A worksheet on mathematical induction. The exercises require to prove 10 statements using this method of proof.

A comprehensive, no-prep resource packed with 10 structured algebraic problems to master proof by induction. This progressive worksheet seamlessly guides pupils through formal mathematical proofs involving summation series, divisibility rules, and algebraic inequalities. Ideal for A-Level Maths (Pure Mathematics) and Further Mathematics revision, this print-ready resource includes a complete, step-by-step worked memorandum/answer key to support independent study, revision blocks, and hassle-free peer assessment!

Take the stress out of teaching formal proofs with this complete, scaffolded Proof by Induction Worksheet pack!
Mastering the logic of mathematical induction can be highly challenging for students. This carefully structured 10-problem booklet provides rigorous, high-quality practice covering all major styles of induction questions. It is thoughtfully organized to build student confidence, making it ideal for core teaching, independent classwork, homework assignments, or structured exam preparation.

What is Included?
• 10 Comprehensive Proof Problems: Spanning the three main categories of mathematical induction.
• Complete Step-by-Step Solutions: 6 dedicated answer pages showing every single base case, inductive hypothesis, and algebraic manipulation clearly—perfect for self-checking or displaying live on the board!
• Zero-Prep Download: Just print and you are ready to teach!

Breakdown of Proof Types Included
• Summation Series (Problems 1, 2, 3, & 7): Classic sequence proofs, including odd numbers, even numbers, standard integers, and sum of cubes (e.g. proving that the sum of r^3 from 1 to n equals [n(n + 1) / 2]^2).
• Divisibility Proofs (Problems 4, 5, & 6): Proving multi-step algebraic expressions are divisible by specific integers (e.g. proving 3^n - 1 is a multiple of 2, or 4^n + 2 is a multiple of 3).
• Inequality Proofs (Problems 8, 9, & 10): Advanced problems establishing structural boundaries across positive integers (e.g. proving 2^(n+1) is greater than n + 2).

Curriculum Focus & Target Audience
• A-Level Maths & Further Maths (Ages 16–18 / Years 12–13): Designed specifically to align with exam board modules covering formal algebraic proof.
• Core Skills: Formulating a base case, constructing an inductive hypothesis, executing rigorous algebraic steps, and writing concluding mathematical arguments.