Knowing the right SAT Math formulas can save time, reduce unnecessary algebra, and prevent avoidable mistakes.
The Digital SAT gives students a reference sheet with several common formulas. However, the reference sheet does not replace knowing how and when to use those formulas.
This guide focuses on the formulas and mathematical relationships students should be comfortable recognizing quickly across:
- Algebra
- Advanced Math
- Problem-Solving and Data Analysis
- Geometry and Trigonometry
Important: Bluebook provides a Math reference sheet during the SAT. You do not need to panic-memorize every geometry formula. Focus instead on formulas and relationships that require quick recognition, rearrangement, or application.
1. Learn the Slope Formula
Formula:
m = (y₂ − y₁) / (x₂ − x₁)
Use slope for:
- Linear relationships
- Rates of change
- Parallel and perpendicular lines
- Interpreting graphs
On the SAT, slope is often hidden inside a word problem rather than asked directly.
2. Know Slope-Intercept Form
Formula:
y = mx + b
Where:
- m = slope
- b = y-intercept
Practice moving equations into this form quickly and interpreting what the slope and intercept mean in context.
3. Use Point-Slope Form
Formula:
y − y₁ = m(x − x₁)
Point-slope form is useful when you know:
- A slope
- One point on the line
It can be faster than solving for the y-intercept first.
4. Use the Distance Formula
Formula:
d = √[(x₂ − x₁)² + (y₂ − y₁)²]
The distance formula is essentially the Pythagorean theorem on the coordinate plane.
You can also solve many distance questions by identifying the horizontal and vertical changes and using a right triangle.
5. Know the Midpoint Formula
Formula:
((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint questions are usually straightforward when you recognize that you are averaging the x-coordinates and y-coordinates separately.
6. Memorize the Quadratic Formula
For:
ax² + bx + c = 0
The quadratic formula is:
x = [-b ± √(b² − 4ac)] / 2a
The quadratic formula is a reliable backup when factoring is difficult.
On the Digital SAT, Desmos may also solve many quadratic questions quickly, but you should still understand what the roots represent.
7. Know the Axis of Symmetry
Formula:
x = −b / 2a
For a quadratic written as:
ax² + bx + c
this formula gives the x-coordinate of the vertex.
It is especially useful for:
- Maximum questions
- Minimum questions
- Symmetry
8. Understand the Discriminant
Formula:
b² − 4ac
The discriminant tells you how many real solutions a quadratic has.
- Positive discriminant: Two distinct real solutions
- Zero discriminant: One repeated real solution
- Negative discriminant: No real solutions
The SAT may ask about the number of solutions without requiring you to solve the entire quadratic.
9. Review Exponent Rules
Product Rule
aᵐ · aⁿ = aᵐ⁺ⁿ
Quotient Rule
aᵐ / aⁿ = aᵐ⁻ⁿ
Power of a Power
(aᵐ)ⁿ = aᵐⁿ
Negative Exponent
a⁻ⁿ = 1/aⁿ
Fractional Exponent
a^(1/n) = ⁿ√a
Advanced Math questions frequently test whether you can rewrite expressions into equivalent forms.
SAT Tip: Exponent fluency is often more important than memorizing one isolated formula.
10. Know Percent Change
Formula:
Percent Change = [(New − Original) / Original] × 100%
Be careful about which value is the original.
Many SAT percentage mistakes come from dividing by the wrong reference amount.
11. Understand Exponential Growth and Decay
A common growth model is:
y = a(1 + r)ᵗ
A common decay model is:
y = a(1 − r)ᵗ
Where:
- a = starting amount
- r = rate written as a decimal
- t = time or number of periods
The SAT often tests interpretation:
- What does the base mean?
- What does the exponent represent?
- How does a percentage rate translate into a growth factor?
12. Know How to Calculate the Mean
Formula:
Mean = Sum of Values / Number of Values
A useful rearrangement is:
Sum = Mean × Number of Values
This can make “a new value is added” questions much faster.
13. Review Probability
Formula:
Probability = Favorable Outcomes / Total Possible Outcomes
For conditional probability or table questions, the denominator changes based on the group you are conditioning on.
SAT Tip: Read the wording carefully before deciding what belongs in the denominator.
14. Know the Circle Equation
Formula:
(x − h)² + (y − k)² = r²
Where:
- Center = (h, k)
- Radius = r
Remember that the signs appear opposite inside the parentheses.
15. Use the Pythagorean Theorem
Formula:
a² + b² = c²
The Pythagorean theorem is foundational for:
- Right triangles
- Coordinate geometry
- Diagonal problems
- Distance problems
16. Recognize Special Right Triangles
45-45-90 Triangle
The side relationship is:
x, x, x√2
30-60-90 Triangle
The side relationship is:
x, x√3, 2x
These relationships appear on the SAT reference material, but you should still recognize them quickly.
17. Know Basic Trigonometry
For right triangles:
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
The SAT does not require advanced trigonometry.
You should be comfortable choosing the correct ratio and interpreting angles in right triangles.
18. Understand Arc Length and Sector Area
For a central angle of θ degrees:
Arc Length
Arc Length = (θ/360) × Circumference
Sector Area
Sector Area = (θ/360) × Circle Area
These formulas are easier to remember conceptually:
The angle tells you what fraction of the full circle you are using.
SAT Formulas You Get vs. Formulas You Should Know
Bluebook includes a reference sheet with commonly used geometry formulas.
That means memorization should not become the center of your SAT Math preparation.
Instead, focus on relationships that appear across many question types, including:
- Slope
- Quadratic structure
- Percent change
- Exponent rules
- Circle equations
- Averages
- Probability
- Common algebraic forms
How to Study SAT Math Formulas
Group Formulas by Concept
Study related formulas together instead of memorizing them randomly.
Apply Each Formula
For each formula, solve several SAT-style applications.
Practice Rearranging Formulas
Don’t only practice formulas when the desired variable is already isolated.
Learn What Each Variable Means
Understand what every variable represents in context.
Use Desmos When Appropriate
Desmos can help verify or visualize your work, but make sure you can recognize the mathematical structure first.
The Biggest SAT Math Formula Mistake
Students often believe a formula sheet will fix a Math weakness.
It won’t.
The SAT rarely says:
“Use this formula now.”
The real skill is:
Recognize the relationship → Translate the problem → Apply the relationship → Execute without an algebra error
Frequently Asked Questions
Does the SAT give you a formula sheet?
Yes. Bluebook provides a reference sheet with commonly used formulas on tests that include Math questions.
Practice with the reference sheet before test day so you know what is already available.
Do I need to memorize the quadratic formula for the SAT?
It is strongly useful to know.
Desmos can solve many quadratic questions, but the quadratic formula and discriminant are useful for symbolic questions and for understanding how the number of solutions changes.
Should I memorize every geometry formula?
No.
Know the common relationships and understand the formulas on the reference sheet.
Spend more time learning how geometry questions are structured than memorizing obscure formulas.
Ready to Strengthen Your SAT Math Skills?
Knowing formulas is only one part of SAT Math preparation.
The real advantage comes from recognizing which mathematical relationship a question is testing and choosing the most efficient way to solve it.
Ready for more targeted SAT Math preparation? Explore SC Tutoring’s SAT Math tutoring resources and get started today