How do I revise Number for Pearson GCSE?

Memorise square numbers up to 144.

What exam tips are there for Number? (2)

Practice rationalising denominators with conjugate pairs.

What exam tips are there for Number? (3)

Check your answers by squaring them.

What mistakes should I avoid in Number?

Incorrectly simplifying surds, e.g., √12 = 2√6.

What are common errors in Number exams? (2)

Forgetting to rationalise the denominator fully.

Number

PEARSON

GCSE

Surds involve irrational numbers expressed in square root form. Learners must simplify surd expressions, perform calculations, and rationalise denominators.

Objectives

Exam Tips

Pitfalls

Key Terms

Mark Points

Subtopics in this area

Number

Topic Overview

Number is the foundation of all mathematics, covering the properties and operations of integers, fractions, decimals, percentages, and surds. In the Pearson GCSE Mathematics curriculum, this topic ensures students can confidently manipulate numbers in both abstract and real-world contexts, from calculating interest rates to interpreting statistical data. Mastery of Number is essential for progression into algebra, ratio, and problem-solving, as it underpins every other mathematical discipline.

This topic includes place value, the four operations (addition, subtraction, multiplication, division), order of operations (BIDMAS/BODMAS), factors and multiples, prime numbers, powers and roots, standard form, and rounding. Students also explore the relationships between fractions, decimals, and percentages, and learn to work with upper and lower bounds. A strong grasp of Number allows students to approach more complex topics with confidence, as it provides the numerical fluency required for accurate calculation and logical reasoning.

In the Pearson GCSE exams, Number questions appear across all three papers (non-calculator and calculator), often as standalone problems or embedded within multi-step questions. Success in this topic requires not only procedural fluency but also a deep conceptual understanding—for example, knowing why dividing by a fraction yields a larger number, or how to estimate to check the reasonableness of an answer. By mastering Number, students build the numerical intuition that is critical for higher grades and real-life applications.

What You Need to Demonstrate

Key skills and knowledge for this topic

Simplify surds by factoring out square factors.
Add, subtract, multiply, and divide surds correctly.
Rationalise denominators with one or two terms.
Expand brackets involving surds.
Solve equations involving surds.
Converts between terminating decimals and fractions.
Defines percentage as 'number of parts per hundred'.
Interprets percentages and changes as fractions or decimals.

Marking Points

Key points examiners look for in your answers

Simplify surds by factoring out square factors.
Add, subtract, multiply, and divide surds correctly.
Rationalise denominators with one or two terms.
Expand brackets involving surds.
Solve equations involving surds.
Converts between terminating decimals and fractions.
Defines percentage as 'number of parts per hundred'.
Interprets percentages and changes as fractions or decimals.
Expresses one quantity as a fraction of another.
Applies multiplicative reasoning to percentage problems.
Use correct vocabulary for squares, cubes, and roots.
Calculate powers and roots accurately.
Recognise powers of 2, 3, 4, and 5.
Apply index notation correctly.
Use place value for decimals and integers.
Order positive and negative numbers correctly.
Identify prime numbers and factors.
Calculate highest common factor and lowest common multiple.
Award credit for correctly converting numbers into standard form with A between 1 and 10 and n as an integer.
When multiplying or dividing, credit independent handling of the A parts and the powers of 10, then adjusting the result to standard form if needed.
For addition or subtraction, credit students who first convert both numbers to the same power of 10 before operating on the A values.
Full marks depend on presenting the final answer in correct standard form unless the question specifies otherwise.

Examiner Tips

Expert advice for maximising your marks

💡Memorise square numbers up to 144.
💡Practice rationalising denominators with conjugate pairs.
💡Check your answers by squaring them.
💡Memorise common conversions like 1/2 = 0.5.
💡Practice percentage change calculations.
💡Check answers by reversing operations.
💡Memorise common powers (e.g., 2^5=32).
💡Check calculations by reversing operations.
💡Use a calculator for complex roots but show working.
💡Practise ordering negative numbers on a number line.
💡Use factor trees for prime factorisation.
💡Check answers by reversing operations.
💡Always check that your final answer has A between 1 and 10; if not, adjust the power of 10 accordingly.
💡For addition/subtraction, rewrite the number with the smaller exponent so it shares the larger exponent before combining A values.
💡Use your calculator effectively: many models have a standard form (SCI) mode that can verify your manual working.
💡Show clear steps: when dividing, subtract exponents; when multiplying, add exponents—but only after dealing with the A parts separately.

Common Mistakes

Pitfalls to avoid in your exam answers

Incorrectly simplifying surds, e.g., √12 = 2√6.
Forgetting to rationalise the denominator fully.
Mixing up addition and multiplication rules for surds.
Confuses fraction and decimal conversion methods.
Misinterprets percentage increase vs decrease.
Fails to simplify fractions correctly.
Confusing square roots with squares.
Miscalculating negative powers.
Forgetting that the square root of a number can be positive or negative.
Misplacing decimal points.
Confusing factors and multiples.
Errors in prime factorisation.
Failing to ensure that A is at least 1 and strictly less than 10, e.g., writing 0.5 × 10^3 instead of 5 × 10^2.
Adding or subtracting numbers with different powers of 10 without first adjusting one of them, leading to an incorrect A value.
Misinterpreting negative powers: thinking a negative power yields a negative number, e.g., 5 × 10^{-2} is positive 0.05, not negative.
When multiplying, incorrectly adding the powers of 10 but forgetting to multiply the A parts, or vice versa.

Frequently Asked Questions

Common questions students ask about this topic

Key Terminology

Essential terms to know

Simplifying surds

Rationalising denominators

Conversion between fractions, decimals, percentages

Percentage change

Squares and cubes

Index notation

Roots

Place value

Ordering numbers

Prime numbers and factors

Standard form representation

Calculations with standard form

Likely Command Words

How questions on this topic are typically asked

Simplify

Calculate

Rationalise

Expand

Solve

Convert

Interpret

Express

Evaluate

Find

Order

Identify

Use

Ready to test yourself?

Practice questions tailored to this topic

Number

Subtopics in this area

Topic Overview

What You Need to Demonstrate

Marking Points

Examiner Tips

Common Mistakes

Frequently Asked Questions

Key Terminology

Likely Command Words

Ready to test yourself?

Related Topics in PEARSON GCSE Mathematics

Probability

Probability

Statistics

E2E stub topic

Number

Subtopics in this area

Topic Overview

What You Need to Demonstrate

Marking Points

Examiner Tips

Common Mistakes

Frequently Asked Questions

How do I add and subtract fractions with different denominators?

What is the difference between factors and multiples?

How do I calculate a percentage increase?

What is standard form and when do I use it?

Why is dividing by a fraction the same as multiplying by its reciprocal?

How do I find the highest common factor (HCF) and lowest common multiple (LCM)?

Key Terminology

Likely Command Words

Ready to test yourself?

Related Topics in PEARSON GCSE Mathematics

Probability

Probability

Statistics

E2E stub topic