formulas to know for the psat

CimarronTexas Editorial Teams

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10-01-2025

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PSAT Formulas You Absolutely Need to Know

The PSAT can feel overwhelming, but mastering a few key formulas significantly boosts your score. This isn't about memorizing every equation under the sun; it's about understanding the fundamental math concepts tested and knowing how to apply them efficiently. This guide focuses on the most frequently appearing formulas across the Math sections.

I. Geometry:

• Area of a Rectangle: Area = length × width This seemingly simple formula is the basis for many more complex geometry problems. Mastering it unlocks solutions for complex shapes broken down into rectangles.

• Area of a Triangle: Area = (1/2) × base × height Remember that the height is the perpendicular distance from the base to the opposite vertex, not necessarily a side length.

• Area of a Circle: Area = πr² and Circumference of a Circle: Circumference = 2πr Knowing both is crucial. Many problems involve both area and circumference calculations. Remember that π (pi) is approximately 3.14.

• Pythagorean Theorem: a² + b² = c² This is essential for right-angled triangles. a and b are the lengths of the legs, and c is the length of the hypotenuse (the side opposite the right angle). Understand its applications in finding side lengths and distances.

• Volume of a Rectangular Prism (Box): Volume = length × width × height This is fundamental for 3D geometry problems.

• Volume of a Cylinder: Volume = πr²h This formula is a combination of the area of a circle and the height of the cylinder.

II. Algebra:

• Slope of a Line: Slope (m) = (y₂ - y₁) / (x₂ - x₁) This is crucial for understanding the relationship between two points on a line and for writing linear equations.

• Slope-Intercept Form of a Line: y = mx + b Where m is the slope and b is the y-intercept (the point where the line crosses the y-axis). This is the most common way to represent a linear equation.

• Point-Slope Form of a Line: y - y₁ = m(x - x₁) This form is useful when you know a point on the line and its slope.

• Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a Used to solve quadratic equations of the form ax² + bx + c = 0. Know how to identify a, b, and c from the equation. This is a powerful tool for finding roots or x-intercepts.

• Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²] This finds the distance between two points (x₁, y₁) and (x₂, y₂) in a coordinate plane. It's essentially a clever application of the Pythagorean theorem.

III. Data Analysis:

While not strictly formulas, understanding concepts like mean (average), median (middle value), and mode (most frequent value) is crucial for the data analysis section. Knowing how to calculate and interpret these measures is key.

IV. Beyond Formulas: Strategies for Success

• Practice Regularly: Consistent practice is far more valuable than just memorizing formulas. Work through practice problems to solidify your understanding.

• Understand the Concepts: Don't just memorize formulas; understand why they work. This helps you adapt them to different problem types.

• Identify the Question Type: PSAT math problems often require more than just plugging numbers into a formula. Carefully read the question to identify what's being asked.

• Use Process of Elimination: If you're stuck, eliminate obviously wrong answers. This can significantly increase your chances of guessing correctly.

By mastering these key formulas and practicing diligently, you'll significantly improve your PSAT math score. Remember, understanding the underlying concepts is just as important as memorizing the formulas themselves. Good luck!