Stage 5 Mathematics – Key Vocabulary

Vocabulary flashcards covering core algebraic and equation-solving terms featured across Quadratics, Cubics, Algebraic Fractions, and Inequalities topics.

Algebraic Fraction

An expression that contains a fraction whose numerator, denominator, or both include algebraic terms (variables).

Quadratic Equation

An equation of the form ax² + bx + c = 0 where a, b and c are constants and a ≠ 0.

Cubic Equation

An equation that includes a variable raised to the third power, generally written as ax³ + bx² + cx + d = 0 with a ≠ 0.

Quadratic Formula

A method for solving ax² + bx + c = 0: x = [−b ± √(b² − 4ac)] ⁄ 2a.

Completing the Square

A technique that rewrites a quadratic ax² + bx + c in the form a(x − h)² + k to facilitate solving or graphing.

Making the Subject

Rearranging an equation so that a specified variable is isolated on one side (e.g., solving for x in terms of other variables).

Inequality

A mathematical statement that compares two values using

Number Line

A straight line on which real numbers are represented by points, used to graph solutions of inequalities.

Quadratic Inequality

An inequality that contains a quadratic expression, such as ax² + bx + c < 0.

Algebraic Manipulation

The process of rearranging and simplifying algebraic expressions and equations using mathematical operations and properties.

Domain Restriction

Limiting the set of permissible input values to avoid undefined operations (e.g., division by zero).

Sphere Volume Formula

V = 4⁄3 πr³, where V is volume and r is the radius of the sphere.

HSC (Higher School Certificate)

The credential awarded to secondary school students in New South Wales, Australia, upon successful completion of Stage 6 studies.

Path B / Path C

Course difficulty or content streams used to categorize question sets within the Stage 5 mathematics curriculum.

Graphing Solution

Visual representation of the set of values that satisfy an equation or inequality, often on a coordinate plane or number line.

Exact Value

A solution expressed in symbolic form (e.g., √2, 4/3) rather than a decimal approximation.

Factorisation

Rewriting an expression as a product of its factors, e.g., x² − 9 as (x + 3)(x − 3).

Rationalising the Denominator

Eliminating radicals or surds from the denominator of a fraction through multiplication by a suitable form of 1.

Sign Analysis

Determining intervals on which an expression is positive or negative to solve inequalities.

Discriminant

The quantity b² − 4ac in the quadratic formula that indicates the nature and number of roots of a quadratic equation.