Oakton Community College
MAT 149   PreCalculus
Section 004:   MW  10am - 12:20   Room 2759   DP Campus
Paul Boisvert     Professor of Mathematics 
Spring Semester  2011
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Homework Assignments
Note:  Below, exponents are written with the wedge ^ notation.  So "x raised to the third power" would be "x^3". 
Fractions are written with slashes and parentheses:  A fraction with a + b in the top and c - d in the bottom is written as  ( a + b )  /  ( c - d ) .
Square Roots are written as "sqt(x)", and higher roots as fractional exponents, i.e.,  cube root of x would be  "x^(1/3)"
Date Page.  Problems Read Sections
Wed
1/19		 p. 11 11-14 ALL ,   39, 41,   51-57 odd,   59- 65 odd,   67-83 odd,   85-95 odd,  97-109 odd
Answers:  
12)  False      14)  False                                                                                                                                                                                                                     .		 P.1
Mon
1/24		 p. 11  97-109 odd  
  p. 20  5-57 odd  P.2 
Wed
1/26		 p. 20 59-69 odd, 71, 73   
  p. 32 1-37 odd, 39 - 67 odd,  69 - 75 odd,  81 - 91 odd,
Board Problem :
     A)  Simplify using fractional exponents.  Write answer with fractional exponent, THEN ALSO change it to a root.   [Cube root of x^8]  [ Square Root of x] /  [4th Root of x^5 ]
   
Answer:  A)  x^(23/12)  ...   OR, as Root:   12th Root of (x^23)
 		 P.3
Mon
1/31		   NO CLASS -- I will be off campus.     
  
Wed
2/2		   NO CLASS  College Closed
Mon
2/7		 p. 42 21, 23, 24, 29-33 odd, 43-47 odd, 49-55 odd, 61, 63, 67-73 odd
ALSO, do these--I forgot to assign these in class!  [If you see a fellow student from the class, please tell them about these additional problems!]
      Short Division:  #77, 79, 93
      Long Division:   #83, 87, 89, 91, 97

Answers:  24)  -5x^2y^2  - 3xy + 8x -  4y		 P.4 
  p. 52 Factor using GCF, Grouping, Trial and Error, and/or Difference of 2 squares.     No "cubes" problems, that method will not be on this test.
 5-9 odd,  13, 15, 27-33 odd, 36, 39, 43, 55, 57

Answers:   36)  (3t - v)(3t + v)		  P.5
Wed
2/9		   REVIEW For Test 1    Click on preceding link to go to online version of Review Sheet handed out in class today.  If you missed class,
make sure you do the Review Sheet before Test.  		  
Mon
2/14		   TEST 1    Covers all material on which HW was asssigned, up through Factoring in P.5 (but not "cubes")
Closed Book, No Notes.

BRING SOME PAPER of your own.   This can be paper you will rip out of a notebook (as long as it has nothing written on it.)  Or any other kind of blank paper you wish.  Bring several sheets.  BRING your OWN Calculator.  NO SHARING of calculators during the test

If you MISS this Test, there will be a 7% penalty to take it as a Makeup in the Testing Center within 1 week.  You must start by 10 AM, Monday 2/21.  Please email me if you miss the Test--but the makeup test will automatically be there in the testing center for you once I see you don't attend the regular test.		  
Wed
2/16		    Review Sheet, AND All HW assigned before Test 1, are DUE.    
   p. 52 49, 50, 51,  63-71 odd, 83, 85

Answers:  50)  (1 - 2a^2 ) ( 1 + 2a^2 + 4a^4 )		  
  p. 62 15-21 odd, 31-37 odd, 34,
53, 54, 55, 56, 61, 62, 63,  73-79 odd, 74, 76

Answers:  34)  9(a + b) / 2        54)  (2a - 7b) /  3a^2 b^2          56)  (2x + 8) / [ (x + 3) ( x - 3) ]        
62)    (4x - 5)  /  (x + 1) ( x + 3) ( x - 2)          74) corrected:  (4y - 3y^2 ) / ( 4x + 6y^2 )      
76)   1 / ( abc^2 + a^3 b )		 P.6
Mon
2/21		   NO Class -- College closed.    
Wed
2/23 		 p. 71 13-17 odd, 23-27 odd, 31, 33,   35-38 ALL ,  55, 61, 63  ,  65-73 odd

Answers:  36)  1           38)   -i          		P.7
  p. 86 17, 19, 23, 25, 37, 38, 39, 41, 47, 51

Answers:  38)  x = 6          		 1.1 
Mon
2/28 		 p.97  7, 9, 11, 15, 17, 19  1.2 
  p. 112  19, 23, 35, 39, 41, 43, 44, 69, 71, 73

Answers:  44)  (x + 1)^2  + (y + 6)^2   =  1/9		 1.3 
Wed
3/2		 p. 126  9, 15, 19, 21, 35, 37, 39, 41, 48, 51, 67, 69, 71,  
75-81 odd

Answers:  48)  Graph goes through (0,1) which is the y-intercept.  Using slope of 2/3 = h/w says go 3 spaces to right, 2 spaces up, to (3, 3).  Draw line through those two points. 		 1.4 
  p. 147  9, 11, 13, 15, 17, 47-55 odd,  82,  89-97 odd

Answers:  82)   [ 1  +  sqrt(3) ]  /  7 		 1.6 
Mon
3/7		    REVIEW For Test 2    Click on preceding link after 3pm Monday 3/7 to go to online version of Review Sheet handed out in class today.  If you missed class, make sure you do the Review Sheet before Test.  NOTE:  Answers for Review are mostly on a hard-copy sheet only, see me.  Only a few are on the online version.  
Wed
3/9		    TEST 2    Covers all material on which HW was asssigned, up through section  1.6
Closed Book, No Notes.

BRING SOME PAPER of your own.   This can be paper you will rip out of a notebook (as long as it has nothing written on it.)  Or any other kind of blank paper you wish.  Bring several sheets.  BRING your OWN Calculator.  NO SHARING of calculators during the test

If you MISS this Test, there will be a 7% penalty to take it as a Makeup in the Testing Center by Wed within 1 week, and a 14% penalty if it is your second missed test..  You must start by 10 AM, Wednesday 3/23, after Spring Break.  Please email me if you miss the Test.		  
Mon
3/14
 and
Wed
3/16 		   SPRING BREAK     COLLEGE CLOSED   
Mon
3/21 		   HW Due from before Test 2   
   p. 161 17-25 odd, 45-53 odd, 55, 56, 57

Answer:  56)   [-3, 2]		 1.7 
p. 184 65-75 odd, 87, 89 2.1
Wed
3/23 		   MAKEUP TEST for TEST 2 must be started by 10 am Today!   
  p. 196  35-41 odd 2.2 
Mon
3/28		 p. 223 11-14 ALL
23-29 odd, SKIP the parts about the "domains"
47-50 ALL
51-61 odd, SKIP the parts about the "domains".

Answers:  
12)  -b^2 + 2b - 3     14)  (b - 3)/(b^2 - b)          48)  w         50)  9m^2  -  6m  + 2   		2.4
  p. 236  49,  67, 73, 74, 77   In each case, use the "switch and solve" method.

Answers:  74)   (6x - 1)/(x - 2)  =  f-inverse (x) 		2.5 
Wed
3/30 		 p. 266  41, 43, 45, 51, 52  For these, graph parabola BY HAND, showing intercepts (0, ? ) (? , 0), (? , 0), and Vertex V(-B/2A, ?)
77, 79, 81, 82  For these quadratic inequalities, use GRAPHING Calculator to graph function, find zeroes using Zero Menu Option, then say which points above or below axis make the inequality true.

Answers:  52)  Negative coeff. of x^2 means it opens downward    (0, -6) is y-intercept,  there are NO x-intercepts (since Q.F. gives sqrt(-2) is imaginary),
                         Vertex V (1, -5)  so Axis of Symmetry is vertical line x = 1.  Graph those points, check on graphing calculator.
82)  [-5, -3]		 3.1 
  p. 280 35-38 ALL,  55, 56    Factor these by graphing on graphing calculator, finding zeroes, and converting each zero to a factor.  
                                   Remember, if zero is  x = + 3,  the factor is (x - 3), note sign change.  And if zero is -5,  factor is (x + 5).
Remember that a zero where the graph just barely touches the axis is from an EVEN power factor (x - r)^2 .  
Factors where the curve crosses the axis come from 1st (or odd) power factors.
Also, a "touching" zero may be troublesome to find on graphing calculator using the zero menu option--if the calculator can't find it, TRACE over to it and assume that it equals what it approximately looks like.

Answers:  36)   (x  + 5) (x + 4) ( x - 1)              38)  (x - 2) (x - 4) ( x - 6)    
56)  Zeroes are x = -2 , x = 1,  x = 3   Book did not ask for factoring, but I will on a test:  (x + 2) (x - 1) (x - 3)		 3.2 
Mon
4/4		   Board Problems:    Solve using graphing calculator to find zeroes of  y = f(x) = 0.   Remember to set equation equalt to ZERO first!
A)  Solve  30x^3 - 47x^2 - x  =  -6             B)  Solve 3x^3  = 4x - 1

Answers:  A)  Set equation  = 0, and get  30x^3 - 47x^2 - x + 6 = 0.    Graph y = f(x) = 30x^3 - 47x^2 - x + 6 , then find zeroes on calculator.
    You get   x1 =   -.3333 =  -1/3  and   x2 =  .4 = 2/5     and    x3  =  1.5  =  3/2
    Note:  although I did not ask for factors here, I might on the test.  The factors of  f(x) would be (x + 1/3) (x - 2/5) (x- 3/2).  Since when you multiply these out  this creates x^3 + ..., rather than 30x^3 + ..., the real factorization would need a missing constant of 30.  So the true factorization would be 30(x + 1/3) (x - 2/5) (x- 3/2)
     Another way to deal with the missing "30" is to multiply each fractional factor by its own little LCD.
     That is, multiply (x + 1/3) by 3 to get (3x + 1).  Multiply (x - 2/5) by 5 to get (5x - 2).   And multiply (x - 3/2) by 2  to get  (2x - 3).  
   So the factorization would now be (3x + 1)(5x - 2)(2x - 3).  This already equals  30x^3 + ... ,  and so this factorization does not need the extra constant of 30.
    Note that the "30" equals the product of the little LCD's, (3)(5)(2) !

B)  Set equation  = 0, and get  3x^3  - 4x + 1  =  0    Graph y = f(x) = 3x^3  - 4x + 1  , then find zeroes on calculator.
    You get   x1 = -1.264     and     x2 =  0.264      and    x3  =  1
    Note:  The first two decimals do not equal any obvious fractions, so no simple factoring is possible here.  However, the third zero,  x = 1, does
      create a factor of  (x - 1).  If you long divide (x - 1) into the function 3x^3 - 4x + 1, the answer will be 3x^2  + 3x - 1.  If you then solve that equation = 0,
      that is, solve  3x^2  + 3x - 1 = 0  using the Quadratic Formula, you will get the other two roots that you found above for x1 and x2.		  
  p. 301 3, 5, 7, 9, -- Solve by Factoring (and or separating, and or quadratic formula if factoring fails)
11, 13, 15, 19 -- Solve by isolating square root, then squaring both sides.  Be sure to check each answer in the original equation.
27-34 ALL  -- solve by applying the reciprocal exponent to both sides.

Answers: 28)   x = +  (1/2)^3/2   =   +  0.3536         30)  w = 1/9              32)  t = 4          34)  s = 11		 3.4 
Wed
4/6		 p. 354  13-31 odd,  33-37 odd
47, 48-- show 3 key values and any shifted asymptote

Answers:  48)  New shifted Asymptote is at  y = 1.   3 Key Points will have orginally been [before the shift up by 1]:    (0, 1)  (1, 1/3) and (-1, 3)
                       After shifting up by 1,  new 3 Key points will be at:   (0, 2)  (1,  1.333)  and  (-1, 4)   Graph those points show new asymptote, make it look like all
                       exponentials  should look when they have a negative x up in the exponent.		 4.1 
  p. 367  17-31 odd, 59-77 odd  4.2 
Mon
4/11		   REVIEW For Test 3    Click on preceding link after 3pm Monday 4/11 to go to online version of Review Sheet handed out in class today.  If you missed class, make sure you do the Review Sheet before Test.  Note, Answers to Review not online, see me for hardcopy.  
Wed
4/13		    TEST 3    Covers all material on which HW was asssigned, up through section  4.2
Closed Book, No Notes.

BRING SOME PAPER of your own.   This can be paper you will rip out of a notebook (as long as it has nothing written on it.)  Or any other kind of blank paper you wish.  Bring several sheets.  BRING your OWN Graphing Calculator.  NO SHARING of calculators during the test

If you MISS this Test, there will be a 7% penalty to take it as a Makeup in the Testing Center by Wed 4/20 within 1 week, and a 14% penalty if it is your second missed test..  		  
Mon
4/18 		   HW and Review Due    
    Board Problems:  Solve for x:  if logarithmic equation, exponentiate both sides using the Base B of the logarithm.  If exponential equation, apply ln(  ) to both sides.
A)  2 - 3 ln(x + 5)  =  8                   B)  5 ln (x^2)  =  8                 C)  7 - 4e^(3x - 2)  =  2  

Answers:   A)  x =  -4.865          B)  x = 2.226,  x = -2.226  Note:  +/- sqrt  is  needed!              
C)   x  =   0.741  		  
  p. 380  NOTE:  I made a mistake in class while assigning HW today.  63-69 odd should have been from this page, page 380, NOT from p. 392
11-31 odd,  41-59 odd, 63 - 69 odd,  71-76 ALL

Answers:   72)  1.424                74)   14.356         76)  26.593		 4.3 
  p. 392  1-11 ALL   In these,  rewrite in exponential form, then solve the equation by your normal methods [from Test 1, 2, or 3]--Linear, Factor, Separate, Q.F., whatever.
41-47 odd  
And See NOTE for p. 380 Above.

Answers:  2)  x = 1        4)  x = 16           6)  x = 2, x = 3             
8)   x = 2  [or x = -2, from +/- sqrt, BUT  a negative number cannot be the base of a log, so x = -2 is NOT a solution.]      
10)   x = 1/81
 4.4 
Wed
4/20		 p. 417  13, 15,   21-39 odd,  53-65 odd,  67-74 ALL, 75-87 odd, 93-100 ALL,  103-109 odd, 111 [Do NOT do 112 after all]

Answers:  68)  255 degrees               70)   390 degrees             72)  -1620 degrees               74)   25.898 degrees                  94)  III        
96)  I            98)  II               100)  III                112)  Not assigned after all  		 5.1 
  p. 430  31-41 odd  ONLY!  
 NOTE:  Sorry, I did NOT mean to assign 51-61 odd!  Do NOT do them yet--they will be assigned next time. 		 5.2 
Mon
4/25		 p. 430  1-81 odd, (but don't repeat 31-41 odd or 51-61 odd if you already did them earlier.) 5.2 
  p. 458  5-51 odd  5.4 
Wed
4/27		 p. 444  63, 65-69 odd, 37, 38   In all of these, GRAPH BY HAND the function, showing new Period, Amplitude, and shifted up or down by relabeling y-axis, if needed.
When you finish, you can of course check it on your graphing calculator.

Answer:  38)  New Period:  2pi/3      Marks of 4 equal spaces on x-axis are at pi/6, pi/3, pi/2, and 2pi/3.  
Function starts at bottom at -2 , then goes zero, top(+2), zero, bottom, zero, etc.
2nd period is out to 4pi/3.   NO shift up or down.   Show little tail on each end going UP from bottom point.
Draw graph, check on graphing calculator.		 5.3 
  p. 469  1-67 odd
Board Problems:  Solve for x.   Give answers in Radians,  in form { x1 , x2 , + 2kpi}
A)  Solve  4 sin (x) + 5  = 2   Use inverse-trig fcn. on calculator for first solution , then think quadrants and ref. angles for 2nd solution
B)  Solve  10 cos(x) - 2  =  6   Use same approach here as in problem A)
C)  2 cos (x)  = -1   Use exact values for special angles here, NO Calculator needed!  

A)  x1 = -0.85 rad  in IV       x2  is in III, where sine is also negative, with ref. angle alpha = 0.85,  so  x2 = 2.29     Answer:  { -0.85, 2.29, +2kpi}
B)  x1 = 0.644 rad  in I         x2  is in IV, where cosine is also positive, with ref. angle alpha = 0.644,  so  x2 = -0.644     Answer:  { 0.644,  -0.644, +2kpi}
C)  x1 = arccos  (-1/2) = special angle with ref. angle of pi/3, but in II where cosine is negative.  That would be 2pi/3 in II.  
      x2 = angle in III where cosine is also negative, still with ref. angle of  pi /3.  In III, that would be 4pi/3.
      Answer:  {2pi/3, 4pi/3, +2kpi}		 5.5
  p. 480 27-33 odd  5.6 
Mon
5/2 		    REVIEW For Test 4    Click on preceding link after 3pm Monday 5/2 to go to online version of Review Sheet handed out in class on Monday.  If you missed class, make sure you do the Review Sheet before Test.  Answers Included on Online Version
NOTE:  If you left class early today, there were several changes (or missing answers) on the Answer Sheet.  
Here they are:  Corrected or Missing Answers:     D) iii)  7pi/12       L)  x = 2.219      M)  s = 7.33 inches
    Q)  The "4" in the denominator of the answer is wrong--it should be a "625".
Check Online version for ALL ANSWERS.		  
Wed
5/4		    TEST 4    Covers all material on which HW was asssigned, up through section  4.2
Closed Book, No Notes.  BRING SOME PAPER of your own.   This can be paper you will rip out of a notebook (as long as it has nothing written on it.)  Or any other kind of blank paper you wish.  Bring several sheets.  BRING your OWN Graphing Calculator.  NO SHARING of calculators during the test

IMPORTANT:  If you MISS this Test, you will NOT have a full week to make it up.  It must be made up by or before Monday, May 9, starting before 10am in the Testing Center.  This is because I will return the tests at that time.   If you have not made it up by then, you will get a zero for it.  Usual late penalties apply.		  
Mon
5/9 		   Return Test 4    Makeup Test for Test 4 must be taken before 10am today.

REVIEW for Final Exam  [you should already have reviewed all old HW and old Tests and old Reviews before you come into class this day.]
Bring your BOOK to class for the review.  Bring a GRAPHING CALCULATOR, too		  
Wed
5/11		    Last HW Assignments Due.     

FINAL EXAM:  Bring Paper, 2 Pencils or Pens, and a GRAPHING Calculator of your Own!

YOU MAY USE ONE 8 1/2 BY 11 NOTESHEET FOR THIS TEST.  (OR SMALLER.)  
BOTH SIDES OF THE PAPER IS FINE.    No other notes or books allowed

Starts on Time.  If you are late, you get no extra time. 
Plan to get here 1 hour early, just in case of unforeseen events!

If you miss the Final Exam, you will get a ZERO for it, which will destroy your grade.  
If you have an emergency, call me IMMEDIATELY at 847-635-1935 and leave a detailed message with the nature of the emergency, YOUR PHONE NUMBER, and when you can make up the test.   Also email me the same information.   Emergency situations will still need to be made up soon, with a late penalty.
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Final Grades will be available online through MyOakton shortly after they are due, which is TUE May 17.  You can check 
starting Wed,  May 18.   I am not allowed to give out grades by email or phone, which are not secure.  If you wish to see your final exam, email me after Wed May 18 and set up a time to come in and look at it.  I will be available sporadically over the summer.  Or you can see it in the Fall.

  
       
       
       
         
   
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