SAT Math Formulas to Memorize (and What's Given)

The digital SAT gives you a reference sheet with basic geometry formulas, but most of the formulas that actually decide your score are not on it. You need to memorize roughly two dozen: slope and line equations, the quadratic formula and vertex shortcut, the circle equation, exponential growth and decay, percent change, and right-triangle trigonometry. This guide lists exactly what is provided, what is not, and how each formula shows up.

What formulas are on the SAT reference sheet?

In the Bluebook app you can open a reference sheet at any time during the Math section. It includes:

It also states that a circle has 360 degrees of arc (2π radians) and that the angles of a triangle sum to 180 degrees.

Even though these are provided, memorize them anyway. Opening the sheet costs time and breaks focus, and strong scorers rarely look at it.

Linear equation formulas to memorize

Linear equations are the single most tested idea on the SAT. Know these cold:

• Slope: m = (y₂ − y₁) / (x₂ − x₁)
• Slope-intercept form: y = mx + b, where b is the y-intercept
• Point-slope form: y − y₁ = m(x − x₁)
• Standard form: Ax + By = C, with slope −A/B
• Parallel lines: equal slopes
• Perpendicular lines: slopes are negative reciprocals (2 and −½)

Example: A line passes through (1, 4) and (3, 10). What is its equation?

Slope = (10 − 4) / (3 − 1) = 3. Then 4 = 3(1) + b, so b = 1, giving y = 3x + 1.

In word problems, slope is the rate (cost per item, miles per hour) and the y-intercept is the starting value. Our SAT algebra guide covers how these are tested in context.

Quadratic formulas to memorize

For worked examples of every quadratic question type, see SAT quadratics.

Exponent and exponential formulas

Exponent rules:

• xᵃ · xᵇ = xᵃ⁺ᵇ
• xᵃ / xᵇ = xᵃ⁻ᵇ
• (xᵃ)ᵇ = xᵃᵇ
• x⁰ = 1
• x⁻ᵃ = 1 / xᵃ
• x^(a/b) = the b-th root of xᵃ

Exponential growth and decay:

• Growth: y = a(1 + r)ᵗ
• Decay: y = a(1 − r)ᵗ

Here a is the starting amount and r is the rate as a decimal. If a population grows 4% per year, the factor is 1.04. If a car loses 15% of its value each year, the factor is 0.85.

Example: A value of 500 doubles every 3 years. Write it as a function of t years: y = 500 · 2^(t/3).

Percent formulas

Percent questions appear in both the Problem-Solving and Data Analysis domain and in word problems throughout the test.

• Percent of a number: part = (percent / 100) × whole
• Percent change: (new − original) / original × 100
• Increase by p%: multiply by (1 + p/100)
• Decrease by p%: multiply by (1 − p/100)

Example: A price rises 20% and then falls 20%. The net change is 1.2 × 0.8 = 0.96, a 4% decrease, not zero. This exact trap appears often.

Statistics and probability formulas

• Mean: sum of values ÷ number of values
• Median: middle value when ordered (average the two middle values if the count is even)
• Range: maximum − minimum
• Probability: favorable outcomes ÷ total outcomes
• Conditional probability from a table: count in the cell ÷ total of the given row or column

Also know the concepts behind the numbers: adding an outlier shifts the mean more than the median, and a larger sample generally gives a smaller margin of error.

Geometry and circle formulas not on the sheet

• Circle equation: (x − h)² + (y − k)² = r², center (h, k), radius r
• Arc length: (θ / 360) × 2πr
• Sector area: (θ / 360) × πr²
• Degrees to radians: multiply by π / 180
• Distance: √((x₂ − x₁)² + (y₂ − y₁)²)
• Midpoint: ((x₁ + x₂)/2, (y₁ + y₂)/2)
• Similar figures: if side lengths scale by k, area scales by k² and volume by k³
• Interior angle sum of a polygon: (n − 2) × 180

When a circle equation is given in expanded form like x² + y² − 6x + 4y = 12, complete the square on x and y to find the center (3, −2) and radius 5. That is one of the most common hard circle questions.

Trigonometry formulas to memorize

• SOH-CAH-TOA: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent
• Complementary angles: sin(x) = cos(90° − x)

Example: In a right triangle, sin(A) = 3/5. What is cos(B), where B is the other acute angle? Because A and B are complementary, cos(B) = sin(A) = 3/5.

Our SAT geometry and trigonometry guide has more examples of these.

How to memorize SAT math formulas efficiently

1. Group them by topic, as above, instead of memorizing a random list.
2. Learn each formula with one example problem. A formula you have used is a formula you remember.
3. Write the list from memory once a week and check what you missed.
4. Practice in timed sets. The goal is recognizing which formula a question needs within a few seconds.
5. Know when Desmos replaces a formula. Graphing a circle or a parabola can give you the center, vertex, or intercepts directly.

How Ivystar can help

Memorizing formulas is the easy part; knowing which one a question is quietly asking for is where points are won. In Ivystar SAT Prep, a 1-on-1 tutor builds that recognition with targeted practice, and our students gain an average of 170 points. Take a free practice SAT or book a free strategy call to get a plan.