MHF4U Final Exam Review

Exam Time Limit: 2.0 hours Name _________________ Exam Instructions:1. Answer all questions in the space provided.2. If you need additional paper or graph paper ask for it, otherwise all

answers should be written on the exam paper.

Part I: Place your answers for Part I in the space provided.

1. The instantaneous rate of change of a function is _____________. (____)A. the domain divided by the rangeB. the change in the dependent variable divided by the change in the

independent variable from one point to anotherC. the range divided by the domainD. how quickly the dependent variable is changing with respect to a unit change

in the independent variable at an instant in time

2. The domain of a function is _______________. (____)A. the entire set of function values (of the dependent variable)

B.

C.D. the entire set of values (of the independent variable) for which the function is

defined

3. The range of a function is _______________. (____)A. the entire set of function values (of the dependent variable)

B.

C.D. the entire set of values (of the independent variable) for which the function is

defined

4. Which one of the following is a polynomial function? (____)

A.

B.

C.

D.5. The ____ row of differences for quartic functions are all the same. (____)

A. 1st

B. 2nd

C. 3rd

D. 4th

6. Even functions have which of the following characteristics? (____)

A.

B. C.

7. The Remainder Theorem states ___________. (____)A. When a polynomial is divided by the remainder isB. If , then is a factor of C. The remainder in the division is D. If divides with a remainder of zero, then is a factor of

8. The Factor Theorem states ___________. (____)A. When a polynomial is divided by the remainder isB. If , then is a factor of C. The remainder in the division is D. If divides with a remainder of zero, then is a factor of

9. What is the domain of ? (____)A.

B.

C.D.

10. What is the horizontal asymptote for ? (____)A.

B.C.D.

11. What is the vertical asymptote for ? (____)A.

B.

C.D.

12. In a right angled triangle (____)

A. B. C.

D. E.

13. In a right angled triangle (____)

A. B. C.

D. E.

14. In a right angled triangle (____)

A. B. C.

D. E.

15. In a right angled triangle (____)

A. B. C.

D. E.

16. In a right angled triangle (____)

A. B. C.

D. E.

17. In a right angled triangle (____)

A. B. C.

D. E.

18. (____)

A. B. 1 C. D. E.

19. (____)

A. B. 1 C. D. E.

20. (____)A. -1 B. 1 C. D. 0 E. undefined

21. To convert degrees to radians, multiply by _________ (____)

A.

B. C. D. E.

22. (____)

A.B. C. D. E.

23. (____)

A. B. C. D. E.

24. (____)

A. B. C. D. E.

25. Which of the following is equivalent to ? (____)

A. B. C. D. E.

5β

26. Using the diagram at the right, (____)

A. B. C. D. E.

27. (____)

A.

B. C. D. E.

28. (____)

A. B. C. D. E.

29. Determine the equation of the function pictured at the right?(____)

A. B.

C. D.

E.

30. Determine the equation of the function pictured at the right?(____)

A. B.

C. D. E.

31. (____)

A. B. C. D. E.

32. The graph at the right is ______. (____)A.B.C.D.E.

33. What is the amplitude of ? (____)

A. B. 3 C. 5 down D. 2 E. -2

34. What is the amplitude of ? (____)

A. B. C. 6 up D. 1 E. -1

35. What is the period of ? (____)

A. B. C. D. 2 down E. 5

36. The graph shown is ________. (____)A.

B.

C.

D.

E.

37. The graph shown is ________. (____)A.

B.

C.

D.

E.

38. Write in its equivalent logarithmic form. (____)

A. B. C. D.

39. Write in its equivalent exponential form. (____)A. B. C. D.

40. Simplify into one logarithm. (____)

A.

B. C. D.

Part 2: Show all work you do in the space provided for each question in part 2.

1. Use the graph at the right for each of the following questions.

a) Determine Albert’s average velocity from 2 to 6 seconds.

b) Determine Albert’s instantaneous velocity at 4 seconds.

2. Use differences to determine the degree of the polynomial functions that the following tables represent.

x y-2 27-1 -10 -71 -32 -13 -13

x y-2 43-1 00 -71 -22 153 68

a) b)

3. Solve completely by factoring.

a) b)

4. Solve without using technology.

a) b)

-10

-10

-5

5. Sketch the function . Be sure to indicate all asymptotes and intercepts (if any). Show how to get each behavior near any asymptotes.

6. Find the asymptotes for each of the following functions.

a)

-10

b)

7. Solve each of the following rational equations.

a)

b)

8. Use a numerical method to approximate the instantaneous rate of change for the

function where x = 2.8.

9. The radius of the earth is 6380 km. A space shuttle 300 km above the earth

travels around the planet through an angle of radians. How far does the shuttle move?

10. Use a compound angle identity to rewrite as one single trigonometric ratio and then find its exact value.

11.Determine the average rate of change for the function at the right from where x = 0.2 to x = 1.1.

x

y

12. Solve on the interval .

a)

b)

13. Prove each of the following.a)

b)

c)

14. The sunset time varies sinusoidally with time. The sunset time (S) in the town of Parry Sound can be modelled by the equation

, where d is the day of the year. How long a period of time (in days) is the sun setting earlier than 7:00 p.m.? You may use technology to solve this problem. If you do use technology, include a neat labelled sketch with your solution.

15. Evaluate . Explain how you can check this answer.

16. Solve each of the following.a)

b)

17. Evaluate without the use of the log function on a calculator. (Hint: use the log laws)a) b)

18. Simplify each of the following using the three laws of logarithms.a)

b)

c)

19. Solve each of the following.a)

b)

c) [Write the answer in exact form]

d)

20. The magnitude, M, of an earthquake is measured using the Richter scale,

which is defined as I is the intensity of the earthquake, and Io is the intensity of a standard low level earthquake.a) What is the Richter Scale reading for an earthquake that is 45000 times more

powerful than the standard low level earthquake?

b) How much more powerful is a 6.8 Richter Scale earthquake than a 4.0 scale quake?

21. A 60 mg sample of a radioactive isotope decays to 50 mg after 4.7 days.a) Determine the half-life. b) How long will it take for the

amount of the isotope to decrease to 20 mg?

22. Given

and

.a)Graph

-10

-10

y105-5

-5

5

b)Solve the inequality

c) Find and simplify and

d)Explain why you would expect and to be different.