Preparing for the Digital SAT Math requires more than memorizing formulas. Understanding key concepts and knowing when to apply them are essential for solving questions efficiently.
This guide covers essential SAT Math formulas and core concepts across all SAT math domains, helping you identify what’s provided on test day, what you need to memorize, and how to apply formulas to common SAT Math questions.
What SAT Math Formulas Are Provided on Test Day
The Digital SAT provides a built-in Math Reference Sheet in the Bluebook app, accessible throughout both Math modules. It includes formulas for area, circumference, volume, the Pythagorean theorem, and special right triangles.
However, important formulas such as the quadratic formula, slope formula, and exponent rules are not included.
Here’s everything provided on the official SAT Math Reference Sheet.
1. Area and Circumference Formulas
| Shape | Formula |
|---|---|
| Area of a Circle | A = πr² |
| Circumference of a Circle | C = 2πr |
| Area of a Rectangle | A = lw |
| Area of a Triangle | A = ½bh |
Here, (r) is the radius, (l) is the length, (w) is the width, (b) is the base, and (h) is the height.
2. Right Triangle Formulas
Pythagorean Theorem
a² + b² = c²
Here, (a) and (b) are the legs of a right triangle, and (c) is the hypotenuse.
Special Right Triangles
| Triangle | Side Ratios | Opposite Angles |
|---|---|---|
| 30°–60°–90° | 1 : √3 : 2 | 30° : 60° : 90° |
| 45°–45°–90° | 1 : 1 : √2 | 45° : 45° : 90° |
The side ratios correspond to the opposite angles in the order shown. These relationships help you find missing side lengths without using trigonometric functions.
3. Volume Formulas
| Solid | Formula |
|---|---|
| Rectangular Prism | V = lwh |
| Cylinder | V = πr²h |
| Sphere | V = (4/3)πr³ |
| Cone | V = ⅓πr²h |
| Pyramid (Rectangular Base) | V = ⅓lwh |
Here, (V) represents volume, (r) is the radius, (h) is the height, and (l) and (w) represent length and width. For the pyramid, (h) is the perpendicular height.
4. Geometry Facts
- A full circle contains 360 degrees or 2π radians.
- The interior angles of a triangle add up to 180 degrees.
SAT Math Tip: Even though these formulas are provided, knowing the most common ones by heart can save time and help you focus on more challenging questions.
The SAT Math Reference Sheet covers essential geometry formulas, but many important formulas are not provided. Let’s look at the additional SAT Math formulas you should memorize before test day.
What SAT Math Formulas Should You Memorize?
While the official SAT Math Reference Sheet covers basic geometry, many important formulas are not provided. Here are the essential SAT Math formulas worth memorizing, organized by topic for quick review.
1. Linear Equations and Slope Formulas
Linear equations are a major part of SAT Algebra. Understanding slopes, intercepts, and different equation forms can help you solve questions efficiently.
| Formula | Equation | Purpose |
|---|---|---|
| Slope | m = (y₂ − y₁)/(x₂ − x₁) | Rate of change between two points |
| Slope-Intercept Form | y = mx + b | Identify slope and y-intercept |
| Point-Slope Form | y − y₁ = m(x − x₁) | Write a line from a point and slope |
| Standard Form | Ax + By = C | Slope = −A/B, when B ≠ 0 |
Here, m represents the slope and b represents the y-intercept in slope-intercept form.
Here, (m) represents the slope and (b) represents the y-intercept in slope-intercept form.
Remember:
- Parallel lines have equal slopes when their slopes are defined.
- Perpendicular lines have slopes whose product is (-1), when both slopes are defined.
- In word problems, the slope represents the rate of change, while the y-intercept represents the starting value.
Systems of Linear Equations
For two linear equations, compare their coefficients to determine the number of solutions.
| Condition | Number of Solutions |
|---|---|
| Coefficients of x and y are not proportional | Exactly one |
| Variable coefficients are proportional, but constants are not in the same proportion | No solution |
| All corresponding coefficients and constants are proportional | Infinitely many |
SAT Math Tip: When a system contains an unknown constant such as k, check whether the equations represent intersecting, parallel, or identical lines before solving.
2. Quadratic Formulas
Quadratic formulas help solve nonlinear equations and identify roots, vertices, and maximum or minimum values.
Quadratic Formula
For ax² + bx + c = 0, where a ≠ 0:
x = (−b ± √(b² − 4ac))/(2a)
Discriminant
D = b² − 4ac
| Discriminant | Number of Real Solutions |
|---|---|
| D > 0 | Two distinct real solutions |
| D = 0 | Exactly one real solution |
| D < 0 | No real solutions |
Three Forms of a Quadratic Function
| Form | Equation | What It Reveals |
|---|---|---|
| Standard Form | y = ax² + bx + c | Y-intercept |
| Vertex Form | y = a(x − h)² + k | Vertex (h, k) |
| Factored Form | y = a(x − r₁)(x − r₂) | X-intercepts r₁, r₂, when real |
Vertex Formula
x = −b/(2a)
This gives the x-coordinate of the vertex. If a > 0, the parabola opens upward and has a minimum; if a < 0, it opens downward and has a maximum.
3. Exponent Rules
Exponent rules are useful for simplifying expressions, solving equations, and recognizing equivalent mathematical forms.
| Rule | Formula |
|---|---|
| Product Rule | aᵐ · aⁿ = aᵐ⁺ⁿ |
| Quotient Rule | aᵐ/aⁿ = aᵐ⁻ⁿ |
| Power Rule | (aᵐ)ⁿ = aᵐⁿ |
| Zero Exponent | a⁰ = 1 |
| Negative Exponent | a⁻ⁿ = 1/aⁿ |
| Fractional Exponent | aᵐ⁄ⁿ = ⁿ√(aᵐ) |
These rules apply wherever the expressions are defined. In particular, expressions involving division by a require a ≠ 0.
4. Percentages and Exponential Models
Percentage formulas are essential for SAT Problem-Solving and Data Analysis, while exponential models describe growth and decay over time.
| Formula | Equation |
|---|---|
| Percentage Change | (New − Original)/Original × 100% |
| Value After a p% Increase | x(1 + p/100) |
| Value After a p% Decrease | x(1 − p/100) |
| Exponential Growth | y = a(1 + r)ᵗ |
| Exponential Decay | y = a(1 − r)ᵗ |
| Growth Every k Time Units | y = a(1 + r)ᵗ⁄ᵏ |
Here, a is the initial amount, r is the positive rate of change expressed as a decimal, and t represents time. In the last formula, r is the growth rate per k time units.
- SAT Math Tip: Use multipliers for percentage changes. A 15% increase means multiplying by 1.15, while a 20% decrease means multiplying by 0.80. For successive changes, multiply the factors rather than adding the percentages.
5. Statistics and Probability Formulas
Statistics and probability questions focus on interpreting data, calculating averages, and understanding the likelihood of events.
| Formula | Equation | Purpose |
|---|---|---|
| Mean | x̄ = Σxᵢ/n | Average of a data set |
| Total from Mean | Sum = x̄ × n | Find the total from an average |
| Probability | P(A) = Favorable Outcomes / Total Outcomes | Probability when outcomes are equally likely |
| Conditional Probability | P(A ∣ B) = P(A ∩ B) / P(B) | Probability of A given B, where P(B) > 0 |
Key Concepts:
- Outliers: Can affect the mean more than the median.
- Standard Deviation: Measures how spread out values are around the mean.
- Margin of Error: Describes uncertainty in a sample-based estimate.
- Correlation: Does not necessarily imply causation.
SAT Math Tip: For conditional probability questions involving two-way tables, use the total for the given condition as the denominator.
6. Coordinate Geometry and Circle Formulas
These formulas help calculate distances, midpoints, and properties of circles on the coordinate plane.
| Formula | Equation | Purpose |
|---|---|---|
| Distance | d = √[(x₂ − x₁)² + (y₂ − y₁)²] | Distance between two points |
| Midpoint | M = ((x₁ + x₂)/2, (y₁ + y₂)/2) | Midpoint of a segment |
| Circle Equation | (x − h)² + (y − k)² = r² | Center (h, k), radius r |
Remember: The center of a circle is (h, k), and the right side of the equation represents r², not the radius itself.
On the SAT, circle equations may appear in expanded form. Complete the square for both x and y to find the center and radius:
x² + 6x + y² − 4y = 12
⇒ (x + 3)² + (y − 2)² = 25
The center is (−3, 2) and the radius is 5.
7. Arcs, Sectors, and Scale Factors
Arc length, sector area, and scale factors are useful for solving geometry questions involving circles and similar figures.
| Formula | Equation |
|---|---|
| Arc Length (Degrees) | s = (θ/360°) × 2πr |
| Arc Length (Radians) | s = rθ |
| Sector Area (Degrees) | A = (θ/360°) × πr² |
| Sector Area (Radians) | A = ½r²θ |
Here, θ is the central angle and r is the radius. Radian formulas require θ to be measured in radians.
SAT Math Tip: When a figure’s dimensions change by a linear scale factor of k, its area changes by k² and its volume by k³.
8. Trigonometric Ratios
The official SAT Reference Sheet provides special right triangle relationships, but students should also know the three basic trigonometric ratios.
| Ratio | Formula |
|---|---|
| Sine | sin θ = Opposite/Hypotenuse |
| Cosine | cos θ = Adjacent/Hypotenuse |
| Tangent | tan θ = Opposite/Adjacent |
Remember these ratios using SOH–CAH–TOA.
For complementary acute angles:
sin θ = cos(90° − θ)
If sin x° = cos y° and both x and y are acute angles, then x + y = 90°.
Final Thoughts: Master SAT Math Formulas Through Practice
The SAT Math Reference Sheet provides only a portion of the formulas you may need. Focus on three priorities: memorize formulas that aren’t provided, recognize when to apply them, and practice solving questions under timed conditions.
The built-in Desmos calculator can help you graph functions and check answers, but understanding the underlying math is just as important. For more strategies, check out our SAT Math Tips and Tricks.
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