Studied by 21 peopleRational 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
Note
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