Unit 1
Function Review & Algebraic Fluency
- Function notation and evaluation
- Domain and range
- Transformations and symmetry
- Composition and inverse functions
- Algebraic manipulation and equation-solving review
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School Mathematics · Grades 6–12
Algebra 2
An advanced algebra and functions pathway covering polynomial, rational, radical, exponential, logarithmic, trigonometric, sequence, and statistical models.
Course overview
This roadmap extends Algebra 1 into the deeper function families and algebraic techniques expected before or alongside precalculus. Students move from routine manipulation toward choosing representations, analyzing structure, and modeling.
Math Aficionado uses this structure as a tutoring roadmap rather than a fixed school syllabus. Lessons can be reordered around the student's current unit, teacher materials, placement level, assignments, and assessment goals.
Units & topics
Unit 2
Polynomial Expressions & Operations
- Polynomial arithmetic
- Long and synthetic division
- Remainder and Factor Theorems
- Polynomial identities
- Zeros, factors and multiplicity
Unit 3
Quadratic & Complex Number Systems
- Quadratic forms and methods
- Complex numbers and the complex plane
- Conjugates and complex arithmetic
- Discriminant and nature of roots
- Quadratic modeling
Unit 4
Polynomial Functions
- Graphs and end behavior
- Turning points and multiplicity
- Rational Root Theorem
- Factoring higher-degree polynomials
- Polynomial models and technology
Unit 5
Rational Functions
- Simplifying rational expressions
- Domain restrictions
- Asymptotes and discontinuities
- Graphing rational functions
- Rational equations and modeling
Unit 6
Radical Functions & Equations
- Rational exponents
- Radical expressions
- Radical equations and extraneous solutions
- Graphs of radical functions
- Inverse relationships and modeling
Unit 7
Exponential Functions
- Properties of exponential functions
- Growth and decay models
- Transformations and parameter effects
- Compound interest and continuous growth
- Solving exponential equations
Unit 8
Logarithmic Functions
- Definition and inverse relationship
- Logarithm properties
- Change of base
- Solving logarithmic equations
- Logarithmic models and applications
Unit 9
Sequences & Series
- Arithmetic sequences
- Geometric sequences
- Recursive and explicit forms
- Finite sums
- Infinite geometric series and applications
Unit 10
Trigonometric Functions
- Angle measure and unit circle
- Sine, cosine and tangent as functions
- Graphs and transformations
- Inverse trigonometric functions
- Basic trigonometric equations
Unit 11
Statistics, Probability & Data Models
- Sampling and experimental design
- Probability models
- Conditional probability
- Bivariate data and regression
- Evaluating statistical claims
Unit 12
Integrated Functions & Modeling
- Selecting a model family
- Piecewise and combined models
- Parameter interpretation
- Model limitations and residual reasoning
- Precalculus readiness and cumulative review
How the roadmap is aligned
Wisconsin Standards for Mathematics (2021), high-school Algebra, Functions and Statistics strands; pathway also cross-checked against UW–Madison MATH 112/114 preparation.
This is an independent tutoring roadmap, not an official UW–Madison or Wisconsin Department of Public Instruction course. Wisconsin standards are used as the K–12 framework; current UW–Madison course descriptions are used where the pathway overlaps with college-level precalculus and calculus preparation.
Wisconsin Standards for Mathematics (2021) · UW–Madison Mathematics Course Guide
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