Debbie Poss's Blog

Accelerated Math III - Applications of Trigonometry - January 31, 2012

Yesterday students had a quiz on basic law of sines and law of cosines.  Their assignment was a worksheet of word problems.  Today we got solutions to that worksheet and the assignment was from the book - Q1 - Q4, Q7 - Q10 and problems 1-20.

Tomorrow we will look at trig form of complex numbers as another application and make connections about what that means.

Accelerated Math II - Long and Synthetic Division - January 31, 2012

We have started a new unit on polynomials and

Friday we looked at the beginning terminology in class followed by Pg. 69: 1-19 odd, 20 and Pg. 79: 1-17 odd, 18

Monday 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.

Today we looked at long division of numbers and compared that with long division of polynomials. Then we looked at synthetic substitution and compared that with long division.  The assignment is a worksheet that allows students to practice both long and synthetic division.  Tomorrow we make more connections to write some important theorems about polynomials. 

Accelerated Math II - Test Review - January 25, 2012

Today students reviewed for their test on Factoring and Quadratic Functions.  First of all, here are the answers to the review sheet from Monday's blog: Download Quadratic Test Review answers .  Then students received another review: Download Mini-test on Quadratics  (And Tannah gets SOTD for noting that the correct answer to #3 should be 44.)  Answers to the Mini-test are:

1. D    2. E    3. 44     4. E     5. C     6. C     7.  2(x² + 6x + 9) - 7 + 18 = 2(x + 3)² + 11, so the vertex is (-3, 11).  8.  x² - 3x - 7x + 24 > 0, so (x - 6)(x - 4) > 0, so x < 4 or x > 6.    9.  y = 4(x - 2)(x - 4)     10.  (5 - 2x)(7 - 2x) = 31, so 25 - 24x + 4x² = 31, which means 4x² - 24x + 4 = 0, or x² - 6x + 1 = 0.  This means that x = 3 plus or minus 2 sqrt (2) or approximately 5.828 or .1716 .The first one is too large, so the width of the sidewalk is .1716 dkm wide.

Math Team - Practice for the Cobb Winter Tournament at Wheeler on Jan. 30, 2012

Look at these competitions for practice:  Download Cobb Councy 2007 JV Fall written and Download Cobb County 2007 JV Fall ciphering

Accelerated Math III - Law of Sines - January 23 ,2012

We proved the law of sines today and the assignment is Pg. 261: Q2 - Q10 and 1-10.  Enjoy! 

Accelerated Math II - Ball Bounce Lab - January 23, 2012

Students started collecting data for the ball bounce lab.  Many students were successful, but all were not.  The assignments for the next two days, then, is as follows:

1.  Complete the lab.

2.  Finish the application worksheet if you had any difficulties on it.

3.  Watch the tutorials found on http://www.analyzemath.com/quadraticg/Problems1.html and critique them.

4.  Complete the test review attached:  Download Quadratic Test Review

 

Accelerated Math III - Test Review - January 18, 2012

Today we reviewed for the trig test tomorrow.  The standards are on yesterday's blog, and it would be a good idea to look at previous tests to review.  Good luck!

ASE Answers for January 18, 2012

The answers to the short worksheet we had today are:

1.  5(x² + 7)(x + 2)(x - 2)          2.  Can't be factored

3. x² -26x + 169 = (x - 13)²      4. 3x² + 9x + 27/4 = 3(x + 3/2)² 

5.  4(x + 3)(x - 2)                    6.  4(x + 1/2)² - 25

Accelerated Math II - Quiz and Sum to Product Discovery - January 18, 2012

Today we had a quick quiz on factoring, but we also reviewed at least 2 graphing problems and started the discovery worksheet on sums and products Download Making Connections about Roots .  Please be aware that, if you got this worksheet in class, G(x) = 6x² - x - 1 (a typo) and q(x) really can't be factored over the reals, but it still has roots (remember the quadratic formula!).  Also, realize that even if you can't complete the proof on the back (and you really should be able to do that with the hints given!), you can still work the problems at the end of the worksheet.

Here are answers to the Acc. Math II Worksheet #2 on Characteristics of Quadratics in Various Forns.

1)  Vertex:  (3/2, 9)  (Easy to find thanks to vertex form)

    Axis of symmetry:  x = 3/2  (Easy to find knowing the vertex)

    Opens DOWN because the leading coeficient is negative.

   Maximum value is 9 because that's the y-value of the vertex.

   X-intercepts are 0, -3, but we needed to factor the standard form to get that.

   Standard form: y = -4x²+ 12x (because the x terms cancelled.

    Intercept (or factored) form:  y = -4x(x - 3)

2.  Vertex (-3, -6)  (I averaged the x-intercepts.

     Axis of symmetry: x = -3  It opens up and the minimum value of -6.

    The intercepts are -9 and 3 which can be found easily by setting the factors equal to 0 and solving for x.

    Standard form is (1/6)x² + x - 9/2 and vertex form is (1/6)(x + 3)² - 6

3.  Vertex (-1, 18) Axis of symmetry is x = -1 It opens up and has a minimum value of -18.  The x-intercepts are -4 and 2.  In intercept form it is f(x) = 2(x + 4)(x - 2) and in vertex form it is y = 2(x + 1)² - 18

4.  The vertex is (5/3, -16/3) and the axis of symmetry is x = 5/3.  It opens up and has a minimum value of -16/3. The x-intercepts are at 1/2 and 3.  Written in standard form, it looks like y = 3x² - 10x + 3, and written in vertex form, it looks like: 3(x - 5/3)² - 16/3

5.  The vertex is (-2, -4/5) and the axis of symmetry is x = -2.  It opens down and attains a minimum value of -4/5.  There are no x-intercepts, so there is no intercept form.  (There is a factored form, however!  It is y = -2(x +2 + i(sqrt(10))/5)(x + 2 - i(sqrt(10))/5).)  The standard form is y = -2x² - 8x - 44/5.

 

And Selected answers to the back of the "Making Connections..." worksheet are:

f(x) = a(x - r)(x - s) = ax² - a(r + s)x + ars

The coefficient of x² is a = a, the coefficient of x is b = -a(r + s) and the constant term  is c = ars.

-b/a = -(-a(r + s))/a = a(r + s)/a = r + s

You can do the rest!

 

 

 

Accelerated Math III - January 17, 2012 - Applications and trig review

Today we presented the Ferris Wheel task and determined correct answers to the "Second Trig Review".  Here are the rest of the answers to that review.

10.  Theta = pi + 2*pi*n, where n is an integer.

11.  x is equal to 0 or to 2pi/3  (Don't forget that there is a smaller period, here.)

12.  Domain [-1, 3]  and range [-pi/2, 5*pi/2]

13.  -11*sqrt(170)/170

14.  24/25

15.  A)  -sqrt(10)/10      B) -3*sqrt (10)/10      C) 1/3  (Don't forget that tan x = (sin x)/(cos x)

16.  2cos (7*theta)*cos(2*theta)

17.  3(sin 70^o + sin 30^o)

18.  2*cos (5k)*sin (3k)

19.  -2(coa26^o - cos 12^o)

 20. 5cos(theta - 2.49809)

21.  a = 9.3894     b = 17.659   m<B = 62^o 

In order to review for the test, you need to know what it covers.  Here are the main topics and suggested questions from our text:

I.  Basic trig relationships:  (unit circle relationships and special values, reference angles, coterminal angles, degree vs. radian measures, #radians = (arc length)/(radius length), finding values of trig functions using calculators and using points on their terminal rays, finding angles that terminate in quadrants that calculators don't give us, limits on the inverse trig functions, knowledge that a sin^-1 is an angle)  Reference:  Chapter 2:  Pg. 72 odds, Pg. 79 odds, Pg. 83 odds, Pg. 116 odds, Pg. 189 odds,  and unit circle task.  Additional problems: 

1.  If cos x = -.42 and pi < x < 2pi, find x. 

2.  If csc k = 4.362, and tan k > 0, find k.

II.  Graphs of trig functions, including the inverse functions. (domains and ranges, maximimums and minimums, period, amplitude, phase shift, vertical shift, asymptotes of tangents, cotangents, secants and cosecants, and endpoints of Sin-1 and Cos -1, writing equations of them all)  Reference:   Chapter 3: Pg. 104 - 105 odds, Pg. 108 1-14, Pg. 122 odds, Pg. 188 odds,  Additional Problems:

3.  State the domain and range of f(x) = 3sec(3(x - pi)) + 5

4.  State the endpoints of g(x) = 3pi - 4Sin^-10.25(x - 1) 

III.  Trig Identities (All identities on page 240, verifying, solving equations that use them)  Reference:  Chapters 4 and 5: Pg. 167 odds, Pg. 173 odds, Pg. 203 odds, pg. 212 odds, pg. 228, 229 odds, pg. 237 - 239 odds.

IV.  Applications of Trig (so far...)  (SOHCAHTOA, angular velocity, etc., sinusoidal models) Reference:  Pg. 84 - 87 odds, pg, 109 #15, Pg. 132 - 137 odds, Pg. 143 - 147 odds, pg. 174 #37,  Pg. 204 #28, pg. 229 # 31