SAT Math Vocab

Integer

The natural numbers, their opposites, and zero.

Sum

The result of addition.

Product

The result of multiplication.

Difference

The result of subtraction.

Quotient

The result of division.

Remainder

The amount left over after dividing a number.

Divisor

A number by which another number is divided.

Factor

A number or expression that is multiplied by another number or expression to get a product.

Prime Number

A whole number that has exactly two factors: 1 and itself.

Multiple of an Integer

The product of that integer and another integer.

Even Number

A whole number divisible by 2. (Property of 0: even number, not negative, not positive).

Odd Number

Numbers that cannot be divided evenly into groups of two.

Exponent

A mathematical notation indicating the number of times a quantity is multiplied by itself.

Laws of Exponents

Rules that describe relationships between exponents for certain operations.

Negative Exponent

An exponent less than zero (x^{-n} = \frac{1}{x^n}) which causes the base and its exponent to move positions in a fraction.

Fractional Exponent

An exponent where the numerator is the power of the base and the denominator is the type of root (e.g., x^{\frac{a}{b}} = \sqrt[b]{x^a}).

Zero Product Property

If the product of two or more numbers is 0, then at least one of the numbers is 0. (ab = 0 \implies a=0 or b=0).

Distributive Property

A property indicating that each term inside a set of parentheses can be multiplied by a factor outside: a(b + c) = ab + ac.

Property of 1

Multiplying a number by 1 gives that same number (n \times 1 = n).

Percent

A ratio that compares a number to 100. To find the percent of a number, convert the percent to a decimal and multiply by the value.

Ratio

A comparison of two quantities by division (X/Y or X:Y), where the numerator is associated with the word 'to' and the denominator with 'of'.

Proportion

A statement of equality between two or more ratios.

Direct Variation

If y is directly proportional to x, then y = kx.

Inverse Variation

If y is inversely proportional to x, then y = \frac{k}{x}.

Average (Mean)

The total sum of numbers divided by the amount of numbers (\bar{x} = \frac{\sum x}{n}).

Weighted Average

Total weight divided by the amount of people/units weighed.

Median

The middle number in a sorted list of data.

Mode

The most frequently occurring number in a set.

Range

The distance between the highest and lowest scores in a set of data.

Parallel Lines

Lines in the same plane that never intersect; they have equal slopes.

Alternate Interior Angles

Angles within a pair of parallel lines and on opposite sides of a transversal; they are congruent.

Corresponding Angles

Angles in the same relative position at each intersection where a transversal crosses two lines.

Triangle Angle Sum

The measures of the three angles in a triangle add up to 180^{\circ}. In a right triangle, the two acute angles add up to 90^{\circ}.

Pythagorean Theorem

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

Distance Formula

d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Area of a Circle

A = \pi r^2

Circumference of a Circle

C = 2\pi r or C = \pi d

Similar Triangles

Triangles with the same shape but different sizes; corresponding angles are equal and corresponding sides are proportional.

Parallelogram Properties

Opposite angles are congruent and opposite sides are parallel.

Rectangle Properties

All properties of a parallelogram, plus all angles are right angles (90^{\circ}) and diagonals are congruent.

Volume of a Rectangular Solid

V = l \times w \times h; for a cube, V = s^3.

Volume of a Pyramid or Cone

V = \frac{1}{3}Bh, where B is the area of the base.

Slope Formula

m = \frac{y2 - y1}{x2 - x1}

Equation of a Line

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

Slopes of Perpendicular Lines

They are opposite reciprocals; their product is -1.

Equation of a Circle

(x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center and r is the radius.

Probability

\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}

Arithmetic Sequence

A sequence where each term is found by adding the same constant common difference to the previous term.

Geometric Sequence

A sequence where each term is found by multiplying the previous term by the same constant common ratio.

SOH CAH TOA

\sin = \frac{\text{Opposite}}{\text{Hypotenuse}}, \cos = \frac{\text{Adjacent}}{\text{Hypotenuse}}, \tan = \frac{\text{Opposite}}{\text{Adjacent}}