SAT Math: Part 1 – Heart of Algebra

About Course

This micro-course focuses exclusively on the Heart of Algebra domain tested on the SAT. Through five targeted topics—covering linear equations, systems, absolute value, graphing, and inequalities—you’ll build procedural fluency and strategic reasoning. Each module combines concise video lessons, guided practice, and real-world word problems to help you master the algebraic skills most frequently tested. By the end, you’ll solve one- and two-variable equations, analyze systems, interpret absolute value, graph lines, and work with inequalities—all with the confidence and speed needed for top SAT scores.

Solve one-variable equations, including multi-step, fraction, and decimal cases
Rearrange literal equations and handle variables on both sides
Translate complex word problems (mixture, rate, percent, distance) into equations
Apply substitution, elimination, and graphing to solve systems of equations
Interpret absolute value as distance and solve two-case equations
Graph lines in slope-intercept, point-slope, and standard forms and derive equations from data
Understand slope and intercept in real-world contexts; distinguish parallel vs. perpendicular
Solve and graph single-variable, absolute value, and systems of inequalities

Course Content

1. Linear Equations
Explore methods for solving linear equations in one variable, including advanced cases involving multiple steps, fractions, decimals, and literal rearrangements. You’ll also learn to translate common word-problem scenarios into algebraic expressions and validate solutions.

1.1 Solving One-Variable Equations (One-Step, Two-Step, Multi-Step, Fractions & Decimals)
1.2 Variables on Both Sides & Literal Equations (Rearranging Formulas)
1.3 Translating Word Problems (Mixture, Rate, Percent, Distance) & Checking Extraneous Solutions

Systems of Equations
Explore techniques for solving and interpreting systems of two linear equations. You’ll practice substitution, elimination, and graphing, classify solution sets (intersecting, parallel, or coincident lines), and apply these methods to real-world scenarios like cost–revenue and age/work problems.

3. Absolute Value
Understand absolute value as a distance measure, learn two-case solution strategies, recognize impossible cases, and apply absolute value equations to contextual problems.

4. Graphing Linear Equations
Master various linear-equation forms, compute slope, plot lines, derive equations from data or graphs, and interpret slope (m) and intercept (b) in context, including parallel and perpendicular relationships.

5. Linear Inequalities & Systems of Inequalities
Learn to solve, graph, and interpret single-variable and compound inequalities, tackle absolute value inequalities, and shade feasible regions for systems—applying these skills to constraint-based word problems.

About Course

What Will You Learn?

Course Content

1. Linear Equations
Explore methods for solving linear equations in one variable, including advanced cases involving multiple steps, fractions, decimals, and literal rearrangements. You’ll also learn to translate common word-problem scenarios into algebraic expressions and validate solutions.

1.1 Solving One-Variable Equations (One-Step, Two-Step, Multi-Step, Fractions & Decimals)

1.2 Variables on Both Sides & Literal Equations (Rearranging Formulas)

1.3 Translating Word Problems (Mixture, Rate, Percent, Distance) & Checking Extraneous Solutions

2.1 Substitution & Elimination Methods

2.2 Graphical Solutions & Classification (Intersecting, Parallel, Coincident Lines)

2.3 Modeling Real-World Scenarios (Cost vs. Revenue, Age/Mix/Work Problems)

3. Absolute Value
Understand absolute value as a distance measure, learn two-case solution strategies, recognize impossible cases, and apply absolute value equations to contextual problems.

3.1 Interpreting ∣x∣ as Distance on a Number Line

3.2 Solving ∣ax + b∣ = c via Two-Case Analysis & No-Solution Recognition

3.3 Absolute Value in Contextual Word Problems

4. Graphing Linear Equations
Master various linear-equation forms, compute slope, plot lines, derive equations from data or graphs, and interpret slope (m) and intercept (b) in context, including parallel and perpendicular relationships.

4.1 Forms of a Line (Slope-Intercept, Point-Slope, Standard) & Computing Slope

4.2 Plotting Lines & Deriving Equations from Graphs or Tables

4.3 Contextual Interpretation of m & b; Parallel vs. Perpendicular Lines

5. Linear Inequalities & Systems of Inequalities
Learn to solve, graph, and interpret single-variable and compound inequalities, tackle absolute value inequalities, and shade feasible regions for systems—applying these skills to constraint-based word problems.

5.1 One-Variable & Compound Inequalities on a Number Line

5.2 Absolute Value Inequalities (∣ax + b∣ c)

5.3 Systems of Two-Variable Inequalities & Modeling Constraints

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Advanced Polynomial Factoring

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SAT Math: Part 1 – Heart of Algebra

About Course

What Will You Learn?

Course Content

1. Linear Equations Explore methods for solving linear equations in one variable, including advanced cases involving multiple steps, fractions, decimals, and literal rearrangements. You’ll also learn to translate common word-problem scenarios into algebraic expressions and validate solutions.

1.1 Solving One-Variable Equations (One-Step, Two-Step, Multi-Step, Fractions & Decimals)

1.2 Variables on Both Sides & Literal Equations (Rearranging Formulas)

1.3 Translating Word Problems (Mixture, Rate, Percent, Distance) & Checking Extraneous Solutions

2.1 Substitution & Elimination Methods

2.2 Graphical Solutions & Classification (Intersecting, Parallel, Coincident Lines)

2.3 Modeling Real-World Scenarios (Cost vs. Revenue, Age/Mix/Work Problems)

3. Absolute Value Understand absolute value as a distance measure, learn two-case solution strategies, recognize impossible cases, and apply absolute value equations to contextual problems.

3.1 Interpreting ∣x∣ as Distance on a Number Line

3.2 Solving ∣ax + b∣ = c via Two-Case Analysis & No-Solution Recognition

3.3 Absolute Value in Contextual Word Problems

4. Graphing Linear Equations Master various linear-equation forms, compute slope, plot lines, derive equations from data or graphs, and interpret slope (m) and intercept (b) in context, including parallel and perpendicular relationships.

4.1 Forms of a Line (Slope-Intercept, Point-Slope, Standard) & Computing Slope

4.2 Plotting Lines & Deriving Equations from Graphs or Tables

4.3 Contextual Interpretation of m & b; Parallel vs. Perpendicular Lines

5. Linear Inequalities & Systems of Inequalities Learn to solve, graph, and interpret single-variable and compound inequalities, tackle absolute value inequalities, and shade feasible regions for systems—applying these skills to constraint-based word problems.

5.1 One-Variable & Compound Inequalities on a Number Line

5.2 Absolute Value Inequalities (∣ax + b∣ c)

5.3 Systems of Two-Variable Inequalities & Modeling Constraints

Related Courses

Foundations of Polynomial Factoring

Fundamentals of Antiderivatives & Indefinite Integration (5)

Advanced Polynomial Factoring

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1. Linear Equations
Explore methods for solving linear equations in one variable, including advanced cases involving multiple steps, fractions, decimals, and literal rearrangements. You’ll also learn to translate common word-problem scenarios into algebraic expressions and validate solutions.

3. Absolute Value
Understand absolute value as a distance measure, learn two-case solution strategies, recognize impossible cases, and apply absolute value equations to contextual problems.

4. Graphing Linear Equations
Master various linear-equation forms, compute slope, plot lines, derive equations from data or graphs, and interpret slope (m) and intercept (b) in context, including parallel and perpendicular relationships.

5. Linear Inequalities & Systems of Inequalities
Learn to solve, graph, and interpret single-variable and compound inequalities, tackle absolute value inequalities, and shade feasible regions for systems—applying these skills to constraint-based word problems.