M2.1 Indices, Factors, Fractions and Finance
Positive index laws, prime factor decomposition, HCF and LCM, decimal and fraction operations, recurring decimals, repeated change and finance.
How to study for CCEA GCSE Mathematics
Secure fluent methods, explain mathematical reasoning and solve unfamiliar problems with a route-aware balance of non-calculator and calculator practice.
Core concepts
Concept 1
Prime factor decomposition exposes the factor structure used to find HCF and LCM.
Exam cue: Confirm the CCEA unit, tier and calculator condition before selecting a method.
Concept 2
Positive integer index laws describe repeated multiplication and division of like bases.
Exam cue: Choose between additive change and a repeated multiplier, and retain currency precision until the final money answer.
Concept 3
Repeated percentage change applies a multiplier to the current amount at every stage.
Exam cue: Show a complete mathematical chain, use appropriate notation and check that the answer is sensible in context.
Risk pitfalls and guardrails
Adding the same percentage amount repeatedly in a compound-growth context.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Importing a topic boundary, formula sheet or paper convention from an England 9-1 board.
Guardrail: Do not import an England 9-1 convention, omit cumulative prerequisites or present a calculator display as mathematical reasoning.
Giving a calculator display or unsupported answer without the reasoning, units or accuracy the question requires.
Guardrail: M5-M8 Paper 1 is non-calculator; Paper 2 and every M1-M4 assessment use a permitted calculator.
Memory anchors
Prime factor decomposition
A number written as a product of prime powers.
Highest common factor
The greatest positive factor shared by all given numbers.
Lowest common multiple
The smallest positive multiple shared by all given numbers.
Index law
A rule for combining powers with a common base.
Recurring decimal
A decimal with a digit or block that repeats indefinitely.
Multiplier
The factor used for a proportional or percentage change.
Checkpoint rule
Do the check-up only after you can summarize each concept in one sentence and identify one dangerous pitfall from memory.
Knowledge Check (after reading)
Short check-up to confirm understanding of this module.
Check-up Questions
Write 360 as a product of prime powers.
Using their prime factors, determine the greatest integer that divides both 84 and 126.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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