Curriculum · Algebra
Algebra
Functions, polynomials, quadratics, systems, and sequences — where recognizing structure replaces brute force.
Functions & Polynomials
Functions & Transformations
Function notation, composition, inverses, and graph transformations.
- Compose and invert functions
- Shift, stretch, and reflect graphs
- Read functional notation fluently
prerequisite: coordinate-plane-basics
The Polynomial Toolbox
Factoring patterns, the remainder theorem, and root-coefficient thinking.
- Factor with standard identities
- Apply remainder & factor theorems
- Count and locate roots
prerequisite: functions-intro
Quadratics & Vieta's Formulas
The complete quadratic: vertex form, discriminants, and Vieta's formulas — the contest workhorse.
- Convert between quadratic forms
- Use the discriminant to reason about roots
- Apply Vieta's formulas to symmetric expressions
prerequisite: polynomial-toolbox
Structure & Pattern
Systems & Symmetry
Solving systems by elimination, substitution — and by noticing symmetry first.
- Solve 2- and 3-variable systems
- Add equations to exploit symmetry
- Substitute aggregates like x+y
prerequisite: quadratics-vieta
Sequences, Series & Telescoping
Arithmetic and geometric sequences, then the telescoping idea that collapses monsters.
- Sum arithmetic and geometric series
- Recognize telescoping structure
- Partial-fraction a telescoping term
prerequisite: polynomial-toolbox
Exponents & Radicals
Exponent laws, radical manipulation, and rationalization under pressure.
- Apply exponent laws fluently
- Denest and rationalize radicals
- Compare exponential quantities
prerequisite: variables-expressions
Logarithms
Logs as inverse exponentials; the identities and the classic contest patterns.
- Convert between exp and log form
- Apply log identities
- Solve log equations
prerequisite: exponents-radicals