SAT Math Formulas- Essential Equations for Test Success

Every SAT Math Formula You Actually Need

The College Board doesn't hand you a formula sheet. You either know these or you don't. Here's every equation that shows up on test day, broken down by category so you can actually find what you need.

I cut the fat. No motivational garbage. Just the math.

Linear Equations and Algebra

Most SAT math questions test your ability to work with lines, slopes, and basic algebraic relationships. These formulas show up constantly.

Slope and Line Equations

Slope formula:

m = (y₂ - y₁) / (x₂ - x₁)

Point-slope form:

y - y₁ = m(x - x₁)

Slope-intercept form:

y = mx + b

Here, m is the slope and b is the y-intercept. If you forget everything else, remember slope-intercept. It shows up in roughly 30% of algebra questions.

Systems of Equations

When you have two equations with two unknowns, you can solve by:

• Substitution — isolate one variable, plug it into the other equation
• Elimination — multiply equations so one variable cancels out
• Graphing — find where lines intersect ( Calculator section only)

The intersection point (x, y) is your answer.

Quadratic Equations

Quadratics appear in both sections. Know these cold.

Standard Form

ax² + bx + c = 0

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a

This is your last resort. Try factoring first. If that fails, plug into the formula. The expression under the square root — b² - 4ac — is called the discriminant. It tells you:

• Positive = two real solutions
• Zero = one solution
• Negative = no real solutions (not on SAT)

Factoring Patterns

a² - b² = (a + b)(a - b)

a² + 2ab + b² = (a + b)²

a² - 2ab + b² = (a - b)²

These difference of squares and perfect square trinomials patterns save you time. Memorize them.

Exponents and Radicals

Rules for manipulating powers:

• aᵐ × aⁿ = aᵐ⁺ⁿ
• aᵐ / aⁿ = aᵐ⁻ⁿ
• (aᵐ)ⁿ = aᵐⁿ
• a⁰ = 1 (anything to the zero power equals 1)
• a⁻ⁿ = 1 / aⁿ

For radicals:

• √(ab) = √a × √b
• √(a/b) = √a / √b
• √(a²) = |a| (absolute value, not just a)

That last one trips people up. The square root of a squared number is always positive. If x² = 16, x = ±4, but √16 = 4.

Geometry Formulas

No-calculator section requires you to have these memorized. The calculator section lets you use a graphing calculator, but these still save time.

Area Formulas

• Rectangle: A = lw (length × width)
• Triangle: A = ½bh (base × height ÷ 2)
• Circle: A = πr²
• Trapezoid: A = ½(b₁ + b₂)h

Perimeter

• Rectangle: P = 2l + 2w
• Triangle: P = a + b + c (sum of all sides)
• Circle (circumference): C = 2πr or C = πd

Volume

• Rectangular prism: V = lwh
• Cylinder: V = πr²h
• Sphere: V = (4/3)πr³
• Cone: V = (1/3)πr²h

Right Triangle — Pythagorean Theorem

a² + b² = c²

c is the hypotenuse (longest side, opposite the right angle). a and b are the legs.

This is the most tested geometry concept on the entire SAT. If you remember nothing else, remember this.

Special Right Triangles

45-45-90 triangle:

Legs are equal. If each leg = x, then hypotenuse = x√2.

30-60-90 triangle:

Short leg = x, long leg = x√3, hypotenuse = 2x.

These show up constantly. They're faster than Pythagorean Theorem and give you exact answers.

SOHCAHTOA — Trigonometry Basics

For right triangles only:

• Sin = opposite / hypotenuse
• Cos = adjacent / hypotenuse
• Tan = opposite / adjacent

The SAT gives you SOHCAHTOA on the reference sheet. But knowing what it means matters more than memorizing the letters.

Circle Geometry

• Area: A = πr²
• Circumference: C = 2πr
• Arc length: (fraction of circle) × 2πr
• Sector area: (fraction of circle) × πr²

For arc and sector problems, find the fraction from the central angle: angle / 360.

Statistics and Probability

Mean, Median, Mode

• Mean = sum of values / number of values
• Median = middle value when arranged in order
• Mode = most frequent value

Mean is what the SAT calls "average." Watch for questions asking for "the average of the means" or weighted averages.

Standard Deviation

Measures spread from the mean. Higher standard deviation = data more spread out. The SAT won't ask you to calculate it — just interpret it. If data points are all close to the mean, standard deviation is small.

Probability

P(event) = (number of favorable outcomes) / (total outcomes)

Always between 0 and 1. Express as fraction, decimal, or percent.

Independent events: P(A and B) = P(A) × P(B)

Dependent events: P(A and B) = P(A) × P(B after A)

Questions about "with replacement" = independent. "Without replacement" = dependent.

Proportions and Ratios

a/b = c/d means cross-multiply: ad = bc

Ratios work the same way. If a:b = 2:3 and a = 10, then b = 15.

Complex Numbers

When you see i, you're dealing with complex numbers. Memorize:

• i = √(-1)
• i² = -1
• i³ = -i
• i⁴ = 1

Powers of i cycle every 4. Find the remainder when exponent divided by 4:

• Remainder 1 = i
• Remainder 2 = -1
• Remainder 3 = -i
• Remainder 0 = 1

Absolute Value

|x| = distance from zero on number line. Always positive or zero.

|x| = a means x = a or x = -a

|x| < a means -a < x < a

|x| > a means x > a or x < -a

Getting Started: How to Use This List

Don't try to memorize everything at once. Here's a practical approach:

1. Day 1-2: Learn linear equations, slope, and Pythagorean Theorem. These appear most often.
2. Day 3-4: Geometry formulas — area, perimeter, special right triangles.
3. Day 5-6: Quadratics, factoring patterns, and the quadratic formula.
4. Day 7: Statistics, probability, and complex numbers.

Write each formula on a flashcard. Practice deriving relationships, not just memorizing answers. The SAT tests whether you understand how formulas connect.

Common Mistakes That Cost Points

• Forgetting to distribute negatives — (x - 3)² ≠ x² - 9. Expand it: x² - 6x + 9.
• Mixing up median and mean — median is the middle, mean is the average.
• Using Pythagorean Theorem on non-right triangles — only works for right angles.
• Dropping absolute value signs — √(x²) = |x|, not x.
• Forgetting to convert units — inches to feet, hours to minutes. Check the problem.

Quick Reference Table

Bookmark this page. Come back before every practice test. The formulas you forget are the ones you need most.