A worksheet on proving theorems using direct proof. Detailed solutions are included.

Master the fundamentals of 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 12 carefully scaffolded questions complete with a step-by-step, fully worked mark scheme. Help your students build confidence with direct proofs using integer parity, divisibility laws, and rational number properties.

Save time planning and give your students the exact scaffolding they need to master the art of writing formal mathematical proofs!
This ready-to-print resource features 12 carefully curated direct proof questions designed to transition students from basic number properties to formal, rigorous logical arguments. It covers fundamental mathematical concepts like even and odd integers, consecutive integers, divisibility definitions, inequalities, and the closure of rational numbers. Whether you are introducing proof structure to Year 12 students or running intensive revision sessions for Year 13, this pack has you covered.

What’s Included:
• 12 High-Quality Proof Questions: Covers integer parity (even and odd formulas), divisibility rules (proving a divides b + c), consecutive integer perfect squares, the arithmetic-geometric mean inequality, and proving the sum of two rational numbers is rational.
• 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 template for students learning how to structure an algebraic proof cleanly.

Curriculum & Exam Board Alignment:
• A-Level Mathematics (Year 12 & 13 Pure Maths): Explicitly maps to the foundational 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 and algebraic reasoning.

Ways to Use This Resource in Your Classroom:
• Guided Lesson Support: Walk through the first few proofs together to model definitions before letting students work 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 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.