SAT-MATH

1

SAT- Lesson 1: Introduction to the Variable and Combining Like Terms

This foundational lesson introduces students to the concept of a variable as a placeholder for unknown values and teaches the fundamental rules of combining like terms to simplify algebraic expressions.

2m 13

2

SAT-Lesson-2: Solving Single-Variable Linear Equations

This comprehensive guide teaches students how to systematically isolate a single variable in linear equations using inverse operations, clear fractions, distribute coefficients safely, and recognize common SAT structural shortcuts.

4m 7

3

SAT-Math-3: Setting Up Linear Equations from Word Problems

This lesson teaches students how to accurately translate English word problems into mathematical equations by identifying key operational keywords, defining variables, and structuring equations using real-world rate models.

3m 3

4

SAT-Math-4: Understanding Absolute Value Equations

This lesson covers the geometric and algebraic definition of absolute value, how to solve absolute value equations systematically, and how to identify equations that have no solution.

2m 5

5

SAT-Math-5: The Concept of Slope: Steepness and Direction

This lesson introduces the geometric and practical concept of slope, exploring how it measures the steepness and direction of a line on the coordinate plane, and how to identify positive, negative, zero, and undefined slopes at a glance.

2m 3

6

SAT-Math-6: Calculating Slope ($m = \frac{y_2 - y_1}{x_2 - x_1}$) from Two Points

This lesson teaches students how to use the formal slope formula to calculate the slope of a line when given any two coordinate points, handling negative coordinate traps, and recognizing special cases.

2m 6

7

SAT-Math-7: Slope-Intercept Form in Depth

This lesson explores the most high-yield linear equation format on the SAT: Slope-Intercept Form. Students will learn how to instantly extract the slope and y-intercept from the equation, rewrite equations into this form, and decode its components.

2m 4

8

SAT-Math-8: Point-Slope Form and Standard Form

This lesson covers two alternative linear equation formats—Point-Slope Form and Standard Form—teaching students how to use them to write equations from data points and how to extract information quickly.

2m 3

9

SAT-Math-9: Graphing Linear Equations Quickly

This lesson teaches students how to sketch and read linear graphs efficiently on the coordinate plane using the y-intercept and slope, minimizing dependencies on slow point-by-point plotting methods.

2m 3

10

SAT-Math-10: Interpreting Slopes and Intercepts in Context

This lesson teaches students how to decode the real-world meaning of the slope and y-intercept in linear models, translating abstract coefficients into concrete operational descriptions.

2m 3

11

SAT-Math-11: Parallel Lines and Equal Slopes

This lesson explores the relationship between geometric parallel lines and their algebraic slopes, showing students how to determine if lines never intersect and how to write equations for parallel paths.

2m 3

12

SAT-Math-12: Perpendicular Lines and Negative Reciprocal Slopes

This lesson covers the geometric and algebraic relationship between perpendicular lines, teaching students how to find and apply negative reciprocal slopes to solve coordinate geometry problems.

2m 4

13

SAT-Math-13: Solving Multi-Step Linear Inequalities

This lesson covers how to solve multi-step linear inequalities, emphasizing the foundational rules of balance and the critical rule of flipping the inequality sign when multiplying or dividing by a negative number.

2m 3

14

SAT-Math-14: Graphing Linear Inequalities on the Coordinate Plane

This lesson teaches students how to represent linear inequalities visually on the $xy$-plane by drawing boundary lines and determining the correct solution region through shading.

2m 3

15

SAT-Math-15: Modeling Real-World Scenarios with Inequalities

This lesson teaches students how to construct linear inequalities from real-world constraints, budgets, and minimum/maximum requirements expressed in word problems.

2m 3

16

SAT-Math-16: Systems of Linear Equations: Solving by Substitution

This lesson teaches students how to solve a system of two linear equations using the substitution method, emphasizing when to choose this strategy and how to execute it without arithmetic errors.

2m 3

17

SAT-Math-17: Systems of Linear Equations: Solving by Elimination

This lesson teaches students how to solve a system of linear equations using the elimination method, focusing on multiplying equations to align coefficients and canceling variables efficiently.

2m 3

18

SAT-Math-18: Word Problems Involving Systems of Linear Equations

This lesson teaches students how to break down complex, multi-sentence word problems into a system of two linear equations, focusing on distinguishing between quantity equations and value/cost equations.

2m 3

19

SAT-Math-19: Systems with Infinite Solutions

This lesson teaches students how to recognize systems of equations that have infinitely many solutions, analyzing them both geometrically as identical lines and algebraically using proportional coefficients.

2m 3

20

SAT-Math-20: Systems with No Solution

This lesson teaches students how to recognize systems of linear equations that have no solution, analyzing them geometrically as parallel lines and algebraically as equations with identical variable slopes but different constant values.

2m 4

21

SAT-Math-21: Systems of Linear Inequalities and Bounded Regions

This lesson teaches students how to graph systems of linear inequalities, identify their overlapping solution regions (bounded regions), and determine if specific coordinate points fall within the valid solution set.

3m 7

22

SAT-Math-22: Absolute Value Inequalities on the Number Line

This final lesson of Block A teaches students how to solve and graph absolute value inequalities, translating them into either bounded "sandwich" intervals or split "outer" intervals on the number line.

2m 5

23

SAT-Math-23: Laws of Exponents: Multiplication, Division, and Power-to-Power

This lesson covers the foundational rules of exponent mechanics, teaching students how to simplify expressions involving products, quotients, and powers of exponential terms with identical bases.

2m 3

24

SAT-Math-24: Negative and Fractional Exponents

This lesson covers how to interpret and manipulate expressions with negative and fractional (rational) exponents, teaching students how to flip bases to remove negatives and convert fractions into radicals.

2m 3

25

SAT-Math-25: Simplifying Radical Expressions

This lesson teaches students how to simplify radical expressions by extracting perfect squares, performing arithmetic operations on radicals, and rewriting roots for optimal calculation speed.

2m 3

26

SAT-Math-26: Rationalizing Denominators

This lesson teaches students how to eliminate radicals from the denominator of a fraction, covering both single-term radicals and two-term radical expressions using the conjugate method.

2m 3

27

SAT-Math-27: Introduction to Polynomials: Adding and Subtracting

This lesson introduces polynomials, defining terms like degrees and leading coefficients, and teaches students how to accurately add and subtract polynomial expressions by grouping like terms.

2m 3

28

SAT-Math-28: Multiplying Polynomials (FOIL and beyond)

This lesson teaches students how to multiply polynomial expressions, mastering the FOIL method for binomials and expanding to multi-term distribution systematically.

1m 3

29

SAT-Math-29: Factoring: Greatest Common Factor and Grouping

This lesson teaches students how to reverse polynomial multiplication by extracting the Greatest Common Factor (GCF) from an expression and applying the grouping method to factor multi-term polynomials.

2m 3

30

SAT-Math-30: Factoring: Difference of Squares and Perfect Square Trinomials

This lesson covers two high-yield special factoring shortcuts on the SAT—the Difference of Squares and Perfect Square Trinomials—enabling students to identify patterns and factor quadratic expressions instantly without using the grouping method.

2m 7

31

SAT-Math-31: Factoring Standard Quadratics ($x^2 + bx + c$)

This lesson teaches students how to factor standard trinomial quadratics where the leading coefficient is 1, focusing on the "Product-Sum" method to find the correct binomial factors.

2m 10