Number ToolkitEdexcel IGCSE Maths: Revision notes

An integer is any whole number — positive, negative, or zero — with no fractional or decimal part: $\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots$

Place value tells you what a digit is worth based on its position in a number. In $4207$:

• $4$ is worth $4000$ (thousands)
• $2$ is worth $200$ (hundreds)
• $0$ is worth $0$ (tens)
• $7$ is worth $7$ (units)

Ordering integers: on a number line, values increase left to right. Remember that negative numbers get smaller as their magnitude increases: $-8 < -3 < 0 < 5$.

Use these sign rules when combining negatives:

• Adding a negative = subtracting: $5 + (-3) = 5 - 3 = 2$
• Subtracting a negative = adding: $5 - (-3) = 5 + 3 = 8$
• Multiplying/dividing same signs → positive result: $(-4) \times (-2) = 8$
• Multiplying/dividing different signs → negative result: $(-4) \times 2 = -8$

A quick way to remember: two negative signs next to each other 'cancel' to a positive.

A factor of a number divides into it exactly, with no remainder. A multiple of a number is what you get when you multiply it by an integer.

• Factors of $12$: $1, 2, 3, 4, 6, 12$
• Multiples of $12$: $12, 24, 36, 48, \ldots$

A prime number has exactly two factors: $1$ and itself. The first few primes are $2, 3, 5, 7, 11, 13$. Note that $1$ is not prime (it has only one factor), and $2$ is the only even prime.

Prime factorisation writes a number as a product of primes, often shown with a factor tree, e.g. $60 = 2^2 \times 3 \times 5$.

HCF and LCM:

• Highest Common Factor (HCF): the largest number that divides into two or more numbers.
• Lowest Common Multiple (LCM): the smallest number that is a multiple of two or more numbers.

A square number is an integer multiplied by itself: $n^2$. The first few are $1, 4, 9, 16, 25, 36, 49, 64, 81, 100$.

A cube number is an integer multiplied by itself three times: $n^3$. The first few are $1, 8, 27, 64, 125$.

The square root ($\sqrt{\phantom{x}}$) reverses squaring: $\sqrt{49} = 7$. The cube root ($\sqrt[3]{\phantom{x}}$) reverses cubing: $\sqrt[3]{27} = 3$.

Remember every positive number technically has two square roots (positive and negative), e.g. $\sqrt{25} = \pm 5$, though the $\sqrt{\phantom{x}}$ symbol itself usually refers to the positive root.

Use BIDMAS (or BODMAS) to decide the order of operations:

1. Brackets
2. Indices (powers and roots)
3. Division and Multiplication (left to right, same priority)
4. Addition and Subtraction (left to right, same priority)

Division/multiplication are equal priority — work left to right through the expression. The same applies to addition/subtraction.