Algebra
The language of unknowns. Algebra is where math stops being about specific numbers and starts being about relationships — patterns that hold true no matter what the numbers are.
Start with Order of Operations if you're new to algebra. Otherwise jump to whichever topic you need most. 9 lessons — Beginner to Intermediate.
Order of Operations (PEMDAS / BODMAS)
Why 2 + 3 × 4 = 14 and not 20 — and how to always solve expressions in the right order.
Ratios and Proportions
Comparing quantities, simplifying ratios, solving proportions — with real-world examples from cooking to maps.
Absolute Value
What |x| means, solving absolute value equations and inequalities, and real-world applications.
What is a Polynomial?
Terms, coefficients, degree, types, and how to add, subtract, and multiply polynomials.
What Are Functions?
The idea of input → output, domain and range, function notation, and why functions are the building block of all advanced math.
Solving Linear Equations
How to find the unknown — from simple one-step equations to multi-step problems with variables on both sides.
Inequalities
Greater than, less than, and not equal — solving and graphing inequalities on a number line and coordinate plane.
Systems of Equations
When you have two unknowns — substitution, elimination, and graphical methods with real-world examples.
Exponent Rules
Product, quotient, power, zero, negative, and fractional exponents — every rule explained from first principles.
Factoring Polynomials
GCF, difference of squares, trinomial factoring, and grouping — the essential reverse of expanding brackets.
Quadratic Equations
Three methods for solving quadratics: factoring, the quadratic formula, and completing the square.
What Is Algebra and Why Does It Matter?
Algebra is the branch of mathematics that uses letters and symbols to represent numbers and the relationships between them. When you see an equation like 2x + 5 = 13, algebra gives you the tools to find what x must be. When you see a function like f(x) = x², algebra describes a relationship that works for any value of x, not just one specific case.
Algebra matters because almost everything beyond basic arithmetic depends on it. Physics equations, financial formulas, computer algorithms, and statistical models are all algebraic relationships. Learning to read and manipulate algebraic expressions is like learning to read music — it unlocks a whole world of ideas that are otherwise inaccessible.
The lessons in this section are designed for students who are encountering algebra for the first time or who need to fill in gaps. They start from first principles and assume nothing beyond basic arithmetic.