Unit 1 Quiz Practice

Below are two links that you might find helpful to review sets for tomorrow's quiz.

Review of Complements:
http://www.crctlessons.com/complement-of-a-set.html
Review of Intersections & Unions:
http://www.youtube.com/watch?v=Hek8Y3FlAm0

Answer's to the Unit 1 Practice Quiz:

2a) This number is irrational because it is a non-repeating, non-terminating decimal and therefore can not be written as a fraction.

2b) This number is an irrational number because 150 is not a perfect square, therefore when it is simplified it is a non-repeating, non-terminating decimal.

2c) This number is rational since it can be written as a fraction.  Rational numbers are either terminating or repeating decimals. (Can be written as 7/9)

2d) This number is rational since it can be written in "a" divided by "b" form.  -33/7

3)  Given Expression
      Distributive Property
     Commutative Property of Addition
     Associative Property of Addition
     Additive Inverse
     Additive Identity

4a) -4.6

4b) pi

4c) impossible

4d) -7

5a) The set of natural numbers is closed under addition because whenever you add two natural numbers together the sum will always be another natural number.  (EX: 6 + 56 = 62)

5b) The set of natural numbers is NOT closed under addition because when you divide 6 by 12 (both of which are natural numbers) the quotient is 0.5 which is not a natural number.

6b) E' =  { 1, 3, 5, 7, 9}
      E u P = {2, 3, 4, 5, 6, 7, 8, 10}
      F n P = { 2, 3, 5}
      (E u P) n F = {2, 3, 5, 8}
     (E u F)' = {7, 9}

Good Luck Studying!  Feel free to post questions if you have them!

WELCOME TO THE 2012 - 2013 ALGEBRA BLOG

Mrs. Skinner & Mrs. Walter would like to welcome to the Iroquois Algebra Blog for the 2012- 2013 school year.   We look forward to using this blog to help answer your questions, post answer keys, as well as provide you with extra practice problems before tests and quizzes.  Please follow this blog (use your google doc school account) so that you can be notified when we put up new information!

Here's to a Mathemagical School Year!

Check out REGENTS PREP!!

We know that we have been giving you all a lot of information in class.  If you have questions please do not hesitate to ask but also feel free to check out this website that has lessons, and practice problems with answers the explanations to support the answers.

Regents Prep Website

For example having trouble with Box and Whisker Plots or Histograms check out the lessons and practice offered on these pages.

Unit 11 Hints on Study Guide

A few people have asked for some clarification on certain parts of the study guide. I have tried my best to answer these questions below.  Hope you find this helpful!
If you have more questions -- just post them or e-mail them to me.  I will answer them on the blog so that all your classmates can benefit from the question!

3.   Given a quadratic equation, find the value of the discriminant, state the number and nature of the roots, and tell whether the equation can be solved by factoring

• Remember that the discriminant is the value that "DETERMINES" what kind of solutions (roots) you will have.  The discriminant is calculated using b^2 - 4ac.  
•  If that value is negative then the nature of the roots is that they are not real; hence we say that there are no real solutions.
• If that value is ZERO then the nature of the roots is that there will be exactly one rational solution.  This means that the equation is factorable.
• If that value is positive but NOT a perfect square then the nature of the roots is that there are TWO real, irrational solutions.  This means the equation is not factorable.  
• If that value is positive AND a perfect square then the nature of the roots is that there are TWO real, rational solutions are not real; hence we say that there are no real solutions.  This means the equation is not factorable.

4a. Given the graph of an absolute value function, write the equation of the                                             function in the form y = a Ix-hI+k.
Locate the vertex of the function that is (h,k).  The look at the slope of the lines as that will determine the value of a.  Remember that a will be negative if the function opens down (the vertex is the maximum y-value), while a will be positive if the function opens up (the vertex is the minimum y-value).

6.   Given the equation of a quadratic function in standard form, y = ax^2+bx+c where a = 1, rewrite the function in vertex form by completing the square.  State the vertex, AOS, and range.

Remember that Vertex form looks like y = a (x-h)^2+k.  So if you complete the square using the format given in class, then the vertex is just (h,k) the AOS (axis of symmetry) is x=h.  The range will be based on k.  If the quadratic opens up (hence k is the minimum value) then the range is {y:y>=k} (y is greater than or equal to k).  If the quadratic opens down (hence k is the maximum value) then {y:y<=k) (y is less than or equal to k).


7.   Given the equation of a quadratic function in standard form, find the vertex of the function algebraically using the formula x = (-b)/2a to find the x-coordinate of the vertex and using the equation of the function to find the y-coordinate.
        This stems for the quadratic formula and the completing the square work we did earlier in the unit.  It works great when you have a quadratic function in standard from but "a" is not equal to one.  Hence completing the square to find the vertex is a mess.  Don't stress over where the formula comes from -- JUST MEMORIZE IT!! Trust me on this -- where it comes from will make sense after you use it for a while.

9.   Given a quadratic function in standard form y=ax^2+bx+c, describe how the graph of the function will be transformed if the value of a is changed in specified ways.

Remember if the absolute value of a is greater than 1 then the quadratic has been "stretched" -- the parabola will be narrower.

If the absolute value of a is less than 1 then the quadratic has bee compressed -- the parabola will be wider.

If a is positive the parabola will open up, while if a is negative the parabola will open down.

Practice Links from Regents Prep:

• Solving Quadratics: http://www.regentsprep.org/Regents/math/ALGEBRA/AE5/indexAE5.htm
• Solving a linear-quadratic system by graphing: http://www.regentsprep.org/Regents/math/ALGEBRA/AE6/LLinQuad1.htm
• Exponential Growth & Decay Practice: http://www.regentsprep.org/Regents/math/ALGEBRA/AE7/indexAE7.htm

  

August 2008 Regents

August 2008 Multiple Choice Submit Form
Due for Team 82 Students on Monday May 7,2012

Completing the Square Help!!

Hints on Homework:

#9:  5x^2 - 20x = 10  -- move the 10 to the left hand side of the equation and then factor out a five.

     5(x^2 - 4x - 2) = 0   Then complete the square using the terms inside of parentheses.  Just don't forget about the factor of five!!

5 [(x^2 - 4x + ___) - 2 - ___] = 0

5[(x^2 -4x + 4) -2 - 4] = 0

5[(x-2)^2  - 6] = 0  Therefore the factor inside the brackets must be equal to zero, since the only other factor is five.

(x-2)^2 =6 -- now use the square root rules from there.

#11: x^2 - 5x = 2  -- move the 2 to the left hand side of the equation.  Then use completing the square as show in class.

(x^2 - 5x + ____) - 2 - _____ =0

#13: x^2 - 12x +35 = 0

(x^2 -12x + ____) +35 - ____ = 0    Remember (b/2)^2!!

Hope the above tips help!

Feel free to check out this instructional video as well if you still have questions:
Completing the Square Instructional Video (easy problem)
Completing the Square Instructional Video #2 (harder problem)

Practice Regents Packet

June 2008 -- Part 1 Multiple Choice ONLY
Due Tuesday May 1, 2012 for Team 81 & Team 82
2008 Submit FORM