Algebra and Geometry Concepts

These flashcards cover key concepts and vocabulary relevant to algebra, geometry, and calculus, helping in understanding fundamental principles and terminology.

Surds

Expressions containing a root, such as √a.

Rationalising Denominators

The process of eliminating a radical from the denominator of a fraction.

Composite Functions

Functions that are formed by combining two functions, denoted as (f∘g)(x) = f(g(x)).

Inverse Functions

Functions that reverse the effect of the original function, denoted as f⁻¹(y).

Domain

The set of all possible input values (x) for a function.

Range

The set of all possible output values derived from the domain of a function.

Gradient of a Line

The slope of a line calculated as m = (y2 − y1) / (x2 − x1).

Distance Formula

A formula for calculating the distance between two points: d = √((x2 - x1)² + (y2 - y1)²).

Circle Theorem

Theorems regarding properties of circles, such as angles subtended by the same chord are equal.

Quadratic Formula

A solution method for quadratic equations given by x = (-b ± √(b²-4ac)) / (2a).

Factor Theorem

States that if f(a) = 0, then (x - a) is a factor of f(x).

Differentiation

The process of finding the derivative, or rate of change, of a function.

Second Derivative

The derivative of the derivative, used to determine concavity of a function.

Matrix Multiplication

The process of multiplying matrices, resulting in a new matrix from the dot products of rows and columns.

Geometric Proof

Method of demonstrating geometric truths using axioms and theorems.

Ambiguous Case (Sine Rule)

A scenario with two potential triangles when using the sine rule.

Exact Trigonometric Values

Specific values for trigonometric functions at key angles (e.g., sin(30°) = ½).

Trig Graphs

Graphs representing the periodic functions of trigonometry, characterized by period and amplitude.