Ms. Chase's Blog

Accelerated Math II - Polynomials

Friday, 1/27: Homework is in the Math III book, page 69 odds & #20, page 70 odds & #18

Monday, 1/30:  We looked at transformations in different ways.  We have a transformation worksheet that investigates the generalities of transformations and the book has some interesting problems on pages 74: 1-3, 5, 7, 11, 13, 17 and on page 75: 17 - 20 that students should work.

Tuesday, 1/31:  Long division of numbers vs long division of polynomials and synthetic substitution compared with long division.  HW is a worksheet that allows students to practice both long and synthetic division. 

Wednesday, 2/1: Although I was out today, students had a worksheet that looked at 4 important theorems: 

The Factor Theorem states that x - k is a factor of polynomial p(x) if and only if k is a root of p(x) or in other words, if p(k) = 0.

The Fundamental Theorem of Algebra (technically it's corollary) states that an n^th degree polynomial has n complex roots. 

The Remainder Theorem states that when polynomial p(x) is divided by (x - k), the remainder is p(k). 

The Rational Root Theorem states that any rational root of polynomial p(x) will fit the form of m/n, where m is a factor of the constant term and n is a factor of the leading coefficient.

Assessment problems for these concepts are assigned for homework and below are some selected answers:

1.  A) There are 3 roots because it is a cubic (3rd degree) polynomial.

B) {1, -1, 3, -3, 1/2, -1/2, 3/2, -3/2}

C) Once you synthetically divide by 1, you get a quadratic that factors nicely.

2. B) {1, -1, 2, -2, 4, -4}

C)  You can tell by substituting in 1 that 1 isn't a root, so try one of the other possible rational roots.  Don't complain - there are only 5 others and, yes, you may make a mistake and not find one, but synthetic division is not that hard, so make a choice and just, do it!  (And, for more complicated problems, you can always consider the graph.)

Thursday, 2/2: HW Pg. 87, 1-25 odd and Pg. 91: 1-15  odd

Friday, 2/3:  HW Pg. 88, 3, 9-15 odd and 16 and Pg. 92: odds , 12

Monday, 2/6: Finding zeros and writing polynomials with given roots, end behavior and leading coefficients.  HW page 96: 1-15 odd and page 97: 1-17 odd

Tuesday, 2/7: Turning points and multiplicity of roots.  HW page 102&103 odds 

Wednesday, 2/8:  HW page 100&101 odds.  Student also received a copy of an old "Algebra 2" quiz that covers similar material

Thursday, 2/9: QUIZ

Wednesday, 2/15:  Attached are the answers to the review worksheet Download Polynomial Review Answers

 

 

 

 

AP Calculus AB - Linear Approximation, RAM, Antiderivatives and Definite Integrals

Friday, 1-27:  Attached is the worksheet for homework.  Omit #9.  Download Linear Approximation WS

Wednesday, 2/8 - No homework :)

Monday, 2/13 - Attached are the answers as promised :) Download Answers to unit review RAM definite integrals etc

AP Calculus AB - Curve Sketching

Tuesday, 1/10: Concepts learned today - Major Curve Pieces (descrition of f, f', and f'' given a segment) and Interpreting Graphs.  HW: complete both worksheets

Wednesday, 1/11: Concepts learned today - Extreme Value Theorem, Critical Values (numbers, points), Absolute (or Global) Maximums and Minimums, Relative (or Local) Maximums and Minimums  HW: Worksheet 3, 4, 7-10, 23-43 odd 

Thursday, 1/12: Reinforced concepts from Wednesday.  HW: Worksheet 24-44 even

Wednesday, 1/18: Work on POI and intervals of concavity.  HW: Book page 215: 7-20 all.  Note that 13-20 considers POI as coordinate points.  Make sure to find the y coordinate.

Friday, 1/13: Concepts learned today - Mean Value Theorem (MVT), Increasing/Decreasing Test, 1st Derivative Test.  HW: Worksheet #2, 3, 5, 7, 8, 17, 18, 23, 24, 27, 29, 33, 35, 39, 41, 45, 49

Accelerated Math II - Quadratics

Thursday, 1/12:  We spent a large amount of classtime today going over problems from the PSAT.  Students should review the attached answers from last nights homework.  Download Factoring Worksheet 2 Answers  A new worksheet "Quadratic Extensions" along with the answers were handed out at the end of class.  Student will find many of these problems difficult but we will work to complete them by Tuesday.

Friday, 1/13: We reviewed the "Quadratic Extensions" worksheet and additional hints were given how to make conncections with the previous two worksheets.  Students should work to complete this entire worksheet by Tuesday.  An additional worksheet on "Completing the Square/Changing Forms of Quadratics"  was handed out today.  For the most part these concepts should be review although the methods that students approach each problem may not be the most efficient one.  Students should work towards significant;y completing this worksheet as well.

Wednesday, 1/25: Attached are the answers to the review #1 worksheet. Download Quadratic Test Review #1 Answers  Ms. Poss' blog migh have the answers to the "mini-test" given in class. 

FRIDAY, 2/3: QUADRATIC TEST SCORES AND CORRECTIONS: The tests were returned this week and scores were low.  Students have the opportunity to earn additional points provided they complete the following work:

For each problem that you missed any point on, students must 1) find two problems from homework that are similar to the question asked on the test, identify the title of the worksheet and problem number for each,  copy the problem down and work it correctly; 2) rework the test problem correctly; 3) explain in full sentences why you could not work the problem correctly during the test.

Attached is a pdf of all worksheets that were assigned for homework over this unit.  Download Quadratic Unit Worksheets

All work must be on completed on notebook paper and not on the test.  This is an all or nothing opportunity so incomplete or partial work will not be graded.  A parent signature is required on both the correction and the test.  All work is due Monday, February 13th NLT 8:15 am.  Late work will not be accepted for any reason so plan accordingly.