SAT Math: Part 3 – Passport to Advanced Math

About Course

This specialized course provides comprehensive preparation for the Passport to Advanced Math section of the SAT, equipping students with essential skills in advanced algebraic concepts. Through targeted instruction, extensive practice, and real-world applications, students will gain proficiency in solving quadratic equations, manipulating polynomials, working with rational expressions, and addressing critical exponential and radical equations. Designed to enhance analytical reasoning and problem-solving abilities, this course ensures students are confident and well-prepared to achieve high scores on the SAT.

Course Content

1.Quadratic Equations and Functions
Master multiple solution strategies for quadratic equations—factoring, the quadratic formula, and completing the square—while interpreting the discriminant. Connect these techniques to graphical analysis by identifying vertices, axes of symmetry, and opening direction, then apply insights to solve real-world maxima and minima problems.

1.1 Solving Quadratic Equations (Factoring, Quadratic Formula, Completing the Square, Discriminant Analysis)
1.2 Quadratic Functions and Graphs (Vertex & Axis of Symmetry, Opening Direction, Standard ↔ Vertex Form Conversion)
1.3 Real-world Applications (Projectile Motion, Area Optimization, Maximum & Minimum Values)

2. Polynomials and Factoring
Strengthen understanding of polynomial expressions through operations and identities. Employ diverse factoring methods—from GCF extraction to special patterns—and translate factors into roots for precise graphing and function interpretation.

3. Rational Expressions and Equations
Simplify complex rational expressions and master arithmetic operations with them. Solve rational equations with attention to domain restrictions, verify solutions to eliminate extraneous roots, and model practical scenarios like rates, work, and proportions.

4. Additional Essential Concepts
Solve exponential growth and decay equations and tackle basic radical equations commonly featured in the Advanced Math section, using strategies to interpret contexts and identify invalid solutions

About Course

What Will You Learn?

Course Content

1.1 Solving Quadratic Equations (Factoring, Quadratic Formula, Completing the Square, Discriminant Analysis)

1.2 Quadratic Functions and Graphs (Vertex & Axis of Symmetry, Opening Direction, Standard ↔ Vertex Form Conversion)

1.3 Real-world Applications (Projectile Motion, Area Optimization, Maximum & Minimum Values)

2. Polynomials and Factoring
Strengthen understanding of polynomial expressions through operations and identities. Employ diverse factoring methods—from GCF extraction to special patterns—and translate factors into roots for precise graphing and function interpretation.

2.1 Polynomial Operations (Addition, Subtraction, Multiplication, Key Identities)

2.2 Factoring Techniques (GCF Extraction, Grouping, Difference of Squares, Perfect Square Trinomials)

2.3 Zeros and Roots (Polynomial Factor–Root Relationship, Graphing via Zeros)

3. Rational Expressions and Equations
Simplify complex rational expressions and master arithmetic operations with them. Solve rational equations with attention to domain restrictions, verify solutions to eliminate extraneous roots, and model practical scenarios like rates, work, and proportions.

3.1 Simplifying Rational Expressions (Reduction to Lowest Terms, Domain Restrictions)

3.2 Operations with Rational Expressions (Multiplication, Division, Addition & Subtraction with Common Denominators)

3.3 Solving Rational Equations (Solution Verification, Extraneous Root Identification, Rate/Work/Proportion Applications)

4. Additional Essential Concepts
Solve exponential growth and decay equations and tackle basic radical equations commonly featured in the Advanced Math section, using strategies to interpret contexts and identify invalid solutions

4.1 Exponential Expressions and Equations (Growth & Decay Models, Contextual Interpretation)

4.2 Radical Equations (Basic Radical Solutions, Extraneous Solution Checks)

Foundations of Differentiation: From First Principles to Essential Rules (2)

Fundamentals of Antiderivatives & Indefinite Integration (5)

Systems of Equations: From Linear to Nonlinear Systems

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SAT Math: Part 3 – Passport to Advanced Math

About Course

What Will You Learn?

Course Content

1.1 Solving Quadratic Equations (Factoring, Quadratic Formula, Completing the Square, Discriminant Analysis)

1.2 Quadratic Functions and Graphs (Vertex & Axis of Symmetry, Opening Direction, Standard ↔ Vertex Form Conversion)

1.3 Real-world Applications (Projectile Motion, Area Optimization, Maximum & Minimum Values)

2. Polynomials and Factoring Strengthen understanding of polynomial expressions through operations and identities. Employ diverse factoring methods—from GCF extraction to special patterns—and translate factors into roots for precise graphing and function interpretation.

2.1 Polynomial Operations (Addition, Subtraction, Multiplication, Key Identities)

2.2 Factoring Techniques (GCF Extraction, Grouping, Difference of Squares, Perfect Square Trinomials)

2.3 Zeros and Roots (Polynomial Factor–Root Relationship, Graphing via Zeros)

3. Rational Expressions and Equations Simplify complex rational expressions and master arithmetic operations with them. Solve rational equations with attention to domain restrictions, verify solutions to eliminate extraneous roots, and model practical scenarios like rates, work, and proportions.

3.1 Simplifying Rational Expressions (Reduction to Lowest Terms, Domain Restrictions)

3.2 Operations with Rational Expressions (Multiplication, Division, Addition & Subtraction with Common Denominators)

3.3 Solving Rational Equations (Solution Verification, Extraneous Root Identification, Rate/Work/Proportion Applications)

4. Additional Essential Concepts Solve exponential growth and decay equations and tackle basic radical equations commonly featured in the Advanced Math section, using strategies to interpret contexts and identify invalid solutions

4.1 Exponential Expressions and Equations (Growth & Decay Models, Contextual Interpretation)

4.2 Radical Equations (Basic Radical Solutions, Extraneous Solution Checks)

Related Courses

Foundations of Differentiation: From First Principles to Essential Rules (2)

Fundamentals of Antiderivatives & Indefinite Integration (5)

Systems of Equations: From Linear to Nonlinear Systems

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2. Polynomials and Factoring
Strengthen understanding of polynomial expressions through operations and identities. Employ diverse factoring methods—from GCF extraction to special patterns—and translate factors into roots for precise graphing and function interpretation.

3. Rational Expressions and Equations
Simplify complex rational expressions and master arithmetic operations with them. Solve rational equations with attention to domain restrictions, verify solutions to eliminate extraneous roots, and model practical scenarios like rates, work, and proportions.

4. Additional Essential Concepts
Solve exponential growth and decay equations and tackle basic radical equations commonly featured in the Advanced Math section, using strategies to interpret contexts and identify invalid solutions