 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 y 1 – y 2 x 1 – x 2

 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. 2 nd 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 b 2

 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 2 nd and  to Darken ◦ Hit 2 nd 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 2 nd 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 2 nd 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 2 nd and GRAPH (TABLE) from there you can scroll up or down ◦ You can go to a specific x value by hitting 2 nd 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 2 nd 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 answer 5. 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)