Essential SAT Math Formulas: Your Complete Cheat Sheet for Test Day

When preparing for the SAT, having a solid grasp of essential math formulas can make a huge difference in your score. While the SAT provides a reference sheet with some basic formulas, it’s not enough—you need to know and understand additional formulas to tackle different types of math problems efficiently.

In this SAT formula sheet, we’ve compiled the most important formulas you should memorize before test day.

SAT Reference Sheet vs. Additional Formulas

The SAT reference sheet provided during the exam includes a few formulas for geometry and basic calculations. However, many essential formulas—especially in algebra, advanced geometry, and statistics—are not given, so it’s crucial to know them by heart.

Below is a breakdown of must-know formulas categorized by topic.

Algebra Formulas

These formulas are fundamental for solving equations, inequalities, and functions.

• Slope Formula: m = (y₂ - y₁) / (x₂ - x₁)

• Slope-Intercept Form: y = mx + b

• Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

• Difference of Squares: a² - b² = (a - b)(a + b)

• Exponential Growth/Decay: A = A₀(1 ± r)t

• Product and Sum of Roots of a Quadratic Equation:\n

  • Sum of Roots: -b/a

  • Product of Roots: c/a

• Parallel and Perpendicular Lines:\n

  • Parallel Lines: M₁ = M₂

  • Perpendicular Lines: M₁ × M₂ = -1

• Point-Slope Form of a Line: y - y₁ = m(x - x₁)

• Absolute Value Equations: If |x| = a, then x = ±a

Geometry Formulas

Memorizing these formulas will help with questions on circles, triangles, and other shapes.

• Area of a Triangle: A = ½ × base × height

• Pythagorean Theorem: a² + b² = c²

• Circumference of a Circle: C = 2πr

• Area of a Circle: A = πr²

• Volume of a Cylinder: V = πr²h

• Diagonal of a Rectangle: d = √(l² + w²)

• Equation of a Circle: (x - h)² + (y - k)² = r²

• Sum of Interior Angles in a Polygon: (n - 2) × 180°

• Each Interior Angle of a Regular Polygon: [(n - 2) × 180°] / n

• Exterior Angle Theorem: An exterior angle of a triangle equals the sum of the two opposite interior angles.

Statistics & Probability Formulas

Understanding basic statistical formulas can help with probability and data interpretation questions.

• Mean (Average): Mean = (Sum of Terms) / (Number of Terms)

• Probability: P(A) = (Desired Outcomes) / (Total Outcomes)

• Standard Deviation: Measures how spread out numbers are from the mean.

• Median: The middle value when numbers are ordered from least to greatest.

• Mode: The number that appears most frequently.

• Permutations: P(n, r) = n! / (n - r)!

• Combinations: C(n, r) = n! / [r!(n - r)!]

Trigonometry & Special Right Triangles

Although the SAT does not heavily focus on trigonometry, a few key formulas can be useful.

• Sine, Cosine, Tangent:\n

  • sin θ = opposite / hypotenuse

  • cos θ = adjacent / hypotenuse

  • tan θ = opposite / adjacent

• Special Right Triangles:\n

  • 30°-60°-90° Triangle: Sides are in the ratio 1 : √3 : 2

  • 45°-45°-90° Triangle: Sides are in the ratio 1 : 1 : √2

• Law of Sines: a / sin A = b / sin B = c / sin C

• Law of Cosines: c² = a² + b² - 2ab cos C

Exponents & Logarithms

These formulas are essential for solving exponential and logarithmic problems.

• Laws of Exponents:\n

  • am × an = am+n

  • am / an = am-n

  • (am)n = amn

  • a-n = 1 / an

  • a0 = 1

• Logarithm Rule: logb(x) = y means by = x.

Why Memorizing These Formulas Matters

While understanding concepts is key, quickly recalling formulas saves time and increases accuracy on the SAT. The more familiar you are with these formulas, the more confident you’ll feel on test day.

📌 Tip: Practice using these formulas with actual SAT questions to reinforce your understanding!

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