Cambridge IGCSE Complete Mathematics Vocabulary

Vocabulary flashcards covering core mathematical definitions, principles, and historical figures from the Cambridge IGCSE Complete Mathematics course.

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Srinivasa Ramanujan

A self-taught Indian mathematician ($1887\text{--}1920$) who made major contributions to number theory and mathematical analysis, collaborating with G. H. Hardy at Trinity College in Cambridge.

Ingrid Daubechies

A Belgian physicist and mathematician born in $1954$, best known for her work on image compression technology and image processing methods used on historical artworks and fossils.

Factorising

The reverse process of expanding an expression, where all common factors are placed outside of brackets.

Karl Friedrich Gauss

A mathematician ($1777\text{--}1855$) considered one of the greatest all-round mathematicians of all time, who discovered a method for constructing a regular $17$-sided polygon.

BIDMAS Rule

An acronym establishing the correct order of operations in mathematical calculations: Brackets, Indices, Divide and Multiply, Add and Subtract.

Reciprocal

The number obtained by dividing $1$ by a given number $n$, written as $\frac{1}{n}$ or $n^{-1}$.

Integer

A positive or negative whole number or zero (for example, $-3$, $0$, $2$).

Natural Number

A whole positive number used for counting or ordering (for example, $1$, $2$, $3$).

Prime Number

A whole number greater than $1$ that has exactly two factors: itself and $1$.

Lowest Common Multiple (LCM)

The smallest number that is a multiple of two or more given numbers.

Highest Common Factor (HCF)

The largest number that is a factor of two or more given numbers.

Rational Number

A number that can be expressed exactly as a fraction $\frac{a}{b}$, where $a$ and $b$ are whole numbers and $b \neq 0$.

Irrational Number

A number that cannot be written in the form $\frac{a}{b}$ using whole numbers $a$ and $b$ ($b \neq 0$), such as $\sqrt{5}$ or $\pi$.

Linear Sequence

An arithmetic sequence in which the difference between consecutive terms is constant.

Quadratic Sequence

A sequence where the second differences between consecutive terms are constant, having an $n\text{th}$ term formula of the form $T_n = an^2 + bn + c$.

Exponential Sequence

A geometric sequence where each term is obtained by multiplying the preceding term by a fixed multiplier.

Upper Bound

The maximum possible value of a rounded measurement, calculated by adding half of the unit of measurement to the given value.

Lower Bound

The minimum possible value of a rounded measurement, calculated by subtracting half of the unit of measurement from the given value.

Standard Form

A method of writing very large or small numbers in the format $A \times 10^n$, where $1 \leqslant A < 10$ and $n$ is a positive or negative integer.

Surd

An exact numerical value left in square root form, such as $\sqrt{5}$ or $\sqrt{7}$.

Isaac Newton

An English scientist and mathematician ($1642\text{--}1727$) who made major discoveries regarding calculus, gravitation, and the nature of colors.

Variable

A letter in algebra used to represent an unknown or changing number.

Linear Equation

An equation containing one variable where the highest power of that variable is $1$.

Simultaneous Equations

A set of two or more equations containing multiple unknown variables that are solved together to find a common solution.

Ratio

A mathematical expression showing the relative sizes of two or more quantities, written in the form $a : b$.

Direct Proportion

A relationship between two quantities where an increase in one causes the other to increase at the same rate, expressed as $x \propto y$ or $x = ky$.

Inverse Proportion

A relationship where an increase in one quantity leads to a proportional decrease in another, expressed as $x \propto \frac{1}{y}$ or $x = \frac{k}{y}$.

Simple Interest

Interest calculated solely on the original principal amount invested or borrowed using the formula $I = \frac{P \times R \times T}{100}$.

Compound Interest

Interest calculated on both the initial principal amount and all accumulated interest from previous periods.

Bearing

An angle measured in degrees clockwise from due North, expressed as a three-digit number.

Angle of Elevation

The angle formed between a horizontal line of sight and an observer's line of sight looking upward at an object.

Angle of Depression

The angle formed between a horizontal line of sight and an observer's line of sight looking downward at an object.

Pythagoras' Theorem

A geometric principle stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides ($a^2 + b^2 = c^2$).

Prism

A three-dimensional solid object with identical, parallel cross-sections throughout its length.

Sector

A region of a circle bounded by two radii and an arc.

Chord

A straight line segment whose endpoints both lie on the circumference of a circle.

Segment

The region of a circle cut off by a chord and an arc.

Differentiation

The mathematical process of finding the derivative function $\frac{dy}{dx}$ to determine the gradient of a curve.

Histogram

A graphical representation of continuous data where the frequency is represented by the area of each bar, using $\text{frequency density} = \frac{\text{frequency}}{\text{class width}}$ on the vertical axis.

Cumulative Frequency

The running total of all frequencies up to a specified upper bound of a class interval.