sat formulas to remember

Guri Bee

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22-10-2024

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Essential SAT Formulas You Need to Know: A Quick Reference Guide

The SAT, a standardized test for college admissions, often throws tricky questions at you. But don't worry! There are key SAT formulas you can memorize to ace those math sections. Here's a list of the most important ones, broken down for easy understanding.

1. Slope-Intercept Form of a Line:

Formula: y = mx + b

What it means: This formula is the backbone of linear equations.

• m: Represents the slope of the line (how steep it is). A positive slope indicates an upward slant, while a negative slope indicates a downward slant.
• b: Represents the y-intercept, the point where the line crosses the y-axis.

Example: Let's say we have the equation y = 2x + 3. The slope is 2, meaning for every 1 unit you move to the right, you move 2 units up. The y-intercept is 3, meaning the line crosses the y-axis at the point (0, 3).

2. Quadratic Formula:

Formula: x = [-b ± √(b² - 4ac)] / 2a

What it means: This formula is used to solve quadratic equations, which are equations with an x² term. It finds the x-values where the graph of the equation crosses the x-axis.

Example: For the equation x² - 5x + 6 = 0, we can use the quadratic formula with a = 1, b = -5, c = 6. Plugging in these values, we get x = (5 ± √(25 - 24)) / 2 which simplifies to x = 2 or x = 3. These are the solutions to the equation.

3. Distance Formula:

Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²]

What it means: This formula calculates the distance between two points in a coordinate plane.

Example: To find the distance between the points (1, 2) and (4, 6), we plug in the values: d = √[(4 - 1)² + (6 - 2)²] which gives us d = √(3² + 4²) = 5. So, the distance between these two points is 5 units.

4. Midpoint Formula:

Formula: [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

What it means: This formula finds the midpoint of a line segment connecting two points.

Example: The midpoint of the line segment connecting (2, 5) and (8, 1) is found by: [(2 + 8) / 2, (5 + 1) / 2] = (5, 3).

5. Area of a Circle:

Formula: A = πr²

What it means: This formula calculates the area enclosed within a circle.

Example: A circle with a radius of 5 units has an area of A = π(5)² = 25π square units.

6. Circumference of a Circle:

Formula: C = 2πr or C = πd

What it means: This formula calculates the distance around a circle.

Example: A circle with a diameter of 10 units has a circumference of C = π(10) = 10π units.

7. Pythagorean Theorem:

Formula: a² + b² = c²

What it means: This formula relates the sides of a right triangle. a and b are the lengths of the two legs (the shorter sides), and c is the length of the hypotenuse (the longest side).

Example: In a right triangle with legs of length 3 and 4, the hypotenuse has a length of c = √(3² + 4²) = √(25) = 5.

Bonus Tip:

Always remember the Soh Cah Toa mnemonic! This helps you remember the trigonometric ratios for right triangles:

• Soh: Sine = Opposite / Hypotenuse
• Cah: Cosine = Adjacent / Hypotenuse
• Toa: Tangent = Opposite / Adjacent

Important Note: These formulas are not a substitute for understanding the underlying concepts. Practice solving problems and applying these formulas to ensure you're truly mastering the SAT math concepts.

Further Resources:

• Khan Academy: https://www.khanacademy.org/ (Free online learning platform with SAT prep resources)
• College Board: https://www.collegeboard.org/ (Official SAT website with practice tests and study guides)

By understanding and memorizing these crucial formulas, you'll be well on your way to acing the SAT math section. Good luck!