SAT Math - Medium Difficulty Core Concepts

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Slope-Intercept Form

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The equation **y = mx + b**, where *m* is the slope (rate of change) and *b* is the y-intercept. This is the most efficient form for quickly graphing a line or identifying the starting value in a real-world linear model.

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Linear Inequality Boundary

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A statement that compares two linear expressions using relation symbols like <, >, ≤, or ≥ instead of an equals sign. When multiplying or dividing both sides by a negative number, flip the inequality symbol.

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System of Linear Equations

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A set of two or more linear equations with the same variables. The **solution** is the coordinate pair (x, y) that satisfies **all** equations simultaneously—graphically, it is the point where the lines intersect.

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Quadratic Factoring: Difference of Squares

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An expression in the form **a² - b²** factors into **(a - b)(a + b)**. This is essential for simplifying rational expressions or solving equations where the constant term is negative.

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Quadratic Factoring: Perfect Square Trinomial

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Expressions like **a² + 2ab + b²** factor into **(a + b)²**. Recognizing this pattern (often seen as x² + 6x + 9) allows for quick solving by taking the square root of both sides.