SAT & ACT math glossary
Terms that show up on the test or in our worked solutions, defined the way they're actually used in test prep.
This glossary is deliberately short. The SAT and ACT do not test obscure mathematical vocabulary — but you will see the words below in question stems and answer choices, and a single misread definition can cost you a question. If a term you're looking for isn't here, it's almost certainly not on the test.
- Absolute value
- The distance of a number from zero on the number line, written |x|. Always non-negative. Common SAT trap: |x − 3| < 5 has two cases, x − 3 < 5 and −(x − 3) < 5, which combine to −2 < x < 8.
- Asymptote
- A line that a curve approaches but never touches. Rational functions like 1/(x−2) have a vertical asymptote at x=2 and a horizontal asymptote at y=0.
- Coefficient
- The numerical multiplier of a variable. In 7x², the coefficient is 7.
- Composite function
- A function whose input is another function: (f∘g)(x) = f(g(x)). Read inside-out.
- Discriminant
- For ax² + bx + c, the value b² − 4ac. Tells you the number of real roots: positive = two, zero = one, negative = none.
- Domain
- The set of input values for which a function is defined. Watch for division-by-zero and even roots of negative numbers.
- Exponential growth
- A quantity that multiplies by a constant factor each time period: y = a·b^t. Distinguish from linear growth, which adds a constant.
- Factor
- A number or expression that divides another evenly. Factoring is one of the most useful SAT skills — practice until it's automatic.
- Function
- A rule assigning each input exactly one output. Vertical line test: a graph is a function if no vertical line crosses it more than once.
- Inequality
- A statement comparing two expressions with <, ≤, >, or ≥. Multiply both sides by a negative and you must flip the inequality.
- Interquartile range
- The difference between the 75th and 25th percentile of a data set. Resistant to outliers; the standard deviation is not.
- Linear function
- A function whose graph is a straight line: f(x) = mx + b. Slope m, y-intercept b.
- Mean
- The arithmetic average. Sensitive to outliers — adding one extreme value shifts the mean noticeably but the median barely.
- Median
- The middle value of a sorted data set. Resistant to outliers.
- Mode
- The most frequent value in a data set. Rarely tested directly; sometimes used to set up a trap.
- Parabola
- The graph of a quadratic function. Opens up if a > 0 in y = ax² + bx + c, down if a < 0. Vertex at x = −b/(2a).
- Polynomial
- A sum of terms of the form a·x^n where n is a non-negative integer. Degree is the highest n.
- Quadratic formula
- x = (−b ± √(b² − 4ac))/(2a). Memorize. The fastest way to solve any quadratic where factoring isn't obvious.
- Range
- For a function, the set of output values. For a data set, max minus min.
- Rational expression
- A ratio of two polynomials. Watch for restricted domain values where the denominator is zero.
- Slope
- Rise over run; the change in y per unit change in x. For two points (x₁, y₁) and (x₂, y₂), slope = (y₂ − y₁)/(x₂ − x₁).
- Standard deviation
- A measure of spread around the mean. Larger = more spread out. Both tests test interpretation, not the formula itself.
- System of equations
- Two or more equations to be satisfied simultaneously. On the SAT, almost always solved by substitution or elimination.
- Trigonometric ratios
- In a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent. SOH-CAH-TOA.
- Unit circle
- A circle of radius 1 centered at the origin. The coordinates (cos θ, sin θ) trace the circle as θ varies. Memorize the values at 0°, 30°, 45°, 60°, 90°.
- Vertex form
- For a parabola: y = a(x − h)² + k, with vertex at (h, k). Convert from standard form by completing the square.
- x-intercept
- Where a graph crosses the x-axis (y = 0). Same as a root of the corresponding equation.
- y-intercept
- Where a graph crosses the y-axis (x = 0). For y = mx + b, the y-intercept is b.
Why glossaries can be a trap
Spending a weekend memorizing a 200-term math glossary is one of the worst uses of test prep time. The test does not check definitions for their own sake; it asks you to use them inside problems. Memorizing definitions in isolation produces the appearance of progress without actually moving your score. Use this glossary as a quick reference while drilling actual problems on the topic and subtopic pages, not as a study target on its own.