SAT Math: The 20 Formulas You Must Know
By Study Mondo Team
title: "SAT Math: The 20 Formulas You Must Know" description: "A complete guide to every math formula tested on the Digital SAT — with examples and tips for when to use each one." date: "2025-03-05" author: "Study Mondo Team" tags: ["SAT", "Math", "Formulas"]
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
- Make flashcards — Use our SAT Math Flashcards for spaced repetition
- Practice applying them — Knowing a formula is not the same as recognizing when to use it
- Time yourself — On the real test, you need to recall formulas instantly
Practice all of these formulas with SAT Math practice problems on Study Mondo.