SAT Math Formula Sheet- Essential Equations Reference
The SAT Math Formula Sheet You'll Actually Need
Most students spend hours memorizing formulas they'll never use. Here's the truth: the SAT tests a finite set of equations. Master these, and you're set.
This guide cuts through the noise. No fluff. No 47-page PDF downloads. Just the formulas that actually appear on test day.
Heart of Algebra: Linear Equations
About 33% of SAT Math focuses on linear relationships. These formulas show up constantly.
Slope Formula
When you need the steepness of a line:
m = (y₂ - y₁) / (x₂ - x₁)
Pick two points. Subtract. Divide. That's it.
Slope-Intercept Form
y = mx + b
m = slope, b = y-intercept. This is the form you'll work with most often when graphing lines.
Point-Slope Form
y - y₁ = m(x - x₁)
Use this when you know one point and the slope. Useful for writing equations quickly.
Standard Form
Ax + By = C
A, B, and C are integers. A should be positive. The SAT often asks you to convert from this form to slope-intercept.
Problem Solving and Data Analysis: Ratios and Proportions
About 28% of SAT Math covers this territory. Ratios show up in tables, graphs, and word problems.
Ratio Basics
A ratio of a to b means a/b. When a recipe calls for 3 parts flour to 2 parts water, that's 3:2 or 3/2.
Proportion Setup
a/b = c/d means ad = bc
Cross-multiply when solving proportion problems. This saves time on test day.
Percentage Formula
Part = Percent × Whole
Convert percent to decimal first. So 15% of 80 = 0.15 × 80 = 12.
Percent Change
(New - Old) / Old × 100
Positive = increase. Negative = decrease. Simple.
Advanced Math: Quadratics and Polynomials
About 28% of SAT Math involves nonlinear expressions. Quadratics dominate this section.
Quadratic Standard Form
ax² + bx + c = 0
You'll spend most of your time here. Factoring, graphing, and finding roots all start from this form.
Factoring Patterns
Memorize these three patterns. They appear constantly:
- Difference of squares: a² - b² = (a + b)(a - b)
- Perfect square trinomials: a² + 2ab + b² = (a + b)²
- Factored form: a(x - r₁)(x - r₂) where r₁ and r₂ are roots
Quadratic Formula
When factoring fails:
x = (-b ± √(b² - 4ac)) / 2a
The discriminant is the part under the square root: b² - 4ac. It tells you everything about the roots:
- Positive = two real roots
- Zero = one repeated root
- Negative = no real roots
Vertex Form
y = a(x - h)² + k
(h, k) is the vertex. This form makes graphing parabolas straightforward. The axis of symmetry is x = h.
Geometry and Trigonometry
About 27% of SAT Math requires geometric knowledge. The College Board provides some formulas, but not all.
Areas
- Rectangle: A = lw
- Triangle: A = ½bh
- Circle: A = πr²
- Trapezoid: A = ½(b₁ + b₂)h
Perimeters
- Rectangle: P = 2l + 2w
- Square: P = 4s
- Circle (Circumference): C = 2πr
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. This shows up in distance problems, coordinate geometry, and special right triangles.
Special Right Triangles
45-45-90 triangle sides: s, s, s√2
30-60-90 triangle sides: s, s√3, 2s
These ratios appear frequently. If you recognize the pattern, you skip calculations entirely.
Trigonometry Basics
SOH CAH TOA
- sin(θ) = opposite / hypotenuse
- cos(θ) = adjacent / hypotenuse
- tan(θ) = opposite / adjacent
You only need basic trig. The SAT rarely goes beyond these three ratios.
Circle Equations
Standard form: (x - h)² + (y - k)² = r²
(h, k) is the center. r is the radius. This is essential for circle problems in the coordinate plane.
Statistics and Probability
These formulas cover the remaining SAT Math questions. They show up in the no-calculator and calculator sections.
Mean (Average)
Mean = Sum of values / Number of values
Add everything up. Divide by how many numbers you have.
Median
Arrange values in order. The middle value is the median. If two middle values exist, average them.
Standard Deviation
The SAT won't ask you to calculate this from scratch. But understanding it helps: standard deviation measures spread from the mean. Larger spread = larger standard deviation.
Probability
P(event) = Favorable outcomes / Total outcomes
Probability is always between 0 and 1. Express as fraction, decimal, or percent.
Independent Events
P(A and B) = P(A) × P(B)
Multiply probabilities when events don't affect each other.
Dependent Events
P(A and B) = P(A) × P(B|A)
P(B|A) is the probability of B given that A happened. Adjust for conditional probability.
Quick Reference Table: Core Formulas
| Category | Formula | Use When |
|---|---|---|
| Slope | m = (y₂ - y₁) / (x₂ - x₁) | Finding line steepness |
| Linear | y = mx + b | Writing line equations |
| Quadratic | x = (-b ± √(b²-4ac)) / 2a | Solving any quadratic |
| Pythagorean | a² + b² = c² | Right triangle problems |
| Circle area | A = πr² | Circle area questions |
| Triangle area | A = ½bh | Triangle area questions |
| Probability | P = Favorable / Total | Basic probability |
| Percent | Part = Percent × Whole | Percentage calculations |
How to Use This Formula Sheet Effectively
Step 1: Sort What You Know From What You Don't
Go through each section. Mark formulas you already know cold. Identify gaps. Focus your study time there.
Step 2: Practice Deriving, Not Just Memorizing
Know why the quadratic formula works. Understand how slope connects to rise over run. Derivation builds retention. You won't freeze up if you forget a formula—you can rebuild it.
Step 3: Timed Practice With Formula Access
Do practice problems with this sheet in front of you. Build recognition speed. The goal is instant recall, not fumbling through references.
Step 4: Remove the Sheet
After practice, test yourself without the reference. Note which formulas trip you up. Drill those specifically.
Step 5: Focus on Weak Areas in Real Tests
On test day, skip what you don't know. Answer what you can. Come back if time allows. Don't waste minutes on one stubborn problem.
What the SAT Math Section Actually Tests
The College Board organizes SAT Math into four categories:
- Heart of Algebra — Linear equations, inequalities, systems
- Problem Solving and Data Analysis — Ratios, percentages, statistics
- Passport to Advanced Math — Quadratics, polynomials, complex equations
- Additional Topics — Geometry, trigonometry, complex numbers
Each category uses a limited set of formulas. This sheet covers them all.
Common Mistakes to Avoid
- Confusing slope formulas — Rise over run, not run over rise. Watch the order.
- Forgetting negative signs — Point-slope form demands attention to signs. Many errors happen here.
- Mixing up area and perimeter — Area is inside. Perimeter is border. Different formulas.
- Skipping units — Check whether answer needs inches, feet, or square units.
- Overlooking the discriminant — Always check b² - 4ac first when analyzing quadratics.
The Bottom Line
You don't need 200 formulas. You need these formulas, practiced until they're automatic. Work through problems. Build speed. Know which formula applies before you start solving.
That's the entire game.