SAT MATH

integer

the natural numbers, their opposites, and zero

sum

add

product

multiply

difference

subtraction

quotient

division

remainder

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

odd number

Odd numbers can NOT 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 which causes the base and its exponent to move positions in a fraction

fractional exponent

The numerator is the power of the base, the denominator is the type of root

properties of square roots

multiplication of the roots

if the product of two or more numbers is 0, what do you know about the numbers?

one of the numbers is 0

distributive property

a property indicating a special way in which multiplication is applied to addition of two or more numbers in which each term inside a set of parentheses can be multiplied by a factor outside the parentheses, such as a(b + c) = ab + ac

properties of 0

integer, not negative, not positive, even number

properties of 1

Multiplying a number by 1 gives it that number

percent

A ratio that compares a number to 100

how do you find a percent of a number?

convert percent to a decimal and then multiply times the value

ratio

A comparison of two quantities by division (X/Y or X:Y-- numerator associate with word "to" and denominator "of"

proportion

A statement of equality of two or more ratios.

directly proportional

if y is directly proportional to x, then y = kx

inversely proportional

if y is indirectly proportional to x, then y = k/x

average

the total sum of numbers ÷ the amount of numbers

weight averaged

total weight ÷ amount of people weighed

median

Middle Number

mode

Most frequently occurring number

straight angle

An angle that is 180 degrees

parallel lines

lines in the same plane that never intersect

alternate interior angles

Angles that lie within a pair of lines and on opposite side of a transversal.

alternate exterior angles

Angles that lay outside the parallel lines and are on opposite sides of the transversal; They are congruent.

corresponding angles

Angles formed by a transversal cutting through 2 or more lines that are in the same relative position.

same side interior angles

two interior angles on the same side of the transversal

measures of the 3 angles in a triangle

should add up to 180

measures of the 2 acute angles in a right triangle

should add up to 90

how do you solve distance problems

D= √(x₁-x₂)²+(y₁+y₂)²

how do you find the distance between 2 points?

c² = a² + b²

counting principal

uses multiplication to find the number of possible ways two of more events can occur

exterior angle of a triangle

An angle that forms a linear pair with an angle of the triangle

Pythagorean theorem

a²+b²=c²

properties of a 45-45-90 triangle

properties of a 30-60-90 triangle

triangle inequality theorem

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

formula for the area of a CIRCLE

A=πr²

special formula for the area of a triangle

a= 1/2 bh

similar triangles (and their properties)

Similar triangles have the same shape: corresponding angles are equal and corresponding sides are proportional

what is true about the areas of similar triangles?

A correlation coefficient shows the relationship between two sets of numbers.

exterior angle of a polygon

an angle formed by a side and an extension of an adjacent side

properties of a parallelogram

opposite angles are congruent

properties of a rectangle

all properties of a parallelogram, all angles are right, diagonals are congruent

properties of a square

The measure of each angle is 90

formulas for the area of a parallelogram, rectangle, and a square

length x width

what is pi?

3.14

formula for the circumference of a circle

C = 2πr

how do you find the length of an arc of a circle?

how do you find the area of a sector of a circle

what is the relationship between a radius of a circle and a line that is tangent to the circle?

A tangent line is always perpendicular to the radius

formula for the volume of a rectangular solid and a cube

Cube: V=side³ Rectangular solid: lwh

the formula for the surface area of a rectangular solid and a cube

2(area of base) + (base perimeter)(height of prism)

formula for the volume of a PYRAMID or CONE

V=1/3BH

how do you find the x-intercepts and the y-intercepts of a graph?

Substitute them for zero

midpoint formula

(X1 + X2)/2 and (Y1 + Y2)/2

distance formula

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

slope of a line

y=mx+b

what is true about the slopes of parallel lines?

They are equal

what is true about the slopes of perpendicular lines?

They are opposite reciprocals (product of negative 1).

equation of a line

y=mx+b

how do you find the probability that an event will occur?

Number of favorable outcomes/total number of possible outcomes

what is the probability of an event that cannot occur?

0

venn diagram

A diagram that uses circles to display elements of different sets. Overlapping circles show common elements.

function

a rule relating an input value to an output value. Each input value can only be paired with one output value.

if you are given the graph y=f(x), what does f(a) represent

that represents the y value when x is equal to a

what are the relationships between the graphs of y=f(x) and the graphs of y=f(x)+a, y=f(x)-a, y=f(x+a), y=f(x-a)

it moves the graph up and down and left and right

what proportion do you use to solve percent problems?

x/100

order of operations

PEMDAS

greatest common factor

The largest factor that two or more numbers have in common.

least common multiple

the smallest number that two or more numbers will divide into evenly.

arithmetic sequence

a sequence in which each term is found by adding the same number to the previous term

geometric sequence

a sequence in which each term is found by multiplying the previous term by the same number

range

Distance between highest and lowest scores in a set of data.

mean

Average

vertical angles

A pair of opposite congruent angles formed by intersecting lines

equation of a circle

(x-h)²+(y-k)²=r²

sine of an angle

The ratio of the length of the side opposite the angle to the length of the hypotenuse.

cosine of an angle

Adjacent/Hypotenuse

tangent of an angle

The ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

system of equations

A set of equations with the same variables.

slope formula

(y₂- y₁) / (x₂- x₁)