Integers, Powers & Roots — GCSE Mathematics Revision
Revise Integers, Powers & Roots for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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Go to Factors, Multiples & PrimesWhat is Integers, Powers & Roots?
Integers are whole numbers including negatives and zero. Powers (or indices) tell you how many times to multiply a number by itself — for example, 2³ = 2 × 2 × 2 = 8. Roots are the inverse of powers: the square root of 9 is 3 because 3² = 9. You need to be confident with prime factorisation, index laws, and recognising cube numbers up to 10³.
Board notes: All boards (AQA, Edexcel, OCR) test index laws at both Foundation and Higher. Negative and fractional indices are Higher only.
Step-by-step explanationWorked example
Simplify 2⁴ × 2³ ÷ 2⁵. Using index laws: add powers when multiplying (4+3=7), subtract when dividing (7-5=2). Answer: 2² = 4.
Mini lesson for Integers, Powers & Roots
1. Understand the core idea
Integers are whole numbers including negatives and zero. Powers (or indices) tell you how many times to multiply a number by itself — for example, 2³ = 2 × 2 × 2 = 8.
Can you explain Integers, Powers & Roots without copying the notes?
2. Turn it into marks
Simplify 2⁴ × 2³ ÷ 2⁵. Using index laws: add powers when multiplying (4+3=7), subtract when dividing (7-5=2).
Underline the method, evidence, or command-word move that would earn credit in GCSE Number.
3. Fix the likely mark leak
Watch for this mistake: Confusing (-3)² = 9 with -3² = -9 — the brackets matter because the exponent only applies to what is directly before it.
Write one correction rule before doing another practice question.
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Integers, Powers & Roots practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Integers, Powers & Roots is testing.
Answer: Integers are whole numbers including negatives and zero. Powers (or indices) tell you how many times to multiply a number by itself — for example, 2³ = 2 × 2 × 2 = 8.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Integers, Powers & Roots question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Confusing (-3)² = 9 with -3² = -9 — the brackets matter because the exponent only applies to what is directly before it." What should their next repair task be?
Answer: Do one Integers, Powers & Roots question and review the mistake type.
Mark focus: Error correction and next-step practice.
Integers, Powers & Roots flashcards
Core idea
What is the main idea in Integers, Powers & Roots?
Integers are whole numbers including negatives and zero. Powers (or indices) tell you how many times to multiply a number by itself — for example, 2³ = 2 × 2 × 2 = 8.
Common mistake
What mistake should you avoid in Integers, Powers & Roots?
Confusing (-3)² = 9 with -3² = -9 — the brackets matter because the exponent only applies to what is directly before it.
Practice
What is one useful practice task for Integers, Powers & Roots?
Answer one Integers, Powers & Roots question and review the mistake type.
Exam board
How should you use board notes for Integers, Powers & Roots?
All boards (AQA, Edexcel, OCR) test index laws at both Foundation and Higher. Negative and fractional indices are Higher only.
Common mistakes
- 1Confusing (-3)² = 9 with -3² = -9 — the brackets matter because the exponent only applies to what is directly before it.
- 2Forgetting that any number to the power of 0 equals 1, not 0.
- 3Mixing up square roots and cube roots — √64 = 8 but ∛64 = 4.
- 4Not simplifying index expressions fully, e.g. leaving 2⁴ × 2³ as two separate terms instead of 2⁷.
Integers, Powers & Roots exam questions
Exam-style questions for Integers, Powers & Roots with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Integers, Powers & Roots
Core concept
Integers are whole numbers including negatives and zero. Powers (or indices) tell you how many times to multiply a number by itself — for example, 2³ = 2 × 2 × 2 = 8. Roots are the inverse of powers: …
Frequently asked questions
What are the index laws for GCSE Maths?
The three main index laws are: aᵐ × aⁿ = aᵐ⁺ⁿ (multiply → add powers), aᵐ ÷ aⁿ = aᵐ⁻ⁿ (divide → subtract powers), and (aᵐ)ⁿ = aᵐⁿ (power of a power → multiply). You also need a⁰ = 1 and a⁻ⁿ = 1/aⁿ.
Do I need to know cube numbers for GCSE?
Yes. You should memorise cube numbers up to 10³ = 1000 and their cube roots. These appear in non-calculator papers and in questions on volume.