SAT Math — Formulas & Facts to Know Cold flashcards

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Fifty question-and-answer cards for the formulas and facts the digital SAT Math section expects you to know cold: lines, systems, quadratics, exponents and radicals, exponential and percent models, statistics, probability, circles, trigonometry, volume, absolute value and function transformations.

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What is the slope-intercept form of a line, and what do $m$ and $b$ tell you?

$y = mx + b$ ⁠. The slope $m$ is the change in $y$ for each one-unit increase in $x$ ⁠, and the $y$ -intercept $b$ is the value of $y$ when $x = 0$ ⁠.

Watch out: a negative slope means the line falls from left to right; a slope of 0 is a horizontal line.
Linear Equations
When does a system of two linear equations have exactly one solution, and what does that solution represent?

When the two lines have different slopes. The solution is the single point where the lines cross — the $(x, y)$ pair that satisfies both equations at once.

Why: the same idea answers 'for how many values of $x$ is $f(x) = g(x)$ ⁠?' — count the points where the two graphs intersect.
Systems of Equations
What are the product, quotient and power rules for exponents, and what do zero and negative exponents mean?

$x^a \cdot x^b = x^{a+b}$ ⁠, $\frac{x^a}{x^b} = x^{a-b}$ and $(x^a)^b = x^{ab}$ ⁠. Any nonzero base to the zero power is 1, and a negative exponent means a reciprocal: $x^{-n} = \frac{1}{x^n}$ ⁠.

Watch out: the rules need the same base — $2^3 \cdot 3^2$ cannot be combined into a single power.
Exponents & Radicals
What is the general form of an exponential growth or decay model, and what does each part mean?

$y = a(1 + r)^t$ for growth and $y = a(1 - r)^t$ for decay, where $a$ is the starting amount, $r$ the rate per period as a decimal and $t$ the number of periods.

Written as $y = ab^t$ ⁠: $b > 1$ means growth, $0 < b < 1$ means decay.

Example: a car worth 20,000 that loses 12% of its value each year is worth $20000(0.88)^t$ after $t$ years.
Exponential Models
What is the formula for percent change, and what is the classic mistake?

Percent change is $\frac{N - O}{O} \times 100$ ⁠, where $N$ is the new value and $O$ the original. Always divide by the original value, never by the new one.

Example: a price that goes from 80 to 100 rose 25%, but a price that falls from 100 to 80 fell only 20%.
Percents · Ratios & Rates
What is the basic probability formula, and how do you find the probability that an event does not happen?

Probability is the number of favorable outcomes divided by the total number of equally likely outcomes, and it always lies between 0 and 1. The complement rule gives the opposite event: P(not A) = 1 − P(A).

Example: the probability of rolling a number other than 6 on a fair die is $1 - \frac{1}{6} = \frac{5}{6}$ ⁠.
Probability
What is the standard equation of a circle, and how do you read the center and radius from it?

$(x - h)^2 + (y - k)^2 = r^2$ ⁠, with center $(h, k)$ and radius $r$ ⁠.

Watch out: the right side is the radius squared and the signs inside flip — $(x - 1)^2 + (y + 2)^2 = 25$ has center $(1, -2)$ and radius 5, not 25.
Circles
What do sine, cosine and tangent mean in a right triangle?

SOH-CAH-TOA: $\sin\theta = \frac{o}{h}$ ⁠, $\cos\theta = \frac{a}{h}$ and $\tan\theta = \frac{o}{a}$ ⁠, where $o$ is the side opposite the angle $\theta$ ⁠, $a$ the side adjacent to it and $h$ the hypotenuse.

Watch out: opposite and adjacent are measured from the acute angle in question, never from the right angle; the hypotenuse is always the side across from the right angle.
Triangles & Trig
How do you solve an absolute-value equation such as $|2x - 1| = 7$ ⁠, and an inequality such as $|x - 5| < 3$ ⁠?

An absolute value equal to a positive number splits into two equations: $2x - 1 = 7$ or $2x - 1 = -7$ ⁠, giving $x = 4$ or $x = -3$ ⁠. An absolute value less than a number is a band: $|x - 5| < 3$ means $2 < x < 8$ ⁠, the values within 3 of 5.

Watch out: $|ax + b| = c$ has no solution when $c$ is negative, and $|x - a| > d$ is two separate rays: $x < a - d$ or $x > a + d$ ⁠.
Absolute Value
What does $f(x)$ mean, and how do you evaluate a composition such as $f(g(2))$ ⁠?

$f(x)$ is the output that the function $f$ gives for the input $x$ ⁠. For a composition, work from the inside out: find $g(2)$ first, then feed that number into $f$ ⁠.

Example: with $f(x) = x^2 + 1$ and $g(x) = 3x$ ⁠: $g(2) = 6$ ⁠, so $f(g(2)) = f(6) = 37$ ⁠. By contrast $g(f(2)) = g(5) = 15$ — order matters.
Functions & Transformations

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About these cards

Review status: Second-reader reviewed, with corrections applied.

Checked against:

Checked against the digital SAT Math reference sheet and the Assessment Framework for the Digital SAT Suite (version 4, September 2026) as published by College Board; reference only, all wording original.
OpenStax College Algebra 2e and OpenStax Introductory Statistics 2e, consulted as references; no text copied.

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