1. Concept Review
Purpose: The purpose of the following set of slides is to review the major concepts for the math course this year. Please look at each problem and how to solve them. Then attempt to solve the second problem on your own. If you have difficulty it would be good to come see me and ask questions.

2. Exponents
With exponents it is important to remember that the variables can represent any number. We cannot do anything with a variable that we could not do with a number, because variables are any number.
A good strategy when working with exponents is to put a number in for the variable. If it works with the number than this would be how you would solve the problem with exponents.
*** Refer back to the exponent lesson under the trimester two heading for a more in depth explanation.

3. Exponents continued Simplify 1) X SOLUTION: A) * X = 1 X = 0 X X
X = (XXXXXXXX) B)
X (xxx) **Multiply by reciprocal
(XXX)
C (XXXXXXXX) (XXX) = (XXXXXXXXXX) or X 8 -N -3 N 8 -3 11

4. Practice
Simplify
X X
X X 7 -5 2 7

5. Exponents Continued Simplify: X F X F X Solution
Rewrite it so that all of the X’s are together and all of the F’s are together then add the exponents.
X F -6 3 3 -5 - 5 2 -2

6. Exponents Continued
Solve: 4 -6

7. Pattern
Another way to understand exponents and x to the negative n is to look at the pattern
5 = Each time we divide by 5. Therefore
5 = = x 1/5 when we
5 = invert and multiply we get 1/5.
5 =
5 = /5 3 2 1 -1

8. Concept 2
Solve 4 * 7 We use the same method as with exponents. Solution: 1 X X 49 = -7 2 7

9. Practice
Solve
1) * 2 -3 3 -2 3

10. Consider this x x x 10 1 0 5 = 1 5 or .20 1 -1 -1-1
x x x
5 = 1
5 or .20 -1
Converting 1/5 into a decimals you
divide the denominator into the numerator
and get .20

11. Defining y=mx using similar triangles and Linear Equations

12. Defining y=mx using similar triangles and Linear Equations
The equation y = mx is the algebraic way of representing what is drawn on the graph.
The m is the y or rise over the run. Looking at the coordinate plane above we can then x
begin to graph the line. Caution : Remember that points are expressed as (x,y) Don’t
Reverse the m and place the x or y in the incorrect position. This will flip the line your
Intending to express.
Note that the line on the graph forms triangles in a linear fashion. You can use similar
Triangles to determine if a line is linear. The slopes should be the same when simplified.

13. Example Problem
y = mx
Given an m value of 1 please graph 3 (x,y) points and use similar triangles to show 2
that the line is linear.
Note: the y or rise value is 1 and the x or
run value is 2. That means for every 1 I
rise I move over two. This pattern continues.
There are three triangles found at each point
That all simplify to a 1:2 ratio.
Triangle 1 (2,1)
Triangle 2 (4,2)
Triangle 3 (6,3)
Solution:

14. Practice Problem
y = mx
Given an m value of 3 please graph 3 (x,y) points and use similar triangles to show 4
that the line is linear.
Solution:

15. Practice Problem y = mx Given the equation y = -4 x please graph. 2
Note: The negative refers to the rise
Not the run so we will be in quadrant 4
The next x, y would be either (-8,4) or 0,0
Solution:

16. Practice Problem y = mx Given the equation y = 4 x please graph. -2
Note: The negative refers to the run
Solution:

17. Practice Problems Given the equation y = 3 x please graph. 2-2
Given the equation y = 3 x please graph.
- 2
Given the equation y = -3 x please graph. 2

18. y = mx + b
Thus far I have only presented you with lines that pass through the point of origin or (0,0). By adding b to the equation y = mx +b we can shift the line up or down on the y axis depending on whether the value for b is positive or negative.
The original lines
Slope of ½ has not
changed it simply has
been shifted from (0,0)
on the y axis to (3,0)
making the equation
y = 1 x + 3 2

19. Practice Problems with y = mx + b
Given the equation y = 3 x + 3please graph. 2
Given the equation y = -3 x please graph. -2
Given the equation y = -3 x + 5 please graph. 2
Caution: When we did not have a
value for b the first point matched
the slope values. This will not be the
case with a b value. Follow the slope
as a like a set of directions form the
b value or new origin.
Given the equation y = 3 x please graph.
- 2

20. Scientific Notation
Scientific Notation: When working with Scientific Notation it is helpful to understand our number system works.
We have a base 10 system which means that once we have a group of ten items we regroup them.

21. Scientific Notation 1 2 3 4 5 6 7 8 9 1
10 or 1 group of ten individuals

22. Going to the right we use base ten with quantities that are less than 1.1 .2 .3 .4 .5 .6 .7 .8 .9
1. or 1 group of ten tenths

23. Going to the left we deal with quantities greater than 110 20 30 40 50 60 70 80 90
100. or 1 group of ten tens

24. How we tend to represent it-1 2 1
Hundreds tens ones decimal tenths
X X X X x -1 2 1 -1

25. How we tend to represent it-1 2 1
Hundreds tens ones decimal tenths
We can use the base ten system to help us with scientific notation.
If we have the number 342,000. we can rewrite it as 3.42 X 10.
If we have the number we can write it as 3.42 X 10 5 -5

26. Scientific Notation Practice Problems
Convert to Scientific Notation

27. Scientific Notation Practice Problems
Covert from Scientific Notation
5.67 X X 10 7 -7