Chapter 1
Chapter 1: Real Numbers
Fundamental Theorem of Arithmetic, prime factorisation, HCF/LCM and proofs of irrationality.
6 topics15 skillsWorksheets available
Practice questionsWorksheets availableMore practice coming soonProgress tracking after sign-in
Topic: Prime Factorisation
2 skillsSkill: Identify prime and composite numbersClassify numbers as prime, composite or neither using divisibility and factor checks
Practice areaSkill: Express numbers as product of primesWrite a natural number uniquely as a product of prime factors
Practice areaTopic: Fundamental Theorem of Arithmetic
2 skillsSkill: State the Fundamental Theorem of ArithmeticExplain existence and uniqueness of prime factorisation with examples
Practice areaSkill: Use prime factorisation to compare numbersCompare and reason about numbers using their prime factor forms
Practice areaTopic: HCF and LCM
5 skillsSkill: Find HCF using prime factorisationCalculate highest common factor from common prime powers
Practice areaSkill: Find LCM using prime factorisationCalculate least common multiple from maximum prime powers
Practice areaSkill: Verify the HCF-LCM product relationUse HCF × LCM = product of two numbers and check when it applies
Practice areaSkill: Solve daily life problems using HCFModel grouping, sharing and arrangement situations using HCF
Practice areaSkill: Solve daily life problems using LCMModel repetition, timing and synchronization situations using LCM
Practice areaTopic: Irrationality Proofs
4 skillsSkill: Recognise proof by contradiction in irrationalityFollow the contradiction structure used in irrationality proofs
Practice areaSkill: Prove √2 is irrationalWrite a complete algebraic proof that √2 is irrational
Practice areaSkill: Prove √3 and √5 are irrationalAdapt the irrationality proof method to √3 and √5
Practice areaSkill: Prove numbers like 3 + 2√5 are irrationalUse closure and contradiction to prove expressions involving surds are irrational
Practice areaTopic: Real Number Reasoning
1 skillSkill: Identify common errors in irrationality argumentsDetect invalid assumptions and incomplete contradiction steps
Practice areaTopic: Real Number Applications
1 skillSkill: Connect FTA to real-life counting contextsUse prime factors to explain packaging, tiling and repetition patterns
Practice area