Algebra
Letters stand in for numbers, and the rules of arithmetic still hold. What can you say, and solve, once you work with numbers you do not yet know?
Where you are 9 inside
What this area is about
Algebra is arithmetic with unknowns. A letter stands for a number, and every rule of arithmetic still applies to it, so expressions can be rewritten and equations solved without knowing the number first. The branch runs from single letters to quadratics and sequences.
How these fit together
The language. Expressions: variables, evaluating, and the rewriting moves, from combining like terms to factoring.
Solving. Linear equations find the unknown when it appears only to the first power. Inequalities find whole stretches of numbers instead. Systems of equations satisfy two or more conditions at once.
Lines. Linear relationships: slope and every form of a line’s equation.
Beyond lines. Polynomials add, multiply, factor and divide. Radicals and rational expressions handle roots and polynomial fractions. Quadratics solve and graph ax^2 + bx + c with a \ne 0.
Patterns. Sequences and series find the nth term of an ordered list and the sum of its terms.
A path through it
Expressions first. Then linear equations and polynomials. After linear equations: linear relationships and inequalities. Systems need both of those. Radicals and rational expressions follow linear relationships and polynomials, and sequences follow linear relationships. Quadratics come after radicals; quadratics, inequalities and systems refer to each other, so take them side by side.
After this: functions, rules that turn one number into exactly one other.