Exam Review

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Exam Review

• By John Misiewicz
• Jeremiah Johnson

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1st Power Equations

• -Has no exponents
• -Make the equation equal the variable

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1st Power Examples
Ex1 x-23
Answer x 5
Ex2 x12x12
Answerx so the answer is All real numbers
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1st power Examples cont.

• Ex3

Answer x 20
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Properties

• Addition/ Subtraction property of Equality- If
  the same number is added/ subtracted to equal
  numbers the sums/ differences are equal
• acbc a-cb-c
• Multiplication/ Division property of Equality- If
  equal number are multiplied/ divided by the same
  (non zero) in the case of division number the
  products/ quotients are equal
• cacb

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Properties

• Reflexive property- all numbers equal themselves.
  aa
• Symmetric Property- If one number equals another
  than the other number equals the first number.
  ab, ba
• Transitive Property- If ab and bc than, ac

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Properties

• Associative Property of Addition- (ab)ca(bc)
• Associative Property of Multiplication-
  (ab)ca(bc)
• Commutative property of Addition- abba
• Commutative Property of Multiplication- abba

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Properties

• Distributive Property-a(bc)abac
• Property of Opposites- a(-a)0 -aa0
• Property of Reciprocals-
• Identity Property of Addition- a0a 0aa
• Identity Property of Multiplication-
• Multiplicative property of zero-
• Closure property of addition-ab
• Closure property of multiplication- ab

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Properties

• Power of a product property-(2t)2 22 x t2
• Product of a power property- 84 x 46
• Power of a power property- (84)5
• Quotient of powers property-
• Power of a quotient property-
• Zero power property-(x5)(x-8)0

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Properties

• Negative power property- -3-31/27
• Zero product property-(x10)(x-15)0 x-10 or
  x15
• Product of roots property-v9 xv5 v45
• Quotient of roots property-v225v9x25 3x5 15

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Inequalities in one variable

• x-8lt15 solve and graph
• 3x-5gt1 solve and graph
• 13-7nlt8 solve and graph
• 4y3gt7 solve and graph
• 2x7gt3 solve and graph

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(No Transcript)
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Conjunctions

• 2mlt4 and 122mlt0 solve and graph
• 2d-5gt-8 and -2d-5ltd-3 solve and graph
• -32ltx-22lt42 solve and graph
• 5-2pgt-8 and -2d-5ltd-3 solve and graph

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Disjunction

• 2w-1lt3 or 3wgtw10 solve and graph
• 5-2pgt11 or 5-2plt-1 solve and graph
• -6gt18 or 123rgt0 solve and graph
• H5lt-2 or h5gt2 solve and graph

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IMPORTANT!!!!!!!!!!!!!!!!!!!!!!

• When solving these equations conjunctions join
  the sentences together using the word and (just
  like in a sentence in english class). In a
  conjunctions you will find that both of the
  sentences are true. In a disjunction the word or
  is used. This means that at least ONE sentence is
  true and it cancels out the other sentence.

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Linear Equations in Two Variables

• 4x3y10 here are a list of ordered pairs (4,-2)
  (-2,6) (2,3) (8,5) plug these in to see which one
  fits the equation.

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All Equations For All Lines

• Standard/General- axbyc
• Point slope form- y-y1m(x-x1)
• Slope intercept form- ymxb
• equation of a horizontal line-yb
• Equation of a vertical line- xa

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Slopes for all lines

• The slope for a rising line is positive.
• The slope of a falling line is negative.
• A line that is parallel with the bottom of the
  graph has a slope of zero because it never rises.
• A verticle line has a slop that is undefined
  because it it has no run.

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How to Graph

• Using the equation ymxb
• y the equation of the line
• mx the rise over the run or the slope of the
  line
• And b is the where the line crosses the
  y-axis

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Linear System

• Substitution Method- 2xy25
• 4x3y32
• Solution- y25-2x (plug this equation into your
  second one)
• 4x3(25-2x)32
• X21 y67

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Linear Systems cont.

• Addition/Subtraction Method- 5-y12
• 3xy4
• solution is- 8x16
• Final solution is x2 y-2

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Linear Solution Commonalities
Solution- Intercept point Consistent System
Solution- A.R.N. Dependent System
Solution- Null set Inconsistent System
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Factoring Polynomials

• 5a3b3 Solution is
• 5(a3b3)
• axbx-bx-by solution is
• a(xy)-b(x-y)
• 5a3-5a210a-10 solution is
• (a-1) (5a210)

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Quadratic Equations

• Factoring- 20x2-49x30
• (5x-6) (4x-5)
• Quadratic Equation-ax2bxc0

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Functions

• Quadratic Functions-Graphing the Parabola y ax2
  bx c
• 1.    Determine whether the parabola opens upward
  or downward.
• a.    If a gt 0, it opens upward.
• b.    If a lt 0, it opens downward.
• 2.    Determine the vertex.
• a.    The x-coordinate is .
• b.    The y-coordinate is found by substituting
  the x-coordinate, from          Step 2a, in the
  equation y ax2 bx c.
• 3.    Determine the y-intercept by setting x 0.
• 4.    Determine the x-intercepts (if any) by
  setting y 0, i.e., solving the equation       
  ax2 bx c 0.
• 5.    Determine two or three other points if
  there are no x-intercepts.
• Remember point slope form and domains and ranges

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Simplifying expressions with exponents

• (2r3s2)(-5r5s)
• Solutions is
• 10r8s3
• Important to note that the powers add together
  not multiply only the numbers multiply together

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Simplifying Expression with Radicals
Rationalizing Denominators-
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Now Onto the Word Problems
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• One rectangles length is five more (ft.) than
  twice as long as the width. If the area of the
  rectangle is 35ft what is the width

2w5
w
Wthe square root of 15
So your equation is
And your solution is
2w2535
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• The sum of two numbers is 100. Five times the
  smaller is 8 more than the larger. Find the
  number(s)

The numbers are
18 and 82
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A 200 coat is on sale for 166. What is the
percent of discount.
.
17
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You put 1000 into an investment yielding 6
annual interest you left the money in for two
years. How much interest do you get at the end of
those two years?
IPrt
IPrt
IPrt
120
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• The sum of two numbers is 100. Five times the
  smaller is 8 more than the larger. Find the
  number(s)

The numbers are
18 and 82
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Line of Best Fit

• Use this when- you have a linear regression and
  you need to find a general estimate of the best
  line.
• Your Calculator helps by having the technology to
  find the exact estimate and pick any one of the x
  or y axiss.

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• For extra help try these websites-
• http//www.mathtv.com/
• http//www.coolmath.com/

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The End