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Edexcel IGCSE Maths (4MA1) · Revision notes · Numerical Reasoning

IGCSE Maths Number Revision Notes

Short, plain-English notes on number systems & accuracy for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Each of the 9 sub-topics has what you need to know and one example with its answer. Cover the answer and try the example first, then practise the topic with worked solutions.

Rounding & Calculator Skills

Significant figures, decimal places, calculator-based estimations.

‘Significant figures’ (s.f.) count from the first non-zero digit. Rounding to 3 s.f. means keeping the three most important digits.

Example: Use your calculator to evaluate (4.72 × 18.9) ÷ (3.14 − 1.09). Round to 3 s.f.

Answer: Full answer 43.51..., so to 3 s.f. → 43.5.

Practise it: Rounding and Bounds questions and answers

Prime Factor Decomposition

Expressing numbers as products of primes, finding HCF and LCM.

‘Prime factor decomposition’ means writing a number as a product of prime numbers using powers.

Example: Express 120 as a product of its prime factors.

Answer: 120 = 2³ × 3 × 5.

Practise it: HCF, LCM and Prime Factors questions and answers

Fraction Arithmetic

Addition, subtraction, multiplication and division of compound / mixed numbers.

Mixed numbers are whole + fraction (e.g. 1¾). Convert to improper fractions first when adding, subtracting, multiplying or dividing.

Example: Work out 1¾ + 2⅔ as a mixed number.

Answer: = 7/4 + 8/3 = 21/12 + 32/12 = 53/12 = 4 5/12.

Practise it: Fractions and Decimals questions and answers · Recurring Decimals questions and answers

Percentages & Compound Measures

Percentage multipliers, percentage change, compound interest.

A percentage multiplier turns ‘×20% increase’ into a single number (1.20). Compound interest uses the multiplier once per year.

Example: £4000 invested at 3.5% compound interest for 3 years — total value?

Answer: 4000 × 1.035³ = £4434.87.

Practise it: Percentages questions and answers

Standard Form

Converting, multiplying and dividing numbers in scientific notation (A × 10ⁿ).

Standard form writes a number as A × 10ⁿ where 1 ≤ A < 10.

Example: Write 0.00000384 in standard form.

Answer: = 3.84 × 10⁻⁶.

Practise it: Indices and Standard Form questions and answers

Ratio & Proportion

Sharing amounts in standard/complex ratios, unitary problem solving.

A ratio shares a quantity into parts. To split £X in the ratio a:b:c, work out one part (£X ÷ (a+b+c)) then multiply.

Example: Divide £240 in the ratio 3:5:4.

Answer: 12 parts total → 1 part = £20 → £60 : £100 : £80.

Practise it: Ratio questions and answers · Exchange Rates and Best Buys questions and answers · Direct and Inverse Proportion questions and answers

Upper & Lower Bounds

Determining limits of accuracy for rounded measurements.

A rounded measurement has a lower and upper bound — the range of true values it could really be.

Example: A piece of wood is 2.4 m to the nearest cm. Find the bounds.

Answer: Lower 2.395 m · Upper 2.405 m.

Practise it: Rounding and Bounds questions and answers

Surd Operations

Simplifying surds, adding/subtracting like terms, rationalising denominators.

A surd is a root that can't simplify to an integer (e.g. √2). Rationalising means removing surds from a fraction's denominator.

Example: Simplify √48.

Answer: = √(16 × 3) = 4√3.

Practise it: Surds questions and answers

Laws of Indices

Manipulating indices including zero, negative and fractional powers.

Laws of indices tell you how to multiply, divide and raise powers to other powers.

Example: Simplify ((x⁴)³ × x⁻⁵) ÷ x².

Answer: = x¹² × x⁻⁵ ÷ x² = x⁷ ÷ x² = x⁵.

Practise it: Indices and Standard Form questions and answers

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