Mathematics Revision Topics

Vocabulary flashcards covering core number, geometry, and algebra topics listed in the revision checklist.

Rounding

The process of approximating a number to a specified place value or degree of accuracy, such as to the nearest whole number, decimal place, or significant figure.

Prime factor decomposition

The method of expressing a composite integer as a product of its prime factors.

LCM/HCF

Lowest Common Multiple (the smallest positive number that is a multiple of two or more numbers) and Highest Common Factor (the greatest factor that divides exactly into two or more numbers).

Indices

Powers or exponents that indicate how many times a base number or variable is multiplied by itself, expressed in the form $a^n$.

Converting between Unit

Changing a measurement from one unit of length, mass, or capacity to another by multiplying or dividing by the appropriate conversion factor.

Converting units area

Converting area measurements by squaring the standard linear conversion factor between the units, such as $1\,\text{m}^2 = 10{,}000\,\text{cm}^2$.

Area of rectangle

The measure of two-dimensional space enclosed by a rectangle, calculated using the formula $\text{Area} = \text{length} \times \text{width}$.

Area of triangle

The amount of surface space inside a triangle, calculated using the formula $\text{Area} = \frac{1}{2} \times \text{base} \times \text{perpendicular height}$.

Area of parallelogram

The space enclosed by a parallelogram, calculated by multiplying its base by its perpendicular height: $\text{Area} = \text{base} \times \text{height}$.

Area of trapezium

The space inside a trapezium, calculated using the formula $\text{Area} = \frac{a + b}{2} \times h$, where $a$ and $b$ are the lengths of the parallel sides and $h$ is the perpendicular height.

Perimeter of shapes

The total continuous distance or length around the exterior boundary of a two-dimensional closed shape.

Area of Compound shape

The total area of a complex geometric figure composed of multiple simple shapes, found by partitioning the figure into individual shapes and adding their areas together.

Circumference of a circle

The linear perimeter or total boundary length around a circle, given by the formula $C = 2\pi r$ or $C = \pi d$, where $r$ is the radius and $d$ is the diameter.

Area of the circle

The two-dimensional space enclosed within a circle, calculated using the formula $\text{Area} = \pi r^2$, where $r$ is the radius.

Area of semicircle

Half the area of a complete circle, calculated using the formula $\text{Area} = \frac{1}{2}\pi r^2$.

Area of semi and quarter circle

The enclosed two-dimensional space of half a circle ($\text{Area} = \frac{1}{2}\pi r^2$) and one-fourth of a circle ($\text{Area} = \frac{1}{4}\pi r^2$).

Perimeter of semicircle

The total boundary length of a semicircle, calculated by adding half the circumference to the diameter: $P = \pi r + 2r$ (or $P = \frac{1}{2}\pi d + d$).

Law of Indices

A collection of algebraic rules for simplifying expressions with powers, including $a^m \times a^n = a^{m+n}$, $\frac{a^m}{a^n} = a^{m-n}$, and $(a^m)^n = a^{mn}$.

Collecting like terms

The algebraic simplification method of combining terms that possess the exact same variables raised to the same exponents.

Expanding brackets

The process of multiplying each term inside a set of brackets by the factor outside to remove the brackets.

Factorising

The inverse process of expanding brackets, in which an expression is rewritten as a product of its common factors or bracketed terms.

Forming expression

The process of translating a written problem, relationship, or pattern into an algebraic statement composed of numbers, variables, and operations.

Substitution

Replacing variables or algebraic letters in a formula or expression with specified numerical values to evaluate the result.

Rearranging formulae

Using inverse algebraic operations to alter the subject of an equation or formula so that a target variable is isolated on one side.

Multiplying terms

Multiplying algebraic terms by computing the product of their numerical coefficients and adding the exponents of matching variables using index laws.

Dividing terms

Dividing algebraic terms by dividing their numerical coefficients and subtracting the exponents of matching variables using index laws.

Algebric fractions

Fractions that contain an algebraic expression or variable in the numerator, the denominator, or both.