Algebra (AQA)

Variables

Variables

Letters representing unknown or changing values in algebraic expressions.

Terms

Numbers or letters alone or multiplied together, separated by + or - signs in expressions.

Expressions

Combinations of terms using + or - signs, without an = sign.

Equations

Two expressions set equal to each other with an = sign, indicating equal values on both sides.

Like terms

Terms with the same variable raised to the same power, used for simplifying expressions.

PEMDAS

Order of operations - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Factoring

Breaking down algebraic expressions into simpler forms, often using product and sum methods.

Formulas

Mathematical rules using variables that are always true, allowing substitution of values.

Rearranging Formulas

Moving variables to one side of an equation by using opposite operations.

Composite Functions

Functions where the output of one becomes the input of another function.

Graphs

Representations of mathematical relationships on coordinate planes.

Transformations of Graphs

Movements of graphs vertically or horizontally, and reflections over axes.

Graphs of Lines

Equations in the form y=mx+c, showing slopes and intercepts.

Graphs of Quadratics

Representations of equations in the form y=ax²+bx+c, including turning points and symmetry.

Graphs of Circles

Representations of circles with equations like (x-h)²+(y-k)²=r².

Graphs of Inequalities

Representations of regions where inequalities are true on graphs.

Solving Equations

Finding values that make equations true, often using rearrangement and order of operations.

Simultaneous Equations

Solving systems of equations using substitution or elimination methods.

Solving Quadratic Equations

Finding solutions to equations of the form ax²+bx+c=0 using factoring, quadratic formula, or completing the square.

Inequalities

Expressions showing relationships between values that are not equal, solved similarly to equations but with attention to negatives.

Sequences

Sets of numbers following patterns, including arithmetic, geometric, and linear sequences.

Square numbers

Numbers obtained by multiplying a number by itself, e.g., 1, 4, 9, 16, 25, 36...

Cube numbers

Numbers obtained by multiplying a number by itself three times, e.g., 1, 8, 27, 64, 125...

Triangular numbers

Numbers that can be represented as a triangle of dots, with each term obtained by adding one more than the previous term, e.g., 1, 3, 6, 10, 15...

Triangular numbers nth term formula

The formula to find the nth triangular number is [n(n+1)]/2.

Fibonacci sequence

A sequence where each term is the sum of the two preceding terms, starting with 1, 1, e.g., 1, 1, 2, 3, 5, 8, 13...