Proof by Contradiction Worksheet & Answer Key | Discrete Math

A worksheet on proving statements using proof by contradiction. Detailed solutions are included.

Master the fundamentals of indirect mathematical logic and proof writing with this comprehensive, print-and-go A-Level Mathematics resource! Perfect for Year 12 and Year 13 Pure Maths students, this activity contains 10 classic contradiction questions complete with a step-by-step, fully worked mark scheme. Help your students build confidence with indirect proofs covering integer parity, divisibility, the irrationality of root 2, and the infinitude of primes.

Save time planning and give your students the exact structural scaffolding they need to master indirect proofs!
This ready-to-print resource features 10 classic proof by contradiction questions designed to transition students from basic number properties to formal, rigorous logical arguments. It walks students through foundational concepts like even and odd integer parity, the irrationality of the square root of 2, the infinitude of prime numbers, and algebraic inequalities. Whether you are introducing indirect proofs to Year 12 students or running intensive revision sessions for Year 13, this pack has you covered.

What’s Included:
• 10 High-Quality Proof Questions: Features essential proof benchmarks including proving there is no largest integer, the sum of consecutive integers is odd, the irrationality of root 2, the infinitude of primes, and the difference of two primes.
• Fully Worked Mark Scheme: A comprehensive, step-by-step breakdown of solutions is provided for every single question—perfect for quick teacher assessment or independent student self-checking!
• Structured Learning Framework: Features an organized layout that provides an excellent mathematical template for students learning how to assume the opposite, find a contradiction, and finish a logical argument cleanly.

Curriculum & Exam Board Alignment:
• A-Level Mathematics (Year 12 & 13 Pure Maths): Explicitly maps to the Proof strand across all major UK exam boards including Edexcel, AQA, OCR, and OCR MEI.
• Advanced Higher / International Baccalaureate (IB): Ideal for higher-level math courses requiring formal methods of proof, contradiction logic, and algebraic reasoning.

Ways to Use This Resource in Your Classroom:
• Guided Lesson Support: Walk through classical proof strategies (such as the root 2 proof) together to model writing style before letting students tackle properties of integers independently.
• Independent Homework: Reinforce your daily logical reasoning lesson with targeted skill practice.
• Revision & Exam Prep: Excellent for structured unit reviews ahead of mocks or final A-Level examinations to secure those vital reasoning and proof marks.
• Cover Lessons: Clear question prompts and a complete step-by-step mark scheme make this an incredibly low-maintenance resource to hand over for a cover class.