SAT & ACT Math Glossary

A B C D E F G H I L M O P Q R S T V X Y Z

A 8 terms

Absolute value

|x| is the distance of x from 0 on the number line. Always non-negative. |−7| = 7.

Acute angle

An angle measuring less than 90°.

Adjacent (right triangle)

The leg of a right triangle next to a given non-right angle (not the hypotenuse).

Algebraic expression

A combination of numbers, variables, and operations without an equals sign, e.g. 3x + 2.

Amplitude

For y = a sin(bx), the value |a| — the maximum vertical distance from the midline.

Arithmetic sequence

A sequence with a constant difference between terms: aₙ = a₁ + (n − 1)d.

Asymptote

A line that a curve approaches but never touches.

Average rate of change

(f(b) − f(a)) / (b − a) over the interval [a, b].

B 2 terms

Base (exponent)

In bⁿ, the value b being raised to a power.

Binomial

A polynomial with exactly two terms, e.g. x + 3.

C 10 terms

Centre (circle)

The point (h, k) equidistant from every point on the circle.

Coefficient

The numerical factor in front of a variable term, e.g. the 5 in 5x².

Combining like terms

Adding terms that have the same variable and exponent: 3x + 4x = 7x.

Complex number

A number of the form a + bi where i = √(−1).

Composite function

(f ∘ g)(x) = f(g(x)) — apply g first, then f.

Conditional probability

P(A | B), the probability of A given that B has occurred. P(A and B)/P(B).

Congruent

Same size and shape; corresponding parts are equal.

Conic section

Curves formed by slicing a cone: circle, ellipse, parabola, hyperbola.

Constant

A value that does not change, e.g. the 5 in y = 3x + 5.

Cosine

In a right triangle, cos θ = adjacent / hypotenuse (the C in CAH).

D 5 terms

Degree (polynomial)

The highest exponent of the variable, e.g. degree of 4x³ − x is 3.

Determinant (2×2)

For matrix [[a,b],[c,d]] the value ad − bc.

Difference of squares

a² − b² = (a − b)(a + b). Common factoring pattern.

Discriminant

b² − 4ac inside the quadratic formula. Sign tells you the number of real solutions.

Domain

The set of input values (x) for which a function is defined.

E 4 terms

Equation

A statement that two expressions are equal, with an equals sign.

Exponent

In bⁿ, the value n indicating how many times b is multiplied by itself.

Exponential function

A function of the form y = a·bˣ where b > 0 and b ≠ 1.

Extraneous solution

A solution that arises algebraically but does not satisfy the original equation.

F 3 terms

Factor

A number or expression that divides another with no remainder.

Function

A rule that assigns exactly one output to each input.

Function notation

f(x) means "the value of function f at x".

G 1 terms

Geometric sequence

A sequence with constant ratio: aₙ = a₁ · rⁿ⁻¹.

H 1 terms

Hypotenuse

The side opposite the right angle in a right triangle (longest side).

I 6 terms

Identity

An equation true for all values of the variable, e.g. sin² θ + cos² θ = 1.

Inequality

A relation using <, >, ≤, or ≥ instead of =.

Integer

A whole number — positive, negative, or zero.

Intercept

Where a graph crosses an axis. x-intercept = where y = 0; y-intercept = where x = 0.

Inverse function

f⁻¹(x) — undoes f. f(f⁻¹(x)) = x.

Irrational number

A real number that cannot be written as a/b. Includes √2 and π.

L 2 terms

Linear equation

An equation whose graph is a straight line; degree 1 in the variables.

Logarithm

log_b(x) = y means bʸ = x. The exponent you raise b to.

M 6 terms

Matrix

A rectangular array of numbers arranged in rows and columns.

Mean

The average — sum divided by count.

Median

The middle value of a sorted data set.

Midpoint

((x₁+x₂)/2, (y₁+y₂)/2). The centre of a segment.

Mode

The most frequent value in a data set.

Monomial

A polynomial with one term, e.g. 4x²y.

O 3 terms

Obtuse angle

An angle measuring greater than 90° and less than 180°.

Origin

The point (0, 0) where the x and y axes meet.

Outlier

A data point unusually far from the rest of the data.

P 8 terms

Parabola

The graph of a quadratic function, U-shaped.

Parallel lines

Two lines in the plane that never meet. Same slope.

Percent change

(new − old) / old × 100%.

Perimeter

The total length around the boundary of a shape.

Perpendicular lines

Two lines that meet at 90°. Slopes multiply to −1.

Polynomial

A sum of terms aₙxⁿ where exponents are non-negative integers.

Probability

A number between 0 and 1 measuring how likely an event is.

Pythagorean theorem

In a right triangle, a² + b² = c² where c is the hypotenuse.

Q 2 terms

Quadratic formula

x = (−b ± √(b² − 4ac)) / 2a — solves any ax² + bx + c = 0.

Quadratic function

A function of the form f(x) = ax² + bx + c with a ≠ 0.

R 11 terms

Radian

An angle measure where 180° = π radians.

Radical

An expression involving a root, e.g. √x or ³√x.

Range (data)

max − min of a data set.

Range (function)

The set of output values (y) a function can produce.

Rate of change

How a quantity changes per unit of another. Slope is a rate of change.

Ratio

A comparison of two numbers, written as a:b or a/b.

Rational equation

An equation containing one or more rational expressions.

Rational expression

A ratio of two polynomials, e.g. (x + 1) / (x² − 4).

Real number

Any number on the number line — rational or irrational.

Reciprocal

The multiplicative inverse: reciprocal of x is 1/x.

Right triangle

A triangle with one 90° angle.

S 10 terms

Sample

A subset of a larger population used to estimate properties of the whole.

Scientific notation

A number written as a × 10ⁿ with 1 ≤ |a| < 10.

Sector

A "pie slice" region of a circle bounded by two radii and an arc.

Similar figures

Same shape, possibly different sizes; corresponding sides proportional.

Sine

In a right triangle, sin θ = opposite / hypotenuse (the S in SOH).

Slope

Rise over run: (y₂ − y₁) / (x₂ − x₁). The steepness of a line.

Solution (equation)

A value of the variable that makes the equation true.

Standard deviation

A measure of how spread out data values are around the mean.

Standard form (line)

Ax + By = C with integer coefficients.

System of equations

Two or more equations considered together; a solution satisfies all.

T 4 terms

Tangent (trig)

tan θ = opposite / adjacent (the T in TOA).

Term

A single number, variable, or product separated by + or − in an expression.

Transformation (function)

A change to a graph: shift, stretch, reflect.

Trinomial

A polynomial with exactly three terms, e.g. x² + 5x + 6.

V 4 terms

Variable

A letter representing an unknown or changing quantity.

Vertex (parabola)

The maximum or minimum point of a parabola.

Vertex form (parabola)

y = a(x − h)² + k, with vertex at (h, k).

Volume

The amount of three-dimensional space a solid occupies.

X 1 terms

x-intercept

Where a graph crosses the x-axis (y = 0).

Y 1 terms

y-intercept

Where a graph crosses the y-axis (x = 0).

Z 1 terms

Zero of a function

An x-value where f(x) = 0; same as an x-intercept.