final exam algebra 2014 detroit public safety academy ms. degain review materials
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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…