 Rational Numbers  Any number that can be written as a ratio.  Includes perfect squares, terminating and repeating decimals. ◦ Integers  Includes all whole numbers and their opposites (positive and negative). ◦ Whole Numbers  All positive numbers and zero.  Irrational Numbers ◦ All numbers that cannot be written as a ratio.  In decimal form, an irrational number does not terminate or repeat.  For example:  π or √2

 A method of expressing very large and very small numbers as a product of a number greater than or equal to 1 and less than 10, and a power of 10.  Positive Powers of 10 ◦ When you move the decimal to the left. ◦ USE WHEN THE NUMBER IS GREATER THAN OR EQUAL TO 10.  Negative Powers of 10 ◦ When you move the decimal to the right. ◦ USE WHEN THE NUMBER IS LESS THAN 1.

 A proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant.  k = y / x.  If “k” is the same every time, then the relationship is proportional.

 A rate of change is a ratio of the amount of change in the output to the amount of change in the input.  The slope of a line: ◦ the ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

 A direct variation is a relationship that can be written as ◦ y = kx  “k” must be constant for there to be a direct variation.  If there is a direct variation, then we can say that  y varies directly to x

 Linear equations can be written in the form ◦ y = mx + b.  When b ≠ 0, the relationship between x and y is nonproportional.

 The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. ◦ The x-coordinate of this point is always 0.  The linear equation shown is written in the slope-intercept form of an equation. ◦ y = mx + b  Its graph is a line with slope m and y- intercept b.  A linear relationship has a constant rate of change.

 A system of equations is a set of equations that have the same variables. ◦ An ordered pair is a solution of a system of equations if it is a solution of every equation in the set.

 Step #1: ◦ Find the slope.  Using the formula, rise over run, or looking for key words (per).  Step #2: ◦ Determine the y-intercept by looking at the graph, table, or word problem (initial value).

 Bivariate data is a set of data that is made up of two paired variables. ◦ If the relationship between the variables is linear, then the rate of change (slope) is constant. ◦ If the graph shows a nonlinear relationship, then the rate of change varies between pairs of points.

 A function assigns exactly one output to each input. ◦ The value that is put into a function is the input. ◦ The result is the output.  A boy can only have one girlfriend Not a function Function

 All three angles in a triangle add up to 180 degrees.

 An interior angle of a triangle is formed by two sides of the triangle.  An exterior angle is formed by one side of the triangle and the extension of an adjacent side.  A remote interior angle is an interior angle that is not adjacent to the exterior angle.

 Similar figures have the same shape but may have different sizes.  Two triangles are similar if their corresponding angles are congruent and the lengths of their corresponding sides are proportional.

 We want to put all the variable terms on one side of the equal sign/inequality symbol.  Also we want all of the constant terms on the other side.  To move a term to the other side, you must do the inverse (opposite) operation.

Remember: 270 degrees clockwise is the same as 90 degrees counterclockwise 270 degrees counterclockwise is the same as 90 clockwise

 Dilations change the size (but not the shape) of a figure. ◦ Every dilation has a fixed point called the center of dilation.  Located where the lines connecting corresponding parts of figures intersect.  Also it gives you the scale factor.  The scale factor is the ratio of a length of the image to the corresponding length on the original figure.  A dilation can produce a larger figure (an enlargement) or a smaller figure (a reduction). The scale factor describes how much the figure is enlarged or reduced.

 A scatter plot is a graph with points plotted to show the relationship between two sets of data.  A cluster is a set of closely grouped data.  An outlier is a data point that is very different from the rest of the data in the set.

 A trend line is a straight line that comes closest to the points on a scatter plot.

 A measure of center is a single number used to describe a data set. ◦ One measure of center is the mean  the sum of the data values divided by the number of values in the data set.  A measure of variability is a single number used to describe the spread of a data set. ◦ One measure of variability is the mean absolute deviation (MAD)  the mean distance between each data value and the mean of the data set.

 When information is being gathered about a group, the entire group of objects, individuals, or events is called the population.  A sample is part of the population chosen to represent the entire group.  A sample in which every person, object, or event has an equal chance of being selected is called a random sample. ◦ A random sample is more likely to be representative of the entire population than other sampling methods.

 Interest is the money that you pay to borrow money or use credit. ◦ The interest rate determines in part the cost of a loan or of purchases on a credit card.  Simple interest is earned using the formula: ◦ I = Prt,  where I is the amount of interest,  P is the principal, or the original amount deposited,  r is the interest rate expressed as a decimal,  t is the time in years. ◦

 Compound interest is interest paid not only on the principal but also on any interest that has already been earned.  The formula for compound interest is A = P (1 + r) t, ◦ where P is the principal, ◦ r is the interest rate expressed as a decimal, ◦ t is the time in years, ◦ A is the amount in the account after t years if no withdrawals were made.