Units
Convert standard and compound units and preserve dimensional meaning in numerical and algebraic contexts.
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
Convert related mass, length, time, area, volume and capacity units.
Exam cue: Write the target unit before converting.
Concept 2
Interpret compound units such as speed, price, density and pressure.
Exam cue: Convert every input to a compatible system before substitution.
Concept 3
Use dimensional consistency to test a derived expression or answer.
Exam cue: Track squared and cubed conversion factors explicitly.
Risk pitfalls and guardrails
Applying a linear factor to an area or volume.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Combining quantities expressed in incompatible units.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Dropping the denominator meaning from a compound unit.
Guardrail: Do not treat examples as proof, reverse an implication, cancel a possible zero or rely on calculator-only intuition.
Memory anchors
Unit first
Name the required output unit before calculating.
Compatible inputs
Convert quantities before adding, comparing or substituting.
Square factor
An area conversion uses the square of the length factor.
Cube factor
A volume conversion uses the cube of the length factor.
Compound reading
Read km h⁻¹ or £ kg⁻¹ as a ratio of quantities.
Dimension check
Both sides of a valid physical equation have matching dimensions.
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
A car travels 150 km in 2 h 30 min. What is its average speed in m/s?
A tank holds 2.4 m³. How many 300 cm³ cups could exactly fill it?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
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