Algebra Flashcards

What is a variable?

A variable is a symbol (x, y, n) representing an unknown or changing value in an algebraic expression or equation.

What is a linear equation?

A linear equation has the form ax + b = c. The highest power of the variable is 1. Its graph is a straight line.

What is the quadratic formula?

x = (−b ± √(b²−4ac)) / 2a — solves ax² + bx + c = 0. The discriminant (b²−4ac) determines the number of real roots.

What is factorisation?

Factorisation rewrites an expression as a product of factors. Example: x²−9 = (x+3)(x−3). Simplifies solving equations.

What are simultaneous equations?

Two or more equations with the same unknowns solved together. Methods: substitution and elimination.

What is an inequality?

An inequality compares two expressions using <, >, ≤, ≥. When multiplying/dividing by a negative, the sign flips.

What is BODMAS?

BODMAS is the order of operations: Brackets → Orders (powers) → Division → Multiplication → Addition → Subtraction.

What is an arithmetic progression?

An AP is a sequence where each term increases by a constant (common difference d). Formula: aₙ = a + (n−1)d.

What is a geometric progression?

A GP is a sequence where each term is multiplied by a constant ratio r. Formula: aₙ = a·rⁿ⁻¹.

What are indices (exponents)?

Indices represent repeated multiplication. Key rules: aᵐ·aⁿ = aᵐ⁺ⁿ, (aᵐ)ⁿ = aᵐⁿ, a⁰ = 1.