Units, Number and Exact Calculation
Work fluently with standard and compound units, fractions, indices, surds, standard form, bounds and estimation without a calculator.
How to prepare for the current ESAT
Confirm your course combination, build no-calculator fluency from Mathematics 1 upward, and use official Pearson materials for authentic timing and interface rehearsal.
Core concepts
Concept 1
Convert related units before combining quantities and preserve compound-unit meaning.
Exam cue: Write the target unit beside the quantity before converting.
Concept 2
Use exact fractions, surds, powers and standard form until an approximation is requested.
Exam cue: Look for cancellation and exact structure before doing decimal arithmetic.
Concept 3
Distinguish upper and lower bounds from rounded values and choose appropriate accuracy.
Exam cue: Use interval endpoints when a rounded measurement is involved.
Risk pitfalls and guardrails
Applying a linear conversion factor to area or volume.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Rounding an intermediate value and losing the correct option.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Treating a displayed rounded value as exact.
Guardrail: Do not use calculator-dependent shortcuts, import a fact outside the annual specification or overlook a unit, sign, scale or course-module boundary.
Memory anchors
Unit first
Convert every quantity to compatible units before substitution.
Square and cube
Area factors square; volume factors cube.
Exact before decimal
Keep fractions, surds and π exact until approximation is needed.
Standard form
Write a × 10ⁿ with 1 ≤ a < 10.
Bounds
A rounded value represents an interval, not one exact input.
Estimate
Use simple nearby values to test order of magnitude.
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
Convert 72 km h⁻¹ to m s⁻¹.
A rectangle is 3.2 m by 45 cm. What is its area?
Answer all questions to submit.
Next step personalized recommendations
Continue learning
Move forward only after this module is stable.
What is Pass Harbor?
Completely free exam prep for 247 UK exams.
- Practice questions
- Flashcards
- Study guides
- Mock exams
- No registration
- No paywall
- Start instantly
“No more expensive exam prep. Quality study tools should be accessible to everyone.”