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November 18, 2009 Math 2 Honors Unit TEST

NAME: .MARKS: /60

  1. My brother has a carpentry business and his profits from January 2008 to April 2009 are modeled by the polynomial equation . His profits are given in dollars and x refers the month of the year (using x = 1 to represent January). NOTE: all answers for x should be given numerically as well as in the MONTH is which the event occurs (i.e an answer of 7.6 would be given as JULY) (9M)
  1. Determine his business’s monthly profit in June. (1M)
  1. What was his maximum profit? In what month did he achieve this maximum profit? (2M)
  1. My brother will hire an apprentice in the months in which his business earns at least $2,250 per month. During what months does his business earn at least $2,250? (2M)
  1. During what months were the profits of his business decreasing? (2M)
  1. Determine the zeroes of the polynomial function and interpret their meaning. (2M)
  1. This calculator active question requires you to show supporting algebraic evidence in order to get full credit for your solutions . Mr Santowski and Mrs Kopp are training for a marathon. As part of the training program, every week they monitor the time it takes to complete a 10 kilometer training run. Mrs Kopp’s time is modeled by the equation , where t is time in hours and w is measured in the number of weeks since the training program began. Mr Santowski’s time is modeled by . (8M)
  1. Write an inequality that you will use to determine when Mrs Kopp’s completion time for the 10 K run is less than Mr Santowski’s time. (1M)
  1. Show an algebraic solution in solving your inequality from Part a. (6M)
  1. Explain why this mathematical model of the10K completion time is only valid after the 4th week of the training program. (1M)
  1. This calculator active question requires you to show supporting algebraic evidence in order to get full credit for your solutions. You will work with the rational function . (9M)
  1. Using an algebra method of your choosing, simplify . (4M)
  1. Determine the co-ordinates of the hole(s) (if none, write none). (2M)
  1. Determine the equation of the vertical asymptote(s) (if none, write none). (1M)
  1. Determine the type and equation of the non-vertical asymptote(s) (if none, write none). (2M)

The next 10 questions are CALCULATOR INACTIVE.

  1. If , then the real roots of are: (1M)
  1. If , then the remainder when is divided by is: (2M)
  1. True or false. All cubic’s MUST have a real root. Explain your reasoning. (2M)
  1. Does have vertical asymptotes? If so, where or if not, why not? (1M)
  1. The equation of the non-vertical asymptote of is: (1M)
  1. The equations of asymptotes of are: (2M)

  1. On the grid provided, sketch a polynomial function that has the following three features: (3M)
  1. Even multiplicity of roots at x = 3
  2. Odd multiplicity of roots at x = -2
  3. As x , then f(x)  -
  1. You are given the polynomial function . You are also given a graph and a table of values for . (NOTE: the is NO scale given on the graph)
  1. List all possible rational roots of . (2M)
  1. Determine the remainder when is divided by x – 3. (1M)
  1. Factor completely given that and then rewrite as a product of linear factors. (7M)
x / P(x)
-3 / 45
-2 / 0
-1 / -5
0 / -12
1 / -15
2 / 40
3 / 255
  1. Solve the equation for x. State restrictions upon x. (5M)
  1. Match the equation from the top table with the appropriate graph from the bottom table. Place the letter of the corresponding graph below each equation. (7M)

1. / 2. / 3. / 4.
5. / 6. / 7.
A.
/ B.
/ C

D.
/ E.
/ F.

G.