• Algebra Notes Page
     
    Chapter 9 Lesson 6
    Solving Quadratics by Square Roots
    (PIZZAZ worksheet solutions)
     MOVING WORDS:
     Remember to have positive and negative solutions when taking a square root:
     Moving Words 1-5
     
    Isolate the radicand, then isolate the variable if necessary.
    Moving Words 6-15
     
    Simplify the radical into simple radical form by factoring out perfect squares (4, 9, 25, etc.)
    Moving Words 16-17
     
    Fractions and irrational expressions may be acceptable answers:
    Moving Words 18-20  
     Did you hear about the teacher who told the students ten jokes with no pun in ten did.
     
    April 22, 2013
     
    Graphing Parabolas
    Parabola A Parabola B
    Parabola C  Parabola D
    Parabola E  Parabola F
     
     January 30th, 2014
    Systems of Linear Inequalities worksheet:
    Pizzazz 200  
    January 31st, 2013
     Lesson 6-6 "Linear Inequalities"
     
    MEETPATTY
    Why3PigsLeaveHome  FatherABoar
     
     
    Final Exam Review KEYs
     FER1 key
     
    FER 2 Key  
     
    Algebra FER 3  
    Algebra FER pg4  
     Unit 3 Inequalities
    Lesson 3.3 Solving Inequalities by Multiplying and Dividing:
    Notes #2 Rule with positives  
    Four Examples  
    switching inequalities  
    Example A  Example B  Examples C-D
    Rule with negatives  Two ways to solve
     
    Unit 2 Equations
     
    Lesson 2-1 Solving Two Step Equations
    List Operations  
    Identify Inverse Operations  
    Subtract 1/2 and multiply by 3  
     
     Lesson 2-1 "Solving One Step Equations"
    Example1  Example2
    Ex3  Ex4
    Next Example  Last Example
    Unit 1 Chapter 1
     
    Notes #6 -- September 11, 2012
    "Combining Like Terms"
     
    Think of x2 as a large square, x as a 1*x rectangle, and 1 as a small square (so 5 = 5 squares):
    terms like shapes  
    Now imagine a truck carrying three rectangles and two squares.  How many shapes would two such trucks distribute?
    distribution truck  two times 3x+2
    So in algebra we combine like terms like so:
    algebra example  
     
    Notes #5 -- September 10th, 2012
    "Properties of Real Numbers"
     
     So the Natural Number is is closed under addition and multiplication.
     If you add two natural numbers, you get another natural number.  The answer is in the same set of numbers.
    If you multiply two natural numbers, the product is also a natural number.  This isn't always true for subtraction.
     Closed Under Addition and Multiplication Closed under Subtraction and Division
    If you subtract two integers, you always get another integer.
    The set of integers is closed under subtraction.  This isn't always true for division.
    Rationals are closed under addition, subtraction, multiplication, and division.
    But you can't always take the square root of a rational number and get another rational number.
    However, the set of Reals is closed under +, -, *, /, and square rooting.
     
    There are three other properties of real numbers.
    Associative Numerals  Commutative Numerals
    Associative Card  addition and multiplication  Commutative  add and multiply equations
    These two properties only hold true for addition and multiplication.
    They can be disproved (or refuted) for subtraction and division.
    counter example disproving associative subtraction disproving associative division  
    Come up with two counterexamples that prove the commutative property isn't true for subtraction and division.
     
    The last property is the Distributive Property of Multiplication over Addition.
    distributive numerals  Distributive   distributive EQ
    distributive property  
     
     Notes #4 -- September 6th, 2012
    "Roots and Irrationals"
     HW Review p. 29
    #1-22  
    #23-61  
     and now some notes ...
    Number Systems  
    Reals and irrationals  
    The square root sign was invented by Christian Rudolph and made to look like the letter "r",
    for the Latin word for root, "radix."
    Cube Root  4th root
     
     Notes #3 -- September 4th, 2012
    Powers and Exponents
    power example  
    General Form  
    expanded forms  number 4
    Review #5-10  Power Multiply Value
     
     
     
    Notes #2 -- August 30th, 2012
    Multiplying and Dividing Real Numbers
     
    Multiplication is adding multiple times.  For example, 3(2) is adding two three times (2+2+2).
    So +3(+2) = +6 since a postive times a postive is also positive. What about a positive times a negative?
    3(-2) is subtracting two three times, or -2 -2 -2.  So that's -6.  Positive times negative is negative.
    Postive times postive Positive times negative
     
    How about -3(+2)? A negative times a positive? This means do the opposite of adding 2 three times.
    The opposite of adding 2 is subtracting 2.  And -2 -2 -2 = -6.  So -3(2) is -6.  (-)(+) is negative.
    negative times positive negative times negative
    Finally, how about a negative times a negative, e.g. -3(-2).  This means do the opposite of subtracting 2 three times.
    So add two three times.  2+2+2 is +6.  Therefore, a negative times a negative is positive.  In summary:
     
    Rules
     The inverse of multiplication is division.  Division follows the same rules for positives and negatives as multiplication.
    Fill in multiplier  Fill in divisor
     
    Algebra Pizzaz pg. 15  
     
    Algebra pizzaz pg. 19  
Last Modified on June 16, 2017