IGCSE-Mathematics-Formula-Booklet

Natural Numbers

The set of positive integers starting from 1, commonly used for counting (1, 2, 3, 4, ...).

Whole Numbers

All natural numbers including zero, encompassing 0, 1, 2, 3, 4, ...

Integers

The complete set of whole numbers that includes positive numbers, negative numbers, and zero, e.g., ..., -4, -3, -2, -1, 0, 1, 2, 3, 4...

Rational Numbers

Numbers that can be expressed in the form (p/q), where both p and q are integers and q is not equal to zero.

Irrational Numbers

Numbers that cannot be expressed as the ratio of two integers, including non-repeating non-terminating decimals such as the square root of 2 (√2) and pi (π).

Terminating Decimals

Decimal numbers that have a finite number of digits after the decimal point, such as 0.25 or 3.5.

Recurring Decimals

Decimal numbers where one or more digits repeat infinitely, such as 0.333... or 1.666... .

BODMAS

An acronym that represents the sequence of operations to be followed in mathematical expressions: Brackets, Orders (e.g., powers and square roots), Division, Multiplication, Addition, and Subtraction.

Even Numbers

Integers that can be evenly divided by 2 without a remainder, such as 0, 2, 4, 6, 8, ...

Odd Numbers

Integers that cannot be evenly divided by 2 and have a remainder of 1, such as 1, 3, 5, 7, ...

Significant Figures

The digits in a number that are important to its precision, starting from the first non-zero digit.

Standard Form

A method of expressing numbers as a product of a number between 1 and 10, multiplied by an integer power of ten, e.g., 4,500 can be represented as 4.5 × 10^3.

Conversion Factors

Ratios that are used to convert a quantity expressed in one unit to another unit, facilitating measurement comparisons.

Simple Interest Formula

I = PRT/100

Compound Interest Formula

A = P(1 + r/100)^n

Quadratic Equations

ax² + bx + c = 0

Pythagoras' Theorem

a² + b² = c²

Congruent Triangles

Two triangles that are identical in shape and size, meaning all corresponding sides and angles are equal.

Similar Triangles

Two triangles that have the same shape, indicating that their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Area of Triangle Formula

Area = 1/2 * base * height

Surface Area of Sphere

Surface area = 4πr²

Cumulative Frequency

The total number of observations in a dataset that fall below a particular value, used in statistics to summarize the distribution of data.

Probability

The measure of the likelihood that an event will occur, computed as the ratio of the number of favorable outcomes to the total number of possible outcomes.

Line of Symmetry

A line that divides a shape into two identical halves, such that one half is a mirror image of the other.

Transformations

Mathematical operations affecting the position, orientation, or size of shapes, specifically translation (shifting), rotation (turning), reflection (flipping), and enlargement (scaling).

Vectors

Quantities characterized by both magnitude (size) and direction, often represented as arrows in a coordinate system.

Matrices

Rectangular arrays of numbers or symbols used to represent and solve mathematical equations, especially in linear algebra.

Inverse of a Matrix

A matrix that, when multiplied by the original matrix, results in the identity matrix, effectively reversing the original matrix's transformation.

Bearing

A directional measurement expressed in degrees, indicating the angle from North (0°) to a specific line or path of movement, commonly used in navigation.