SAT Math Level Notes - Vocabulary Flashcards (Video)

A vocabulary set covering key SAT Math topics from the video notes.

Order of operations (PEMDAS)

The rule for evaluating expressions: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right).

DESMOS

An online graphing calculator used to graph functions and solve equations; highlighted in the notes for solving single-variable equations.

Linear function

A function with constant rate of change; its graph is a straight line.

Slope-intercept form

The equation y = mx + b, where m is the slope and b is the y-intercept.

Slope

The rate of change of a line; m = Δy/Δx = (y2 − y1)/(x2 − x1).

Y-intercept

The point where the graph crosses the y-axis (x = 0); the value b in y = mx + b.

X-intercept

The point where the graph crosses the x-axis (y = 0).

Variables

Quantities that can change or vary in an expression or equation.

Constants

Fixed values that do not change in an expression or equation.

Coefficients

Numbers that multiply variables in terms like 3x.

Systems of equations

Two or more equations solved together to find common solutions; often solved graphically or with DESMOS.

Parallel lines

Lines with the same slope that never intersect (in distinct lines).

Perpendicular lines

Lines whose slopes are negative reciprocals; they meet at a right angle.

Systems of inequalities

A set of inequalities solved together; the solution is the region common to all.

Number of solutions of a polynomial function

The number of real roots, corresponding to the number of x-values where the graph intersects the x-axis.

Translating English to math

Rules used to translate phrases: “of” often means multiplication; “is” means equals.

Exponent product rule

x^a · x^b = x^(a+b).

Exponent quotient rule

x^a / x^b = x^(a−b).

Exponent power rule

(x^a)^b = x^(a·b).

Fractional exponents

x^(1/a) = the a-th root of x.

Negative exponents

x^(−a) = 1/x^a.

Zero exponent

x^0 = 1 (for nonzero x).

Complementary angles

Two angles that add up to 90 degrees.

Supplementary angles

Two angles that add up to 180 degrees.

Vertical angles

Opposite angles formed by two intersecting lines; congruent.

Corresponding angles

Angles in the same relative position when a transversal crosses parallel lines; equal.

Interior angles of a polygon

Sum of interior angles of an n-sided polygon is 180(n − 2) degrees.

Isosceles triangles

Triangles with at least two equal sides; base angles are equal.

Equilateral triangles

Triangles with all three sides equal; all angles are 60 degrees.

Density

Density = mass/volume.

Pythagorean theorem

In a right triangle, a^2 + b^2 = c^2 where c is the hypotenuse.

Sine, Cosine, Tangent (SohCahToa)

sinθ = opposite/hypotenuse, cosθ = adjacent/hypotenuse, tanθ = opposite/adjacent.

Perimeter

The distance around a shape; sum of its side lengths.

Area

The measure of the region inside a shape; formula varies by shape.

Volume

The amount of space occupied by a 3D object; measured in cubic units.

Mean

The average: μ = (x1 + x2 + … + xn) / n.

Midpoint

The average point between two points: ((x1+x2)/2, (y1+y2)/2) in 2D.

Median

The middle value of a data set when ordered (or the average of the two middle values if even).

Range

Difference between maximum and minimum values: xmax − xmin.

Integers

Whole numbers that can be positive, negative, or zero; no fractions.

Horizontal shift

f(x) → f(x − h): shift right by h units.

Vertical shift

f(x) → f(x) + k: shift up by k units.

Percentage of

X% of a quantity means the quantity multiplied by the decimal form of the percent (e.g., 30% of x = 0.3x).

Percentage increase

New value = original × (1 + percent).

Percentage decrease

New value = original × (1 − percent).

Circle (general equation)

(x − h)^2 + (y − k)^2 = r^2 for a circle with center (h, k) and radius r.