Number for Edexcel IGCSE Mathematics Specification B: Methods and Worked Examples

Number is where everything starts. If algebra is the language of mathematics, then number is the alphabet. Getting this section right makes every other part of the Edexcel IGCSE Mathematics Specification B course more manageable.

The Number section of the edexcel igcse mathematics specification b number content covers two main areas: Number Manipulation and Measures, Money and Accuracy. Between them, they span everything from prime factorisation to upper and lower bounds. These are not abstract ideas that only show up in their own section. Index laws appear inside algebra questions. Standard form turns up in physics-style contexts. Upper and lower bounds feed into trigonometry and mensuration. You will use Number skills throughout both exam papers, so building a solid foundation here pays off everywhere.

Number manipulation

Primes, factors and multiples

You need to be comfortable with prime factorisation, finding highest common factors (HCF) and lowest common multiples (LCM). The most reliable method uses prime factor trees or repeated division.

Worked example: Find the HCF and LCM of 72 and 120.

Start by writing each number as a product of prime factors:

72 = 2³ x 3²
120 = 2³ x 3 x 5

For the HCF, take the lowest power of each common prime: 2³ x 3 = 24.

For the LCM, take the highest power of every prime that appears: 2³ x 3² x 5 = 360.

Common mistake: Mixing up HCF and LCM methods. Remember: HCF uses the lowest powers (you are finding what is common), LCM uses the highest powers (you need enough to cover both numbers). Think of it like packing a suitcase for two people: the HCF is what you both already own, the LCM is everything you need between you.

Index laws

Index notation and index laws are fundamental to this edexcel igcse specification. You need to handle integer, fractional, and negative powers fluently.

The key rules:

Rule	Example
a^m x aⁿ = a^m+n	2³ x 2⁴ = 2⁷ = 128
a^m / aⁿ = a^m-n	5⁶ / 5² = 5⁴ = 625
(a^m)ⁿ = a^mn	(3²)⁴ = 3⁸ = 6561
a⁰ = 1	7⁰ = 1
a^-n = 1/aⁿ	2^-3 = 1/8
a^1/n = the nth root of a	8^1/3 = 2
a^m/n = (the nth root of a)^m	27^2/3 = (3)² = 9

Worked example: Simplify 16^-3/4.

Step 1: The negative sign means take the reciprocal, so 16^-3/4 = 1 / 16^3/4.

Step 2: The denominator 4 means take the fourth root: the fourth root of 16 = 2.

Step 3: The numerator 3 means cube the result: 2³ = 8.

Step 4: So 16^-3/4 = 1/8.

Surds and rationalising the denominator

Surds are irrational numbers left in root form for exactness. The edexcel igcse exam expects you to simplify surds and rationalise denominators.

Worked example: Simplify 3/(2 + sqrt(5)).

Multiply numerator and denominator by the conjugate (2 - sqrt(5)):

3(2 - sqrt(5)) / ((2 + sqrt(5))(2 - sqrt(5)))

= (6 - 3sqrt(5)) / (4 - 5)

= (6 - 3sqrt(5)) / (-1)

= -6 + 3sqrt(5)

= 3sqrt(5) - 6

Why rationalising matters: Leaving a surd in the denominator is like leaving a fraction unsimplified. It is not wrong mathematically, but examiners expect the rationalised form. More importantly, rationalised expressions are easier to compare, add, and substitute into other calculations. Your number edexcel igcse revision should include plenty of practice with conjugate pairs.

Types of number

You should be able to recognise and distinguish natural numbers, integers, rational numbers and irrational numbers. A rational number can be written as a fraction p/q where p and q are integers and q is not zero. An irrational number cannot: sqrt(2), sqrt(3), and pi are all irrational. This distinction matters when you are asked whether an answer is exact or approximate.

Measures, money and accuracy

Unit conversions and standard form

Standard form (scientific notation) is used for very large and very small numbers. A number in standard form looks like a x 10ⁿ, where 1 <= a < 10 and n is an integer.

Worked example: Calculate (3.2 x 10⁴) x (5 x 10^-2).

Multiply the coefficients: 3.2 x 5 = 16.

Add the powers: 10⁴ x 10^-2 = 10².

So the result is 16 x 10² = 1.6 x 10³.

Notice that 16 x 10² is not in standard form because 16 is not between 1 and 10. Adjusting to 1.6 x 10³ is an essential final step that students often forget in the igcse 4mb1 number exam.

Fractions, decimals, percentages, ratio and proportion

The specification requires you to interchange between fractions, decimals, ratios, proportions and percentages, selecting whichever is most appropriate. In practice, this means being able to move between representations quickly and accurately.

Worked example: A shop reduces the price of a jacket from 80 pounds to 62 pounds. Find the percentage decrease.

Decrease = 80 - 62 = 18.

Percentage decrease = (18/80) x 100 = 22.5%.

The key here is dividing by the original amount, not the new amount. Percentage change always uses the original value as the denominator. This is one of those mistakes that sounds obvious when you read it but catches people under exam pressure.

Accuracy: decimal places and significant figures

Expressing numbers to a given degree of accuracy is a staple of the edexcel igcse mathematics specification b revision notes for Number. You need to round to a given number of decimal places or significant figures, and know the difference.

Worked example: Write 0.004073 correct to 2 significant figures.

Leading zeros do not count as significant figures. The first significant figure is 4, the second is 0. The next digit is 7, which is 5 or more, so round up: 0.0041.

Upper and lower bounds

When a measurement is given to a certain degree of accuracy, its true value lies within a range. The edexcel igcse mathematics specification b notes on bounds require you to find these ranges and use them in calculations.

Worked example: A rectangle has length 12.4 cm and width 7.8 cm, both measured to 1 decimal place. Find the upper and lower bounds of the area.

Lower bound of length = 12.35 cm, upper bound = 12.45 cm.

Lower bound of width = 7.75 cm, upper bound = 7.85 cm.

Lower bound of area = 12.35 x 7.75 = 95.7125 cm².

Upper bound of area = 12.45 x 7.85 = 97.7325 cm².

The bounds trap with division: When dividing, the upper bound of the result uses the upper bound of the numerator and the lower bound of the denominator. Think of it like this: to make a fraction as large as possible, you make the top as big as possible and the bottom as small as possible. Students who mechanically pair upper with upper lose marks here.

Currency conversions

Questions involving money and currency conversions are straightforward once you set up the calculation correctly. The specification expects you to carry out calculations using money, including converting between currencies.

Worked example: The exchange rate is 1 GBP = 1.15 EUR. Convert 250 GBP to euros.

250 x 1.15 = 287.50 EUR.

To convert back: 287.50 / 1.15 = 250 GBP. Always divide by the rate when converting back to the base currency.

Common mistakes in the Number section

Confusing negative indices with negative numbers. 2^-3 is 1/8, not -8. The negative exponent means reciprocal, not negative value.
Forgetting to adjust standard form. After multiplying or dividing, the coefficient must be between 1 and 10. If you get 0.45 x 10⁶, that needs to become 4.5 x 10⁵.
Rounding too early. In multi-step calculations, keep full precision until the final answer. Rounding intermediate values introduces errors that accumulate.
Using the wrong bound. For maximum area, use upper bounds of both dimensions. For maximum speed (distance/time), use upper bound of distance and lower bound of time. Always think about what makes the answer larger or smaller.
Treating leading zeros as significant. In 0.00302, the first significant figure is 3, not zero.

Self-check questions

Test yourself on these edexcel igcse mathematics specification b practice questions. Work through each one fully before checking.

Express 252 as a product of its prime factors. Hence find the HCF and LCM of 252 and 180.
Simplify 8^-2/3.
Rationalise the denominator of 5 / (3 - sqrt(2)).
A car travels 145 km, correct to the nearest 5 km, in 2.3 hours, correct to 1 decimal place. Calculate the lower bound of the average speed.
Write 3.4 x 10^-3 + 2.1 x 10^-4 in standard form.

Solutions

1. 252 = 2² x 3² x 7. And 180 = 2² x 3² x 5. HCF = 2² x 3² = 36. LCM = 2² x 3² x 5 x 7 = 1260.

2. 8^-2/3 = 1 / 8^2/3. Cube root of 8 = 2. Then 2² = 4. So 8^-2/3 = 1/4.

3. Multiply top and bottom by (3 + sqrt(2)): 5(3 + sqrt(2)) / (9 - 2) = (15 + 5sqrt(2)) / 7.

4. Lower bound of distance = 142.5 km. Upper bound of time = 2.35 hours. Lower bound of speed = 142.5 / 2.35 = 60.6 km/h (to 3 s.f.).

5. Convert to the same power: 3.4 x 10^-3 = 34 x 10^-4. Then 34 x 10^-4 + 2.1 x 10^-4 = 36.1 x 10^-4 = 3.61 x 10^-3.

If you found any of these tricky, revisit the relevant section above. The edexcel igcse mathematics specification b explained content on Number is one of those areas where steady, repeated practice makes the biggest difference. Every worked example you complete independently strengthens the skills that will carry you through both papers on exam day.