Integers, Order and Operations
Order positive and negative numbers and calculate accurately with the four operations and order of operations.
How to study for GCSE Mathematics
Use 601 original multiple-choice questions to learn connected methods, explain why they work, practise exact non-calculator execution and use a calculator strategically on designated papers.
Core concepts
Concept 1
Directed numbers and number lines
Exam cue: Translate signs and brackets carefully, complete powers and roots before multiplication or division, then addition or subtraction.
Concept 2
Four operations and inverse operations
Exam cue: Estimate the sign and magnitude, then use the inverse operation to test the result.
Concept 3
Order of operations
Exam cue: Represent the information clearly, choose a justified method and communicate each step with correct notation and units.
Targeted study blocks
Tier coverage
Foundation and Higher
The core techniques are assessed at both tiers. Higher questions can combine them with less scaffolding, algebraic generalisation and unfamiliar multi-step contexts.
Calculator structure
Prepare for calculator and non-calculator papers
Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Risk pitfalls and guardrails
Treating subtraction of a negative number as subtraction of its size.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Giving an unsupported answer when the command requires working, proof, reasoning or interpretation.
Guardrail: Do not hide an invalid model behind arithmetic: check assumptions, signs, bounds, units, scale, required accuracy and the original question.
Assuming a topic belongs only to calculator or non-calculator papers; any specification content can be assessed on any paper.
Guardrail: Any part of a board's specification may be assessed on any paper. Non-calculator does not define a smaller syllabus; questions are designed so exact arithmetic and reasoning are feasible without a calculator.
Memory anchors
Subtracting a negative
Adding the opposite is equivalent to subtraction.
Order of operations
Brackets, indices, multiplication or division, then addition or subtraction.
Multiplicative inverse
A non-zero number and its reciprocal multiply to 1.
Integers, Order and Operations: method
Translate signs and brackets carefully, complete powers and roots before multiplication or division, then addition or subtraction.
Integers, Order and Operations: check
Estimate the sign and magnitude, then use the inverse operation to test the result.
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
Foundation · AO1 technique · Non-calculator — Calculate −7 + 12 − 5.
Foundation · AO1 technique · Non-calculator — Evaluate 18 ÷ (−3) + 4.
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.”