsaurus (Kevin Olding)
  • Proof (exam questions)
• MME
  • C3 Proof: Questions | Answers

Notes

• Physics & Maths Tutor
  • Ch.1 Algebraic Methods: Cheat sheet