SAT Math: The 20 Formulas You Must Know

The Digital SAT provides a reference sheet with some formulas, but knowing them cold saves precious time. Here are the 20 most important formulas organized by topic.

Algebra (8 formulas)

1. Slope Formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Used for: Finding the rate of change between two points.

2. Slope-Intercept Form

$y = mx + b$

Where $m$ is slope and $b$ is the y-intercept. This is the most common equation form on the SAT.

3. Point-Slope Form

$y - y_1 = m(x - x_1)$

Use this when you know the slope and one point.

4. Standard Form of a Line

$Ax + By = C$

Tip: To find the x-intercept, set y = 0. To find the y-intercept, set x = 0.

5. Quadratic Formula

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For $ax^2 + bx + c = 0$. The discriminant $b^2 - 4ac$ tells you the number of solutions:

• Positive → two real solutions
• Zero → one real solution
• Negative → no real solutions

6. Vertex Form of a Parabola

$y = a(x - h)^2 + k$

The vertex is at $(h, k)$. If $a > 0$, the parabola opens upward.

7. Difference of Squares

$a^2 - b^2 = (a + b)(a - b)$

8. Exponential Growth/Decay

$y = a \cdot b^t$

Where $a$ is the initial value and $b$ is the growth factor. If $b > 1$, it is growth; if $0 < b < 1$, it is decay.

Geometry (7 formulas)

9. Area of a Triangle

$A = \frac{1}{2}bh$

10. Pythagorean Theorem

$a^2 + b^2 = c^2$

Know the common triples: (3,4,5), (5,12,13), (8,15,17), (7,24,25).

11. Area of a Circle

$A = \pi r^2$

12. Circumference of a Circle

$C = 2\pi r = \pi d$

13. Volume of a Cylinder

$V = \pi r^2 h$

14. Volume of a Sphere

$V = \frac{4}{3}\pi r^3$

15. Arc Length and Sector Area

$\text{Arc length} = \frac{\theta}{360} \cdot 2\pi r$

$\text{Sector area} = \frac{\theta}{360} \cdot \pi r^2$

Statistics and Probability (3 formulas)

16. Mean (Average)

$\bar{x} = \frac{\sum x_i}{n}$

17. Probability

$P(A) = \frac{\text{favorable outcomes}}{\text{total outcomes}}$

18. Percent Change

$\text{Percent change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100$

Trigonometry (2 formulas)

19. SOH CAH TOA

$\sin\theta = \frac{\text{opposite}}{\text{hypotenuse}}, \quad \cos\theta = \frac{\text{adjacent}}{\text{hypotenuse}}, \quad \tan\theta = \frac{\text{opposite}}{\text{adjacent}}$

20. Special Right Triangles

• 45-45-90: sides in ratio $1 : 1 : \sqrt{2}$
• 30-60-90: sides in ratio $1 : \sqrt{3} : 2$

How to Study These Formulas

1. Make flashcards — Use our SAT Math Flashcards for spaced repetition
2. Practice applying them — Knowing a formula is not the same as recognizing when to use it
3. Time yourself — On the real test, you need to recall formulas instantly

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Practice all of these formulas with SAT Math practice problems on Study Mondo.