PreCalc



OLD POSTS
CHAPTER FIFTEEN!
CHAPTER 15!: Wait, what?! Yes, we are going to move onto Chapter 15.  In this chapter you get to review some more Algebra 2 while going a little further and tying in some Calculus.  Some of the topics will include calculating the roots of polynomial functions, analyzing and identifying discontinuities in rational functions, calculating vertical, horizontal, and slant asymptotes, describing a limit and its relationship with discontinuities, and calculating the derivative of a function.

CHAPTER 15 HOMEWORK:

  1. p.669 [1 - 11all]
  2. p.678-9 [Q1-Q10, 1-6all]
  3. p.679 [7-17odds, 27, 28]
  4. Wkst p. 201-202 [Warmup 3, 5-7, 9; Questions 5, 11, 15, 17, 21, 33, 49]
  5. p.682-684 [Q1-Q7, Q9, Q10, 1, 3, 6]



CHAPTeR SeVeN!
CHAPTeR 7:  In this chapter we start off looking at patterns in, and writing equations for, four types of functions: linear, quadratic, power, and exponential.  We then dive into exponential and logarithmic functions and focus on e and ln.  We will also learn about the logistic function.  There are TONS of real-life applications in this unit and we will look at examples from natural science, popular trends, and investing.  You will get to be a rocket scientist, an investment banker, and a media mogul... all in one chapter!  

 CHAPTeR 7 HOMeWORK:
  1. (7.1) ... p.293 [1-4 all]
  2. (7.2) ... p.254 [4, 8, 10, 14, 15]
  3. (7.2) ... p.262 [4, 6, 10, 11]
  4. (7.3) ... p.257-258 [Q1 - Q10, 1, 7 - 10]
  5. (7.4) ... p.265-266 [Q1 - Q10, 2, 4, 6, 10]
  6. (7.5) ... p.271-272 [Q1 - Q5, Q7 - Q10]
  7. (7.6) ... Application/Word Problems Worksheet [1-6 all]
  8. (7.6) ... Application/Word Problems Worksheet [7-11 all] 
  9. (7.6) ... Application/Word Problems Worksheet [12-16 all]
CHAPTeR 7 ASSeSSMeNTS:
  • QUIZ (7.2 - 7.4) ... Tuesday, 3/12
  • TeAM TeST ... Thursday 3/21
  • INDIVIDUAL TeST ... Thursday 3/28
CHAPTER SIX!
CHAPTER 6 TEST:  One topic that was not covered on the team test, but will be on the individual test is dilations and translations from first semester.  Look at your old tests for examples - they will help!
  • Here are the topics in no particular order:
    • Law of Cosines
    • Law of Sines
    • Area formulas
    • Vectors, bearings, and components
    • Ambiguous Case
    • Dilations and translations
    • Sinusoids
    • Solving trig equations
    • Completing a proof
CHAPTER 6:  We're working with vectors right now and will finish it up this week.  Next week we will examine some real-life problems and solve them using your new knowledge of the Law of Sines, the Law of Cosines, the area formulas, the Ambiguous Case, and Vectors.
CHAPTER 6 HOMEWORK:
  1. (6.2) ... p.253 [Q1 - Q10] and p.261 [Q3 - Q10]
  2. (6.2) ... p.254 [4, 8, 10, 14, 15]
  3. (6.4) ... p.262 [4, 6, 10, 11]
  4. (6.3) ... p.257-258 [Q1 - Q10, 1, 7 - 10]
  5. (6.5) ... p.265-266 [Q1 - Q10, 2, 4, 6, 10]
  6. (6.6) ... p.271-272 [Q1 - Q5, Q7 - Q10]
  7. (6.6) ... p.272-273 [1, 4-7, 10, 11]
  8. (6.6) ... p.272-273 [2, 3, 8, 13-15, 17]
  9. (6.7) ... p.275-276 [Q1-Q10, 1, 2b, 3a, 4a, 5b]
  10. (6.7) ... p277-278 [7, 9-12, 14, 17, 18]
  11. Review ... p.280-283 [R2a-c, R3a-c, R4a-c, R5, R6c-d]
  12. Review ... p.284-285 [T1-9, 11-17, 20]  Extension Problems: T18-19 (Do them if you want)
CHAPTER 6 ASSESSMENTS:
  • QUIZ (6.2 - 6.4) ... Friday, 2/8
  • TEAM TEST ... Friday 2/22 and Monday 2/25
  • INDIVIDUAL TEST ... Thursday 2/28


 OLDER POSTS:


 ANSWERS TO CHAPTER 12 "T" PROBLEMS (1-3, 9, 11-15):
T1: A and C are positive, but different dilations: Ellipse
T2: A and C have opposite signs: Hyperbola
T3: Only one term is squared: Parabola
T4 - 6: DO NOT DO!  (Sorry)
T9: The ratio of the distances (focus to point : point to directrix) is the eccentricity ratio
T11: Graph of a hyperbola, opening in the y-direction, w/ transverse radius of 2, conjugate radius of 6, and focal radius of 6.32... (square root of 40)
T12: x = 3 + 6tanT   y = 1 + 2secT
T13: -x^2 + 9y^2 + 6x - 18y - 36 = 0
T14: For this problem, V = pi r^2 h . You need to solve the ellipse for y and substitute that in. x = 1.154... (radius) and V = 77.388...
T15a: Center: (45, 0); Minor radius is 24 (thousand miles); eccentricity ratio = 0.8823...
T15b: (x - 45/51)^2 + (y / 24)^2 = 1; when x = 0, the y-intercepts are +/- 11.2941...
T15c: 2000 miles of the surface (within 6000 miles of the center of the Earth, but since the Earth's radius is 4000mi, it only comes within 2000 miles).

CHAPTER FIFTEEN!: Wait, what?! Yes, we are going to move onto Chapter 15.  In this chapter you get to review some more Algebra 2 while going a little (or a lot) further and tying in some Calculus.  Some of the topics will include calculating the roots of polynomial functions, analyzing and identifying discontinuities in rational functions, calculating vertical, horizontal, and slant asymptotes, describing a limit and its relationship with discontinuities, and calculating the derivative of a function.

CHAPTER 15 HOMEWORK:
#1 (15.1) ... p.669 [1 - 11all]
#2 (15.2) ... p.678-9 [3 - 17odd, 29 - 32all]
#3 (15.2) ... Wksts 15.2a & 11-7
#4 (15.2) ... p.679-80 [1, 19 - 25odd, 34*, 35*]

CHAPTER FOUR:
We're beginning the fourth unit this week:  Sections 3.8, 4.1 - 4.4, and 4.6.

CHAPTER FOUR HOMEWORK:
#1 (3.8) ... p. 143 - 145 [Q1 - Q10, 1, 3, 5, 7]
#2 (3.8/4.1) ...

CHAPTER THREE HOMEWORK:
#1 (3.1) ... p. 95 [1-9]
#2 (3.2) ... p. 102 - 104 [Q1 - Q10, 1 - 13odd]
#3 (3.2) ... p. 104 - 105 [2, 4, 15 - 23odd, 26, 27]
#4 (3.3) ... p. 108 - 109 [Q1 - Q10, 1-14all]
#5 (3.4) ... p. 115 - 117 [Q1 - Q10, 3 - 43odd, 49 - 51]
#6 (3.4/3.5) ... p. 117 [51 - 54], p. 121 [Q1 - Q10] + Fill out the gold sheet completely!
#7 (3.5) ... p. 121 - 123 [1, 5, 9, 13, 17, 21, 25 - 43odd]
#8 (3.6) ... p. 128 - 129 [Q1 - Q10, 5, 11]
#9 (3.7) ... p. 132 - 136 [Q1 - Q10, 1-7odd, 11]
#10 (Review) ... p. 148 - 150 [Read R0, R1 - R7, no R5a]
#11 (Review) ... p. 153 - 154 [T3 - T7, T10 - T18]
#12 (Unit Circle) ... Practice the Unit Circle
#13 (Review) ... Wkst 3.9

CHAPTER TWO INDIVIDUAL TEST:
The second test was last week.  If you haven't taken it, please be ready to take it this week.

CHAPTER TWO HOMEWORK:
#1... p. 61 [1-4]
#2... p. 65 - 66 [RA, Q1 - Q10, 1 - 19odd, 27, 29]
#3... p. 71 - 72 [Q1 - Q10, 1-6all]
#4... p.72 [7-13odd, 15-22all]
#5... p.78 [Q1-Q10, 1-7all, 11-19odd]
#6... p.79 [21-33odd, 34, 35-43odd, 44]
#7... p.83 [Q1 - Q10, 1-4, 7, 10, 11, 13, 19, 21*]
#8... p.88 - 89 [R0 (just read it), R1 - R5]
#9... p. 91 - 92 [T1 - T21]

This stamp sheet will be due the day after the individual test!

UNIT CIRCLE:
Here are two YouTube clips regarding the unit circle.  You want to understand the connection between the angle of the graph and the corresponding sine and cosine values.  The horizontal (x) values in the unit circle are the cosine values and the vertical (y) values are the sine values.  

You create sine and cosine waves by using the angles as independent variable and the sine/cosine values as the dependent values. 

Unit Circle to Sine Graph: http://www.youtube.com/watch?v=Ohp6Okk_tww

Unit Circle to Cosine Graph: http://www.youtube.com/watch?v=jEcqQkl2_A4&noredirect=1

For those of you who were wondering about "where" the six trig functions come from, here are two pictures (from Wikipedia) to help explain:

Location of sin, sec, and tan in the unit circle: http://en.wikipedia.org/wiki/File:Unitcircledefs.svg

Location of cos, csc, and cot in the unit circle: http://en.wikipedia.org/wiki/File:Unitcirclecodefs.svg

CHAPTER ONE TEST:
If you missed the test, please be ready to take it during the next class period.

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