FINAL EXAM ALGEBRA2014

DETROIT PUBLIC SAFETY ACADEMY

MS. DEGAIN

REVIEW MATERIALS

3RD CARD MARKING

• Slope• Rate of Change• Functions

WHAT IS SLOPE?

• Rise/Run

• Change in y values/Change in x values

• Vertical Change/Horizontal Change

• Up and down difference/left and right difference

REMEMBER SLOPE-INTERCEPT

What does the m represent?What does the b represent?How do you graph this in the calculator?

WHAT IS RATE OF CHANGE?

• The SAME EXACT THING AS SLOPE!!!!!!

WHAT IS A FUNCTION?

• A relationship that will take an input and produce a given output.

• Domain is the x values

• Range is the y values

• The Domain cannot be repeated but the Range can.

• A functions will pass the vertical line test.

NOT A FUNCTION BECAUSE THE X REPEATED (#5)

This is a function because if you draw vertical lines through the curvy red graph it would only intersect it once.

FUNCTIONS CONTINUED

• There are many different types of functions

• Linear

• Quadratic

• Polynomial

• Exponential

• Linear functions are in Slope-Intercept form usually.

• Graph a line (non vertical)

• Quadratic functions have a power of 2.

• Graph a “U” Shape called a Parabola

• Polynomial functions have multiple terms with powers.

• Graph a “W” shape or wavy shape

• Exponential functions have a power that is a variable.

• Graphs look like half of a “U” shape and sharply increase or decrease.

FUNCTION NOTATION (EXAMPLE: )

• f(x) is just like the letter y. It represents the output and range. It is NO DIFFERENT THEN THE LETTER Y WHEN GRAPHING!!

• If an equation has find f(2), or f(x-2) all you have to do is substitute in said values into the equation. These are the INPUTS, and inputs are the x values. Just plug them in.

•

• Plug in 3 into the equation and simplify.

• Take each problem one small step at a time.

4TH CARD MARKING

• Systems of Equations

• Graphing

• Substitution

• Elimination

• Polynomials

• Adding

• Subtracting

• Multiplying

• Factoring

• Radicals

• Simplifying

SYSTEMS OF EQUATIONS: GRAPHING

• The Variable Y, must be isolated.

• Use slope-intercept form to graph

• Calculators can easily find intersection points if in slope-intercept, or you can graph by hand.

• What does infinite solutions graph look like?

• What does no solution graph look like?

• How do you know if the graph has one solution, no solution, or infinitely many solutions?

SUBSTITUTION METHOD

• When one of the equations has a variable isolated and the other one doesn’t, this is the best method to use.

• Take the value of one equation and plug it into the other

• Remember “Help the Helper” and “Help me, help you”?

• Simplifying is key here (take your time on correctly calculating).

• Don’t forget to solve for both variables, not just one.

EXAMPLE:

Y is isolated, so wherever you see the letter y in the first equation, you will SUBSTITUTE 2x instead.

substitute

simplify

simplify

divide on both sides

remember to reduce

Don’t forget to plug the x value into y=2x now.

ELIMINATION

• Best used when there are no variables isolated.

• Goal is to get opposite coefficients of one of the variables.

• If they are not already opposite, then use the LCM to create them.

• Remember to calculate and actually do the operations that you have written down.

WHAT IS A POLYNOMIAL?

• Many termed expression.

• No radicals

• All real numbers

• Cannot equal zero

• Monomial

• One Term

• Binomial

• Two Terms

• Trinomial

• Three Terms

BE CAREFUL WITH EXPONENTS

Adding/Subtracting• Only add/subtract like terms

• Remember to look at the sign in front of each term (determines whether it is positive or negative

• Do NOT add/subtract the exponents.

Multiplying• Distributive/Double Distributive Property

• When the variables are alike, you add the exponents.

• Remember to simplify by combining like terms. (combining means to add/subtract so be careful in this step.)

EXAMPLESAdd/Subtract Multiplying

SIMPLIFYING RADICALS

• GREATEST PERFECT SQUARE FACTOR!!!

• Pull the square roots of numbers out in front of radical.

• Find square roots of variables (trick: divide exponent by 2, that will be the power of the variable on the outside of the radical).

• If a variable has an odd numbered exponent, there should be one variable left inside radical. If even, there shouldn’t be any left inside.

• Common Perfect Squares:

4, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256…