MHF4U1 FINAL EXAM January, 2008

ADVANCED FUNCTIONS 2 Hours

NAME: ______

Category / Knowledge / Application / Communication / Thinking / Total
Mark
Out of

Instructions:

·  Calculators can be used but not shared. Graphing calculators are not permitted.

·  Write solutions other than graphs on the foolscap. Write on one side of the page only and clearly number the questions and the pages. Make sure that all pages and questions are in the proper order when you hand in your exam.

·  Draw graphs for questions #2,3,8,16,18,20 on the grids provided on the exam.

·  Be aware of your timing and good luck!

Knowledge & Understanding (25 Marks)

  1. Given, find a simplified expression for . (4 marks)
  2. Given the function (4 marks)

a)  determine the y-intercept

b)  state the x-intercepts

c)  describe the end behaviour of the function

d)  sketch a graph of the function

  1. Given the function (5 marks)

a)  State the domain of the function

b)  determine the x and y-intercept(s)

c)  determine the equations of any vertical asymptotes of the function

d)  determine the equations of any horizontal asymptotes of the function

e)  sketch a graph of the function

  1. Simplify and evaluate the following. (give exact answers and show at least one step) (4 marks)

a) 

b) 

c) 

d) 

  1. Find the exact value of . (3 marks)
  1. Use a division statement to express as the sum of a polynomial function and a rational function of the form . Indicate what new information this form of gives to assist in graphing . (2 marks)

Application

  1. Sketch the graph of , for the interval . (3 marks)
  1. Factor completely by using the factor theorem. (4 marks)
  2. Solve the inequality . (4 marks)
  1. Solve . (4 marks)
  1. Solve for for . (4 marks)
  2. Prove the identity . (3 marks)

Communication (10 Marks)

Use proper mathematical terminology in your answers.

  1. Describe the effects on the graph of for each of the following transformations: (3 marks)

a)

c)

d)

  1. a) Graph .

b)  On the same grid graph the reciprocal of .

c)  How are the graphs in part a) and part b) related in terms of transformations?

d)  On the same grid graph the inverse of .

e)  Write the equation for the graph in d) in two different forms.

13. The function models the population, in thousands, of a town t years since 1990. Find: a) the initial population.

b) the average rate of change of the population from 1995 to 2005.

c) the rate at which the population is changing in the year 2000. (4 marks)

Thinking

  1. Sketch the graph of over the interval .

(3 marks)

  1. Construction plans for a bomb-shelter call for a rectangular metal structure measuring 5m long by 4m wide by 3m high. The metal structure is to be surrounded on all six sides with a layer of concrete of uniform thickness.

a)  Determine an expression for the volume of the concrete as a function of its thickness. (2 marks)

b)  Find the thickness of the concrete shield if the volume of the concrete is 444 m3. (2 marks)

Grids for questions #2,3,8,16,18,20

#2 #3

#8 #16

#18 #20

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