8th Grade Math Milestones Review

Rational number

a number that can be written as a fraction, when written as a decimal, a rational number either terminates (ends, like ¼ \= 0.25 or ½ \= 0.5) or repeats (like ⅓ \= 0.33333...)

Irrational number

a number that is not rational

Integer

a whole number or the opposite (negative) of a whole number

Base (of an exponential expression)

the number that is multiplied

Expression (mathematical)

a math phrase that has terms (numbers/variables) and operations (addition, subtraction, multiplication, division), there is no equal sign

Square root

a number n such that n^2 \= p, the square roots of 25 are 5 and -5 because 5^2 \= 25 and (-5)2 \= 25

Cube root

a number n such that n^3 \= p, the cube root of 8 is -2 because (-2)^3 \= -8

Equation

a math sentence that has terms (numbers/variables) and operations (addition, subtraction, multiplication, division), there is an equal sign

Perfect square

the product of a rational number multiplied by itself, like 25, ¼, or 81

Scientific notation

a method of writing numbers as a decimal between 1 and 10 multiplied by a power of 10

Decimal notation (standard notation)

the normal way of writing numbers

Proportional relationship

relationship between two equal ratios, like 5 oranges for $2.00, proportional relationships are represented by y \= mx and go through the origin on a graph

Origin (on a graph)

the point (0, 0) on a coordinate grid, where the x-axis and y-axis cross

Unit rate

when the ratio of two quantities is expressed as one number (the other is 1), like 30 mph \= 30 miles in 1 hour

Quantity

a measurable or countable property

Slope

the ratio of the change between two quantities, like - ⅖ for 2 lbs lost in 5 weeks

Similar

having the same shape, proportional sides, and congruent angles

Slope-intercept form

a way of writing the equation of a line, y \= mx + b, where y is the output, m is the slope, x is the input, and b is the y-intercept

Y-intercept

the point where the graph of a line crosses the y-axis, represented by b in y \= mx + b

Linear equation

an equation where each term is a constant or the product of a coefficient and a variable

Term (math)

a number, variable, or combination in a mathematical expression or equation, terms are separated by addition and subtraction symbols

Constant (math)

a number on its own, with no variable

Coefficient

the number multiplied by a variable

Variable

a letter that represents a mathematical quantity, a variable can have one value or can change values

Solution

any and all values of a variable that satisfy an equation or system of equations

Distributive property

allows you to multiply one term by multiple terms

Combining like terms

used to simplify expressions and equations by adding and subtracting similar terms

Linear systems of equations

a set of two linear equations that are solved as the same time, the solution must satisfy both linear equations

Intersection point

where two lines cross

Function

a rule that assigns each input exactly one output

Ordered pair

a pair of numbers (x, y) that represents a location of a point on the coordinate plane

Linear function

a function of the form y \= mx + b whose graph is a straight line

Rate of change

the ratio of the change in one variable relative to another variable, similar to slope

Initial value

the starting value of a function, the value of the output when the input is zero

Increasing function

a function where as the input increases, so does the output

Decreasing function

a function where as the input increases, the output decreases

Congruent

same size and shape, two congruent figures are completely identical except for location

Transformation

the movement of a figure on the coordinate plane, the original figure (before moving) is called the pre-image, the created figure (after moving) is called the image

Rotation

a transformation where a figure spins or turns around a fixed point

Reflection

a transformation where a figure is reflected across a line, creating a mirror image

Translation

a transformation where a figure is moved a specific distance (given by horizontal and vertical directions or operations on x and y)

Dilation

a transformation that changes the size of a figure, but not the shape; a dilation requires a scale factor (greater than 1 \= bigger, between 0 and 1 \= smaller) and a center of dilation (a point that does not change)

Proof

a deductive argument for a mathematical statement

Pythagorean Theorem

in any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse, or a2 + b2 \= c2

Converse of the Pythagorean Theorem

in any triangle, if the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse, or a2 + b2 \= c2, then the triangle is a right triangle

Formula

an equation that expresses a mathematical relationship and is used to solve a problem

Volume

the amount of space inside a solid three-dimensional figure

Cone

a three-dimensional figure with a circular base that tapers to a point, V \= ⅓ 𝜋r2h

Cylinder

a three-dimensional figure with two circular bases, V \= 𝜋r2h

Sphere

a three-dimensional figure that is perfectly round, like a ball, V \= 4/3 𝜋r3

Scatter plot

a graph of points on a coordinate grid that shows the relationship between two quantities

Pattern of association

a description of how one variable relates to another on a graph, including positive, negative, linear, and nonlinear

Clustering

when data is "gathered" around a particular number

Outlier

a data point that is "outside" the trend of other data points

Line of best fit

a straight line drawn through the center of a set of data points, shows the general association

Frequency table

sorts information in a table by category

Relative frequency table

compares how often information occurs by category

Two-way table

organizes data from two categories at the same time