Advanced Math - Overview
Advanced Math builds on Algebra and focuses on nonlinear relationships, functions, equations, and mathematical structures commonly encountered in precalculus and college-level mathematics.
These questions often require deeper reasoning, multiple solution steps, and strong algebraic fluency. Success in this domain comes from recognizing patterns, choosing efficient solution methods, and understanding how different mathematical representations connect.
By working through this domain, you’ll learn how to:
- Manipulate complex algebraic expressions
- Analyze and graph functions
- Solve quadratic, radical, rational, and exponential equations
- Understand polynomial behavior and structure
- Interpret mathematical models in real-world contexts
- Move flexibly between algebraic, graphical, and numerical representations
Course Structure
The Advanced Math domain is organized into six units.
Exponents & Radicals
Develop the tools needed to work with powers, roots, and scientific notation.
Topics include:
- Advanced exponent rules
- Scientific notation
- Simplifying radical expressions
- Solving radical equations
Polynomials
Learn how polynomial expressions behave and how they can be manipulated.
Topics include:
- Adding and subtracting polynomials
- Multiplying polynomials
- Special products
- Polynomial division
- Remainder Theorem
- Polynomial graph behavior
Rational Expressions
Work with algebraic fractions and equations involving rational expressions.
Topics include:
- Simplifying rational expressions
- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions
- Solving rational equations
Functions
Build a deeper understanding of one of the most important concepts in mathematics.
Topics include:
- Function concepts and notation
- Evaluating functions
- Graphical representations
- Even and odd functions
- Domain and range
- Function transformations
- Function composition
- Inverse functions
Quadratics
Study one of the most heavily tested nonlinear relationships on the SAT.
Topics include:
- Recognizing quadratic forms
- Factoring quadratics
- Zero Product Property and roots
- Completing the square
- Quadratic formula
- Graphing parabolas
- Quadratic modeling and applications
Exponential Functions
Explore growth and decay relationships that appear in science, finance, and real-world modeling.
Topics include:
- Exponential growth and decay
- Compound interest
- Percent growth modeling
- Graphing exponential functions
SAT Advanced Math Tips
- Look for structure before beginning calculations.
- Factor whenever possible before using more advanced methods.
- Learn to recognize common function types and their graphs.
- Pay attention to domain restrictions in rational and radical expressions.
- Understand how changes in equations affect graphs.
- Be comfortable moving between equations, tables, and graphs.
Assess Your Progress
After completing the lessons in each unit, reinforce your understanding with:
- Unit assessments
- The Advanced Math Domain Test
- Full-Length SAT Practice Tests
Select a unit from the sidebar to begin.