Prior Content: GCSE/IGCSE Algebraic Proof
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Next Section: Binomial Expansion
Contents
- Whole Topic Notes
- 7D Algebraic Proof
- 7E Proof by Exhaustion, Counter-Example and Using Jotting
- Whole Topic Summary Resources (Including Past Paper Questions)
Whole Topic Notes
Download Full Topic Slides
- Textbook Notes as PPTs – Proof (Courtesy of Owen134866)
- Textbook Notes as PPTs – Whole Chapter (Courtesy of Owen134866)
Full Notes to Accompany Slides
Dr Frost
- Dr Frost Algebraic Methods Section
- Dr Frost Algebraic Methods Slides✦
- Blank Notes to Follow Slides Word Doc & PDF Proof Only (Courtesy of King’s Chester Maths Department)
- Blank Notes to Follow Slides Word Doc & PDF Whole Chapter Notes (Courtesy of King’s Chester Maths Department)
Acute Learning Whole Chapter Problem Pairs
Notes
- Physics & Maths Tutor
- Proof (Year 1): Cheat sheet
7D Algebraic Proof
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 454a: Identify expressions that represent a multiple of an integer.
- 454b: Identify expressions that represent odd/even integers.
- 454c: Prove that a given algebraic expression is always odd/even (no bracket expansion).
- 454d: Prove that a given algebraic expression is always odd/even, requiring bracket expansion.
- 454e: Prove that a given algebraic expression is always a multiple of a number.
- 454f: Prove that a given algebraic expression is always something less or something more than a multiple of a number. (not yet active)
- 454g: Use expressions for consecutive integers.
- 454h: Prove that a sum of consecutive integers has some given property.
- 454i: Prove that the sum or difference of the squares of consecutive integers has some given property.
- 454j: Use expressions for consecutive odd/even integers.
- 454k: Prove that a sum of consecutive odd or even integers has some given property.
- 454l: Prove that a sum of the squares of consecutive odd or even integers has some given property.
- 454m: Use expressions for different odd/even integers, not necessarily consecutive.
- 454n: Prove a property about some arithmetic combination of two different odd/even numbers, not necessarily consecutive.
- 454p: Prove that an algebraic expression is a perfect square.
- 560a: Understand the structure, language and notation of proofs by deduction to show the equivalence of expressions. (not yet active)
- 560b: Use proof by deduction to show that a quadratic expression is always positive. (not yet active)
- 560c: Use proof by deduction to prove some statement about odd and even numbers. (not yet active)
- 560d: Use proof by deduction more generally where there are provided assumptions. (not yet active)
- 454: Exam Practice: Algebraic proofs involving integers
- 560: Exam Practice: Proof by deduction
Other resources
Other Videos
Courtesy of Maths Genie
TL Maths Consequences & Equivalence
TLMaths Deduction
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- mathspad.co.uk If a is an Integer✦
- Median Don Steward Consecutives✦
Worksheets
- Maths4Everyone Booklet (Questions Only), Booklet (With Notes & Examples) & Solutions
- MadAsMaths (T. Madas)
- Series Mixed Exam Questions Q25 (difficulty 5 of 5)
- Inequalities Various Inequalities Q4–7 (difficulty 3–4 of 5)
- Number Theory Q2, 6, 8, 13, 14, 20, 21, 27–30 (difficulty 2–5 of 5)
- Proof (General) Q1–3, 8, 10, 12, 13, 16, 19–21, 25, 28–41, 43 (difficulty 2–5 of 5)
7E Proof by Exhaustion, Counter-Example and Using Jotting
Textbook resources
Courtesy of Owen134866 and Haberdashers’ Adams Maths Dept.
Dr Frost resources
Bicen Maths Live Lesson
Live Lesson Using Dr Frost Based Slides Courtesy of Bicen Maths
Download Blank Notes
(Courtesy of King’s Chester Maths Department)
Download Slides
Extra Questions
- Dr Frost Questions (no Jottings or Exhaustion)
Key Skills
Note all numbers are subject to change and will be updated once all key skills have been finished by Dr Frost
- 561a: Use proof by exhaustion to show some statement is true in a provided finite range. (not yet active)
- 561b: Use proof by exhaustion to show some expression is always odd or always even. (not yet active)
- 561c: Use proof by exhaustion to prove statements involving more general divisibility. (not yet active)
- 453a: Give a counterexample to show that a conjecture is false using properties of numbers.
- 453b: Determine which conjecture is disproved by a given counterexample.
- 453c: Determine a counterexample by substitution into an algebraic expression.
- 453d: Consider the validity of more general algebraic statements, including constraints on the variables or relationships between expressions.
- 561: Exam Practice: Proof by exhaustion
- 453: Exam Practice: Testing conjectures and identifying counterexamples
Practice Questions
Other resources
Other Videos
Courtesy of Maths Genie
TL Maths Exhaustion
TL Maths Counter-Example
Alternative Handouts
- Acute Learning Problem Pairs as PowerPoint or PDF
Activities
- Underground Maths When is 6×7=42 a Counter-Example?✦
Worksheets
- Jethwa Maths Starter Activity (p5-6) (Counter-Examples)
- MadAsMaths (T. Madas)
- Number Theory Q3, 5, 12 (difficulty 2–3 of 5)
- Proof (General) Q4, 5, 11, 18, 24 (difficulty 2–4 of 5)
Whole Topic Summary Resources (Including Past Paper Questions)
Download PPQs as WW Powerpoint for AS Proof
Whole Topic Videos
Bicen Maths Exam Questions
Activities
- Berwick Maths Diagnostic Questions
- Extension Task: The Chalk Face Seven Bridges Ppt & Worksheet
- NRICH (student problems)
- University of Birmingham
External Whole Topic Past Paper Style Questions
- Jethwa Maths Worksheet (NOT Q8-11), Topic Test (NOT Q3, 5 or 6)
- Dr Frost Topic Test✦ (Teacher Log in Required)
- Mathsaurus Mixed Exam Board PPQs
- Crash Maths Topic Test & Solutions
- phildb Proof Worksheet✦ (TES Account Required)
- PMT
- OCR MEI C3 Proof – Method of Proof PPQs✦ & MS✦
- Summary Cheat Sheet
Worksheets
- Physics & Maths Tutor
- crashMATHS
- OCR
✦ Links marked ✦ are also featured and recommended by Jo Morgan on Resourceaholic.