1.3 Index laws including standard form
Interpret index notation, apply index laws and calculate with standard-form values at the correct tier and unit scope.
How to study WJEC GCSE Mathematics and Numeracy
Move from concept and notation to a justified method, show a complete mathematical chain, check scale and units, and interpret the answer in context.
Core concepts
Concept 1
Use positive, zero, negative and fractional index notation where specified.
Exam cue: Confirm the unit, entered tier, calculator condition and available formula list before choosing a method.
Concept 2
Apply multiplication, division and power index laws.
Exam cue: Keep the coefficient in standard form between 1 and 10 and normalise after every operation.
Concept 3
Convert between ordinary numbers and standard form and calculate with standard-form quantities.
Exam cue: Show a complete mathematical chain, use correct notation and units, and interpret or check the result in its original context.
Concept 4
Current matrix coverage: Unit 1, Unit 2, Unit 3. Read the exact subpoint scope in each applicable unit column.
Concept 5
Foundation content is shown in standard type in the specification; bold additions apply only to Higher Tier.
Risk pitfalls and guardrails
Multiplying coefficients correctly but adding or subtracting powers incorrectly when applying an index law.
Guardrail: Do not import the outgoing separate qualifications, assume a universal tier across units or ignore calculator, formula-list, context and accuracy conditions.
Assuming that every subpoint in a cross-unit strand appears in all three papers, rather than reading the correct matrix column.
Guardrail: Read the precise subpoint in the applicable unit column; a cross-unit strand does not mean every subpoint appears in every paper.
Using a Higher-only method or expectation for a Foundation entry, or importing the outgoing Mathematics/Mathematics-Numeracy structure.
Guardrail: Standard type applies to Foundation and Higher; bold specification additions are Higher-only. There is no Intermediate Tier.
Memory anchors
Index
An index records repeated multiplication or a generalised power relationship.
Zero index
For non-zero a, a to the power zero equals one.
Negative index
A negative index represents the reciprocal of the corresponding positive power.
Fractional index
A fractional index combines roots and powers.
Standard form
Standard form is a × 10ⁿ with 1 ≤ |a| < 10 and integer n.
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
Use the index law for equal bases to evaluate 2⁵ × 2³.
Simplify the quotient 5⁷ ÷ 5⁴ to a numerical value.
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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