Math1080 Precalculus
Fall, 2013

Class Notes

• Chapter 2: Sections 2.2 Notes
  
  
• Chapter 2: Sections 2.3-2.4 Notes
  
  
• Chapter 2: Sections 2.5-2.7 and 1.6/1.9 (Review) Notes
  
  
• Chapter 3: Sections 3.1-3.3 Notes
  
  
• Chapter 3: Sections 3.5-3.6 Notes
  
  
• Chapter 4: Sections 4.1-4.3 Notes
  
  
• Chapter 4: Sections 4.4-4.7 Notes
  
  
• Chapter 5: Sections 5.1-5.3 Notes
  
  
• Chapter 5: Sections 5.4-5.6 Notes
  
  
• Chapter 5 & 6: Sections 5.7 & 6.1 Notes
  
  
• Chapter 6: Sections 6.2-6.4 Notes
  
  
• Chapter 6: Section 6.5 and Chapter 7: Sections 7.1 & 7.2 Notes
  
  
• Chapter 7: Section 7.3 and Chapter 8: Section 8.1 Notes
  
  
• Chapter 8: Sections 8.2-8.3 Notes
  
  
• Chapter 8: Sections 8.4-8.7 Notes
  
  
• Appendix D & Partial Fraction Decomposition Notes
  
  

Miscellaneous

• Book/WebAssign information
  
  
• 3.1 Homework Problem Solutions (for those problems I couldn't get to in class)
  
  
• Proof of Divisibility by 9 Test
  
  
• 3.6 Examples 4 and 6 from notes
  
  
• 4.3 #55
  
  
• Unit Circle
  
  
• 5.4 #51
  
  
• Inverse Trigonometry Graphs
  
  

Homework Assignments

Symbols:
* This symbol next to a specific problem means there is an error in the answer to this problem in the book. -- Consult the list of errors below.

& If this symbol is next to a specific problem, it means to use a calculator. For all other, nondesignated problems, please do the problem by hand.



• 1.6 #1, 3, 5, 7ab, 9, 11, 12, 21-29 odd, 31*, 33
• 1.9 #5-23 odd, 41, 43, 45, 47, 53, 55, 57 (Please solve all problems algebraically, not with calculator as books suggests.)
• 2.2 # 1-45 odd, 53, 55*, 57*
• 2.3 # 1-27 odd, 29*, 33*, 35-55 odd
• 2.4 #1-57 odd
• 2.5 #1-43 odd, 47, 51, 53
• 2.6 #1-7 odd, 9*, 11-49 odd, 51*, 57
• 2.7 #1-11 odd, 13-18 all, 19-31 odd, 39, 41*, 43, 45, 51, 53, 57 (Problem 41 doesn't make sense as written. Identify why. Try to rewrite the problem so you can answer the question.)
• 3.1 #3-43 odd, 51, 53
• 3.2 # 1-21 odd, 29-43 odd, 47, 49, 51
• 3.3 #3-27 odd, 35-43 odd, 47*, 51
• 3.5 #1-11 odd, 13-16 all, 17, 19, 27, 29*, 31-57 odd
• 3.6 #1-33 odd, 39-55 odd
• Appendix D #1-47 odd, 52-54 all
• 4.1 #1-49 odd, 55, 57&
• 4.2 #3-47 odd
• 4.3 #1-55 odd
• 4.4 #1&, 3&, 5-19 odd, 21-33(&) odd, 41&, 53
• 4.5 #1-15 odd, 17a&, 19a&, 21a&, 23a&, 25-31(&) odd, 33-53 odd (Make a table to graph problem 43.)
• 4.6 #1-55 odd
• 4.7 #1-47 odd, 51, 53 (For #13-39 odd, give the simplified exact answer. You can check your answer by finding the decimal approximation and comparing to the solutions.)
• 5.1 #1-21 odd, 27-31 odd, 33&, 35, 39&, 41-49 odd, 55&
• 5.2 #1-15 odd, 17&, 19&, 21-39 odd, 47, 49
• 5.3 #1-19 odd, 21*, 23-45 odd, 51
• 5.4 #1-39 odd, 51
• 5.5 #1, 3, 5&, 7acegi, 9acegi, 11, 13, 15, 17ab&, 19ab&, 21-37 odd, 39&, 41&, 43 (For #39 and 41, do graphically and algebraically, like in Example 7 on page 340.)
• 5.6 #1-17(&) odd, 19, 21, 23-43(&) odd, 47&
• 5.7 #1-41(&) odd, 45&, 49&, 57&
• 6.1 #1-29 odd, 31&, 33-49 odd
• 6.2 #1-33 odd, 35&, 37&, 41-57 odd
• 6.3 #1-47 odd, 55
• 6.4 #1-23 odd, 27-37 odd, 43, 45, 47, 49
• 6.5 #1-49 odd (For problems 19 and 21, use polar graph paper which you can find online for free by searching for "polar graph paper.")
• 8.1 #1-53 odd
• 8.3 #1-23 odd, 25&, 27&, 29-37 odd, 39&, 41-47 odd, 53
• 8.4 #1-41 odd, 47, 53
• 8.5 #1-47 odd, 55, 57, 59
• 8.6 #1-29 odd, 37-47 odd, 59
• 7.1 #1-23 odd, 35-49 odd, 55
• 7.2 #1-19 odd, 27-49 odd, 53, 55 (revised as of 12/10/13, do only #1, 3, 7-19 odd, 27-35 odd, 39-49 odd, 55)
• 7.3 #1-17 odd, 25-57 odd (revised as of 12/10/13, do only #1-17 odd, 25-35 odd, 41, 45, 49, 51, 53)
  
  List of Known Errors in book
  

Exam Reviews

• Midterm 1 Review: (covers sections 1.6, 1.9, 2.2-2.7, 3.1-3.2)
  Chapter 1 Review (page 72-73) #39-49 odd, 50
  Chapter 2 Review (page 152-153, Self Test) #1-10 all
  Chapter 2 Review (page 153-154, Practice for Calculus) #5-11 odd, 33-43 all
  Chapter 3 Review (page 214, Self Test) #1, 10
  Chapter 3 Revew (page 215, Practice for Calculus) # 23
  Section 3.1 #52, 54
  
  
• Midterm 2 Review: (covers sections 3.3, 3.5-3.6, 4.1-4.7, 5.1-5.2)
  Section 3.3 #16, 18
  Chapter 3 Review (page 214, Self Test) #1, 2(a,b), 3-8 all
  Chapter 3 Review (page 214, Practice for Calculus) #1-6 all
  Chapter 4 Review (page 277, Self Test) #1-9 all
  Chapter 4 Review (page 278-279, Practice for Calculus) #1-6 all, 33-47 odd, 49-57 all
  Chapter 5 Review (page 369, Self Test) #1
  Chapter 5 Review (page 370, Practice for Calculus) #5-25 odd, 31-35 odd
  
  
• Midterm 3 Review : (covers sections 5.2-5.7, 6.1-6.4, 8.1, 8.3)
  
  1. 5.2 #50; 5.3 #4, 9, 14, 45; 5.4 #36, 49; 5.5 #14, 15, 26, 27, 30
     5.6 #6, 12, 30; 5.7 #16, 23, 25; 6.1 #22, 24, 44
     6.2 #44, 50; 6.3 #25, 45; 6.4 #10, 17, 38
     Chapter 8 Review (page 578, Self Test) #1, 3, 4
     
     
  2. Chapter 5 Review (page 369-370, Self Test) #1, 2, 4, 6, 7, 10
     Chapter 6 Review (page 421, Self Test) #1-9 all
     8.1 #8, 12, 14, 48
     8.3 #16, 20, 24
     
  Midterm 3 Review Key for Even Problems
  
  For this test, you can bring one 8.5x11 inch sheet of paper to use for reference notes, double-sided.
  
  

  Midterm 3 Topics

  
  
  • Trigonometric Computations
    • finding trigonemtric function values for the usual angles as well as the half and double angles
      
    • using right triangle information or Pythagorean Theorem to find trigonometric function values given one piece of information
      
    • finding trigonometric function values for angle given any (x,y) point in 2-d
      
    • using all the given identities to compute trigonometric function values
      
  • Inverse Trigonometric Functions
    
  • Graphs of Trigonometric Functions (transformations, amplitude, period)
    
  • Solving Triangles (Pythagorean Theorem, Law of Sines, Law of Cosines
    
  • Solving Trigonometric Equations
    
  • Verifying Trigonometric Identities
    
  • Sequences and Series: Arithmetic, Geometric, Fibonacci-type
    
  
  
  Final Topics List
  
  • Solve types of equations/inequalities:
    • rational/quadratic/absolute value inequalities (1.6, 1.9)
    • polynomial equations (3.6)
    • radical/rational equations (4.3)
    • exponential/logarithmic equations (4.6, 4.7)
    • trigonometric equations (6.1)
    • systems of equations (8.4, 8.5, 8.6)
    
    
  • Functions:
    • domain/range/graphing (2.2, 2.3)
    • piecewise functions (2.5)
    • arithmetic operations and compositions of functions (2.6)
    • find inverse function (2.7)
    • difference quotient (3.1)
    
    
  • Graphing:
    • Base graphs
    • transformations (2.4)
    • quadratic functions (3.2)
    • polynomial functions (3.5, 3.6)
    • rational/radical functions (4.1, 4.2)
    • exponential/logarithmic functions (4.4, 4.5)
    • trigonometric functions (5.4)
    • inverse trigonometric functions (5.5)
    • conic sections (parabolas/ellipses/hyperbola) (7.1, 7.2, 7.3)
    
    
  • Trigonometry:
    • evaluating expressions (reference angles/ trigonometric function values for common angles/definitions of trigonometric functions in right triangles/inverse trigonometric function values) (5.1, 5.2, 5.3, 5.5, 5.6)
    • solving triangles (Law of Sines/Cosines) (5.7)
    • prove/use identities (6.2, 6.3, 6.4)
    
    
  • Arithmetic/geometric sequences and series (8.1, 8.3)
    
    
  • Matrix algebra (add/subtract/scalar multiplication/matrix multiplication/find matrix inverse) (8.5, 8.6)
  Final Review Sessions Notes