Number
Calculate exactly with signed numbers, fractions, indices, surds and standard form and use bounds, rounding and estimation.
How to prepare for the current TMUA
Secure the shared mathematical specification, practise application in unfamiliar settings, then make every Paper 2 implication and proof step explicit.
Core concepts
Concept 1
Use operations, factors, multiples, powers and exact forms without a calculator.
Exam cue: Look for exact cancellation before decimal approximation.
Concept 2
Move between fractions, decimals, percentages and standard form.
Exam cue: Use prime factorisation when divisibility structure matters.
Concept 3
Interpret rounded measurements as intervals and estimate appropriate magnitudes.
Exam cue: Write lower and upper endpoints for a rounded input.
Risk pitfalls and guardrails
Rounding an intermediate result too early.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Treating a displayed rounded value as exact.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Applying index laws across addition.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Order of operations
Brackets and powers precede multiplication, division, addition and subtraction.
Exact before decimal
Keep fractions, surds and π exact until approximation is requested.
Standard form
Write a × 10ⁿ with 1 ≤ a < 10.
Index product
For the same base, multiplication adds exponents.
Bounds interval
A rounded value represents a range of possible exact values.
Magnitude check
Estimate with nearby simple values before trusting an answer.
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
What is the greatest common divisor of 756 and 630?
What is the least positive integer divisible by 12, 18 and 30?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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