1. Algebra Review

2. The Language of Algebra
Miss Jones is planning on going to Paris. Every week, she puts a certain amount of money into a fund for her trip. Her grandparents gave her $75 to add to the fund. After 12 weeks she has a total of $255. How much does she put into the fund each week?
x = the amount Miss Jones saves each week
12x = the amount she saved so far (12 weeks)
255 = 12x + 75
whatever you do to one side
180 = 12x on an equation you MUST
15 = x do to the other
Add this

3. Combining with geometry
Many problems are related through geometric formulas. Don’t forget that these are on the formula sheet located in the test booklet.
EX.
Mr. Carter has 500 feet of fencing and wants to enclose a rectangular plot along the river to protect his vegetable garden. What is the largest plot he can enclose.
(1) DRAW A PICTURE and
LABEL IT
River x y
(2) THINK ABOUT WHAT YOU KNOW
fencing goes around something
so we are considering perimeter
but we want to maximize the area
(4) Substitute and Solve the equations
A = LW
A = x y
A = (x)(500 – 2x)
A = 500x - 2x2
this is an inverted parabola so there will be a maximum
Either use the calculator and trace the max value
Or complete the square for vertex form
remember that is impacted by the -2
A = -2(x2 -250x )
A = -2(x-125)2
A = -2(x – 125)
Vertex is at (125, 31250)
So an x of 125 gives the largest area enclosed square ft.
(3) Set up equations to relate the variables modifying if necessary
P = L + 2W
Enter values you know
500 = y + 2x
x = y
-31250
+15625
-31250

4. Adding & Subtracting Polynomials
Add & Subtract LIKE terms
(5x2 + 3) – (2x2 + 4x – 7)
(5x2 + 3) + (-2x2 – 4x + 7)
3x2 – 4x + 10

5. Multiplying Polynomials
Multiply every term in the first polynomial by every term in the second polynomial, then combine like terms
(5x2 + 3)(2x2 + 4x – 7)
(multiply all terms by 5x2) (then multiply all terms by 3)
10x4 + 20x3 – 35x2+ 6x2 + 12x – 21
Now add like terms
10x4 + 20x3 – 29x2 + 12x – 21

6. Evaluating equations (extension)
x2 – 2x + 5 = y find y when x = 1
(1)2 – 2(1) + 5 = y
1 – = y
4 = y
Find x when y is doubled
x2 - 2x + 5 = 8
x2 – 2x - 3 = 0
(x – 3)(x + 1) = 0
x-3= 0 x+1=0
x = 3 x = -1
You could use the quadratic equation!

7. Solving Equations
Whatever you do to one side, you MUST do to the other!
3(x-4) – 6 = 2x + 8
3x – 12 – 6 = 2x + 8 distribute
3x – 18 = 2x + 8 combine like terms
move #s to one side
3x = 2x + 26
- 2x -2x variables to the other
x = divide if necessary

8. Degree of a Polynomial The degree of the highest term
Found by adding all the exponents in a term together
Example
The degree of 3x2y3 – 4xy2
degree of each term
5th degree equation

9. Terminology Binomial – two terms in a polynomial
x + 1
Trinomial – three terms in a polynomial
x2 + 2x + 3
Linear equation an equation with degree =1
y = kx
Quadratic equation an equation with degree = 2
y = ax2 + bx + c