Integers- positive and negative numbers with not fractions or decimals◦ …-3,-2,-1,0,1,2,3…

Whole number- positive numbers with no fractions or decimals◦ 0,1,2,3…

Rational Numbers- can be written as a fraction or decimal that either terminates or repeats◦ Includes all integers and whole numbers

Irrational Numbers- cannot be written as a fraction or has a decimal that goes forever with no pattern◦ Includes square roots of numbers that are not perfect squares

as well as pi

When you are solving the goal is to get the variable completely by itself◦ Combine anything alike on each side first.◦ Start on the right, do the opposite of x. Now on

the left do the opposite of number.

Ordered pairs (x,y)◦ + x

◦ - x

◦ + y

◦ - y

Y

X

Origin (0,0)

Slope-Intercept Form: y= mx + b m is your slope b is your y-intercept If b is any number other than 0 the line will not be

proportional Direct Variation: y = kx

k is your constant of variation (same as your slope) A line is a direct variation when it goes through the

point (0,0) If a line is a direct variation, it is proportional

Methods to find slope:◦ Formula m = ◦ On a graph:

Pick 2 points then count rise/run◦ In a table: Pick two ordered pairs and put into the

slope formula. Rate of change, slope, rise/run, and constant rate

of change are all the same thing

y1 – y2

x1 – x2

Domain – all your x-values (AKA independent variables)

Range – all your y-values (AKA dependent variables)

Use depends on to figure out dependent (y) and independent (x) variables

In order to be a function each x-value can have only 1 y-value◦ You can do the vertical line test to see if a graph is a

function◦ X will not repeat in a mapping, table, or list of ordered pairs◦ The same x with 2 different y’s is a no, no no!!

Parallel Lines have the same slope◦ y=2x+3 and y=2x+8◦ This also means that they will never cross and will have

no solution x-intercept is where the graph crosses the x-axis

◦ Point where y = 0 y-intercept is where the graph crosses the y-axis

◦ Point where x = 0 Solution to a system of equations is where they cross

◦ If they cross it will be an ordered pair◦ If they are parallel there will be no solution ◦ If both equations are the same line when graphed there

are infinitely many solutions◦ Put in your calculator under y= and then graph. 2nd trace

5 enter, enter, enter.

Types of associations/correlations: Remember that you can find the equation

for the trend line by finding the slope of the line and the y-intercept◦ Equation will be in y=mx+b form

• a² + b² = c²• Remember: c (your hypotenuse) is always

the longest and doesn’t touch the right angle

a

b

c c

a

b

b2

Cooresponding Angles- Angles in the same position, they will be congruent

Alternate Exterior Angles- Angles on the opposite side of transversal on the outside of the parallel lines, they will be congruent

Alternate Interior Angles- Angles on the opposite side of the transversal between the parallel lines, they will be congruent

Same-Side Interior Angles- Angles on the same side of the transversal between the parallel lines, they are supplementary so they will add to = 180

Vertical Angles- angles who’s corners touch, they will be congruent

• TRANSLATION –SLIDE• REFLECTION –FLIP• ROTATION –TURN• DILATION –CHANGE SIZE

•Think of the pupil of your eye•Dilations involve a scale factor

•WHAT YOU MULTIPLY BY in a dilation that makes something bigger or smaller• SF = New or Image

Old Pre-image

2 shapes are similar if:◦ Same Shape◦ Congruent angles◦ Sides are proportional

If you have 2 shapes that are similar and you are missing one of the sides, set up a proportion to find the missing one

These are also called dilations, you may have a scale factor involved that will tell you how much bigger or smaller the shape is.

Circumference: Distance around a circle

Perimeter: Distance around a polygon◦To find perimeter add all sides

Area:◦2 dimensional: length and width◦To cover a flat surface find its area (ex. Laying carpet)

Surface Area:◦Covers the faces of a 3 dimensional

shape◦2 kinds: Total: Every piece will be covered,

including the bases Think of wrapping a gift

Lateral: All except the bases will be covered (remember 3-D figures are named by the shape of their bases) Think of the label on a soup can

Volume:◦3 dimensional: uses length, width, and height

◦Measures how much something can hold Ex. How much marshmallow cream will fit in the classroom?

• in: means distance (perimeter, circumference)• in²: means area and surface area• in³: means volume

Mean- Average◦ To find the mean add all numbers then divide by how

many there are Mean Absolute Deviation (MAD)- The average

of the distance from each data point and the mean◦ To find MAD find out how far each point is from your

mean, then add them all together and divide by how many there are

◦ A small MAD means there is not much variability in the numbers, a large MAD means that the numbers are spread a lot further apart

◦ Could also be called Mean Average Deviation

Remember to re-write your formulas to make them easier to use

B = area of your base P = perimeter of the base h = height of prism, cylinder, cone, or

pyramid m = slope k = constant of variation (same as slope)

Interest Equations (remember interest is money you pay when you borrow or can earn by investing)◦ I = interest◦ P = Principal (amount borrowed or invested)◦ r = interest rate (will be a percent don’t forget

to change to a decimal to plug into calculator)◦ t = time in years◦ A = amount in account

If your screen is to light or dark◦ Hit 2nd and to Darken◦ Hit 2nd and to Lighten

If your graph is not showing up after you put it into Y=◦ Go back to Y= and make sure that the = is highlighted next

to your equation To go to a specific point on a graph

◦ Hit TRACE, type in your x value and hit enter To look at the table of a function you have graphed

◦ Hit 2nd and GRAPH (TABLE) from there you can scroll up or down

Fractions◦ To get to the fraction menu:

Hit Alpha (green button) and y=(F1) Option 1 is a regular fraction Option 2 is a mixed number Option 3 is to change from top heavy fraction

to mixed number Option 4 is to change from a fraction to a

decimal

To change your viewing window◦ If your graph is not showing up the way you would

like it to you may just need to change your window. There are a few ways to do this: Change Window Manually

Hit Window then change your minimum and maximum values for your x and y to make your graph fit, you can also change the scale (the spacing) to count by something other than one

Change Zoom To zoom in hit ZOOM, 2 and enter, zoom out would be 3

and enter Option 6 gets you back to the standard window

To Plug in a table to graph◦ Go to STAT then hit enter remember L1 is your x values L2

is your Y values◦ Hit 2nd then Y= (STAT PLOT), make sure 1 says on◦ Make sure when you are done that you go back and turn

your stat plot off To look at the table of a function you have graphed

◦ Hit 2nd and GRAPH (TABLE) from there you can scroll up or down

◦ You can go to a specific x value by hitting 2nd and WINDOW (TBLSET), from there change Indpnt to ASK rather than AUTO From there you go back to the table and type in your x

value and enter, it will give you the y value

Some common Errors◦ Syntax- there is an error in the way you typed

something in, go back and double check the way you typed your numbers A lot of times this is because of using a minus

when you should use a negative or vice versa◦ Window Range

This happens when you don’t have the correct window for what you are trying to graph, try either zooming in or out or change your window

If you get an error and absolutely can’t figure out how to fix it clear out the memory and start over:◦ Hit 2nd then + (MEM), choose 7◦ Scroll right to where it says ALL at the top then hit

enter and 2◦ This will clear out everything and put the

calculator back to default setting and should fix any issue you may have

1. Read the question 2 or 3 times if needed to make sure you understand what is being asked.

2. Highlight, Underline, or Rewrite KEY words (you are allowed scratch paper).

3. If needed, draw a picture.4. Answer ALL questions, a blank answer is

always a wrong answer5. Read the directions!!!!6. Don’t Rush!

7. Cross out answer choices you know are incorrect.

8. Show ALL steps (you will get scratch paper).9. Rework “not here” problems.10. Use your Formula Chart!! There are helpful

formulas on there.11. Mark your problems ? (or you can come

up with your own system). The goal is to get at least 40 (preferably more) that you absolutely know are correct (you can keep track of this on your scratch paper)

12. Make sure you have answered the question being asked (don’t stop too soon)