SAT MATHEMATICS
CONCEPT NOTES
Complete Concept-Based Learning Guide
17 Chapters • 4 SAT Math Domains • Concept
Connections
Learn the mathematics behind SAT questions — not just
formulas.
Algebra • Advanced Math • Problem-Solving & Data
Analysis • Geometry & Trigonometry
by NOTEvia
, 2
SAT Mathematics Concept Notes
Complete Concept-Based Learning Guide
A structured guide to understanding the concepts, relationships, representations, and
mathematical ideas tested on SAT Mathematics.
Covers
Algebra
Advanced Math
Problem-Solving & Data Analysis
Geometry & Trigonometry
17 Complete Chapters
Designed for concept learning through:
Understand → Connect → Apply → Check Understanding
This book focuses on building mathematical understanding so that formulas, equations,
graphs, tables, and real-world situations become connected parts of the same
mathematical idea.
How to Use This Book
This book is designed to help you learn SAT Mathematics concepts from the ground
up.
It is not primarily a revision book, formula-cramming guide, or practice-question
collection. The goal is to understand what each mathematical idea means, how it works,
and how different ideas connect.
The Learning Flow
1. Understand
Start with the concept foundation. Learn what the mathematical idea represents and
why it works.
, 3
2. Connect
Look at how the concept connects with equations, tables, graphs, other mathematical
ideas, and real-world situations.
3. Apply
Study the worked concept examples. These examples are included to demonstrate how
an idea is used, rather than to create a large practice set.
4. Check Understanding
Use the chapter takeaways and concept connections to make sure the main idea is
clear before moving forward.
How to Study Each Chapter
Read the concepts in order rather than jumping directly to formulas.
Pay attention to:
● What the concept means
● How it is represented
● Which relationships connect it to other concepts
● How changes in one representation affect another
● Why a particular mathematical method works
When you finish a chapter, use the Chapter Takeaway to review the central ideas and the
Concept Connections to see where the chapter fits into the larger SAT Mathematics
structure.
A Recommended Learning Path
Foundations → Algebra → Functions → Advanced Math → Data Analysis → Geometry
→ Trigonometry
The chapters are arranged so that earlier concepts provide foundations for later ones.
Important Principle
Do not try to memorize every formula before understanding the concept behind it.
A strong conceptual foundation makes formulas easier to remember, recognize, and
use correctly.
, 4
SAT Math at a Glance
SAT Mathematics is organized around four major content domains. Together, these
domains cover the mathematical concepts and relationships needed to understand and
solve SAT Math problems.
1. Algebra
Algebra focuses on relationships involving expressions, equations, inequalities,
functions, and systems.
Key ideas include:
● Algebraic expressions
● Linear equations and inequalities
● Linear functions
● Systems of equations and inequalities
● Relationships between equations, tables, and graphs
Algebra provides the foundation for much of SAT Mathematics.
2. Advanced Math
Advanced Math extends algebraic reasoning to nonlinear relationships and more
complex functions.
Key ideas include:
● Quadratic functions and equations
● Polynomial expressions
● Rational expressions
● Radicals and exponents
● Exponential functions
● Nonlinear functions and equations
These concepts build directly on algebraic foundations.
3. Problem-Solving & Data Analysis
This domain focuses on using mathematics to understand quantities, percentages,
data, probability, and statistical relationships.
Key ideas include:
● Ratios and proportions
● Rates and percentages
● One-variable statistics
● Two-variable data
CONCEPT NOTES
Complete Concept-Based Learning Guide
17 Chapters • 4 SAT Math Domains • Concept
Connections
Learn the mathematics behind SAT questions — not just
formulas.
Algebra • Advanced Math • Problem-Solving & Data
Analysis • Geometry & Trigonometry
by NOTEvia
, 2
SAT Mathematics Concept Notes
Complete Concept-Based Learning Guide
A structured guide to understanding the concepts, relationships, representations, and
mathematical ideas tested on SAT Mathematics.
Covers
Algebra
Advanced Math
Problem-Solving & Data Analysis
Geometry & Trigonometry
17 Complete Chapters
Designed for concept learning through:
Understand → Connect → Apply → Check Understanding
This book focuses on building mathematical understanding so that formulas, equations,
graphs, tables, and real-world situations become connected parts of the same
mathematical idea.
How to Use This Book
This book is designed to help you learn SAT Mathematics concepts from the ground
up.
It is not primarily a revision book, formula-cramming guide, or practice-question
collection. The goal is to understand what each mathematical idea means, how it works,
and how different ideas connect.
The Learning Flow
1. Understand
Start with the concept foundation. Learn what the mathematical idea represents and
why it works.
, 3
2. Connect
Look at how the concept connects with equations, tables, graphs, other mathematical
ideas, and real-world situations.
3. Apply
Study the worked concept examples. These examples are included to demonstrate how
an idea is used, rather than to create a large practice set.
4. Check Understanding
Use the chapter takeaways and concept connections to make sure the main idea is
clear before moving forward.
How to Study Each Chapter
Read the concepts in order rather than jumping directly to formulas.
Pay attention to:
● What the concept means
● How it is represented
● Which relationships connect it to other concepts
● How changes in one representation affect another
● Why a particular mathematical method works
When you finish a chapter, use the Chapter Takeaway to review the central ideas and the
Concept Connections to see where the chapter fits into the larger SAT Mathematics
structure.
A Recommended Learning Path
Foundations → Algebra → Functions → Advanced Math → Data Analysis → Geometry
→ Trigonometry
The chapters are arranged so that earlier concepts provide foundations for later ones.
Important Principle
Do not try to memorize every formula before understanding the concept behind it.
A strong conceptual foundation makes formulas easier to remember, recognize, and
use correctly.
, 4
SAT Math at a Glance
SAT Mathematics is organized around four major content domains. Together, these
domains cover the mathematical concepts and relationships needed to understand and
solve SAT Math problems.
1. Algebra
Algebra focuses on relationships involving expressions, equations, inequalities,
functions, and systems.
Key ideas include:
● Algebraic expressions
● Linear equations and inequalities
● Linear functions
● Systems of equations and inequalities
● Relationships between equations, tables, and graphs
Algebra provides the foundation for much of SAT Mathematics.
2. Advanced Math
Advanced Math extends algebraic reasoning to nonlinear relationships and more
complex functions.
Key ideas include:
● Quadratic functions and equations
● Polynomial expressions
● Rational expressions
● Radicals and exponents
● Exponential functions
● Nonlinear functions and equations
These concepts build directly on algebraic foundations.
3. Problem-Solving & Data Analysis
This domain focuses on using mathematics to understand quantities, percentages,
data, probability, and statistical relationships.
Key ideas include:
● Ratios and proportions
● Rates and percentages
● One-variable statistics
● Two-variable data
