A-Level Math — Core Fundamentals

Front

Set Notation: ∈ and ⊂

Back

The symbol ∈ means 'is an element of' (e.g., x ∈ S means x is in set S). The symbol ⊂ means 'is a subset of' (e.g., A ⊂ B means all elements of A are also in B).

Front

The Discriminant (Δ)

Back

For the quadratic ax² + bx + c, the discriminant is Δ = b² - 4ac. It determines the nature of the roots: Δ > 0 (two real distinct roots), Δ = 0 (one repeated root), Δ < 0 (no real roots).

Front

Function vs. Relation

Back

A function is a special relationship where each input (x-value) has exactly one output (y-value). Vertical line test: If a vertical line intersects a graph more than once, it is a relation, not a function.

Front

Domain and Range

Back

The **Domain** is the set of all possible input values (x) for which the function is defined. The **Range** is the set of all possible output values (y) the function can produce.

Front

Composite Function: fg(x)

Back

The notation fg(x) means applying function g first, then function f to the result. Mathematically, fg(x) = f(g(x)). The domain of fg must be compatible with the range of g.