Corona-Norco Unified School District

NAME Part A CORONA-NORCO UNIFIED SCHOOL DISTRICT ST Non PRE CAL HONORS 1 SEM FINAL EXAM REVIEW (B-4 & CH. 1-5) Calculator 2010 - 2011 DO NOT USE ANY TYPE OF CALCULATOR

  x x  0 1. Given f (x)   Find f (4)  6x x  0 f (x  2)  f (2) 2. If f (x)  x2  2x , find , x  0 x 3. State the domain and range of: y  x  3 graph for #3

1 4. Describe the transformation of the graph of f (x)  x for the graph of g(x)  x  4 3

5. Given f (x)  4  2x2 and g(x)  2  x , find ( f ° g)(x)

6. Given f (x)  1 3x and g(x)  x  2 , find (f-1- g - 1 )(1)

7. Write the given equation in the form y  a(x  h)2  k : y=2 x2 + 4 x - 3

8. Divide using long division: (9x3  6x2  8x  3)  (3x  2)

9. Use synthetic division to factor the polynomial x3  4x2  x  6 completely if 1 is a zero.

10. Write in standard form: 2i4  7i3

3  4i 11. Divide, then write your answer in standard form: 5  2i

1 12. Evaluate: log 4 16

13. Simplify: ln 3 e2 x

14. Convert to radians: 25˚.

7p 15. Convert to degrees: 12

3p 16. Find the point (x, y) on the unit circle that corresponds to the real number t = - 2

Revised July 10 17. Verify the identity: secx+ tan( - x )sin x = cos x

18. Factor and simplify: cos4x+ cos 2 x sin 2 x

19. Determine the period of f (x)  2cos3x   

2 20. Determine the amplitude of f (x)   sin4x 3

21. Describe the horizontal shift of the graph of g with respect to the graph of f. 骣 p f( x )= 4cos( x) and g( x )= 4cos琪 x + . 桫 4

7 22. Find the exact value of sin . 6

23. Find the exact value of cos π.

 2  arccos  24. Evaluate:    2 

 3  25. Evaluate: tanarccos   7 

26. Use the sum/difference formulas to find the exact value for cos 345˚. Use 345˚ = 300˚ + 45˚.

4 27. Use the double angle formulas to find the exact value of cos 2θ, given cos θ =  and tan θ > 0. 7

28. Determine the left-hand and right-hand behavior of the graph: f( x ) 3 x4  2 x 3  7 x 2  x  1

Revised July 10 NAME

Part CORONA-NORCO UNIFIED SCHOOL DISTRICT PRE CAL HONORS 1ST SEM FINAL EXAM REVIEW (B.4 & CH. 1-5) B 2010 - 2011 Calculator CALCULATORS ALLOWED

29. Find all the real zeros of the polynomial function: f (x)  x4  5x2  36

30. Find all the real zeros of the function: f( x )= x3 - 11 x 2 + 3 x + 3 . Use the window: x-min= – 5, x-max=15, y-min= –10, y-max=10.

x3  7x2 1 31. Find the slant asymptote: f (x)  x2 1

32. State the domain and range of f (x)  3  ex

16ln 5 33. Evaluate: 1 2ln 3

3e0.0721 52 34. Evaluate: 1 0.0721

35. State the domain of the function f (x)  3  ln(x 1)

x  2 36. Find the vertical asymptote(s): f (x)  x2  9

37. Solve for x: ln(x- 2) + ln(2 x - 3) = 2ln x

38. Solve for x: log(x- 3) - log( x - 7) = 1

39. Use a graphing utility to approximate any relative minimum or relative maximum of f (x)  2x2  x  3

1 40. An amount of $2000 is invested at a rate of 72 % compounded continuously. What is the balance at the end of 20 years?

41. The perimeter of a rectangle is 12 meters. Use a graphing utility to approximate the maximum area of the rectangle.

Revised July 10 42. Find all of the zeros of the function: f (x)  x4  25x2 144

43. Determine the amount of money that should be invested at a rate of 8% compounded quarterly to produce a final balance of $20,000 in 10 years.

44. Solve for x: 2x1  52x6

45. Evaluate: cot 1.14

46. Find θ in the interval 0°  90 °  such that tan  1.2617

7 47. Find the reference angle for   . 3

48. A pilot of an airplane flying at 12,000 feet sights a water tower. The angle of depression to the base of the tower is 25˚. What is the length of the line of sight from the plane to the tower?

49. Find two values for θ, 0°  360 °  that satisfy cot   0.2679 .

50. Sketch the graph of : f( x )= 3sin(2 x ) from 0＃q 2 p .

Revised July 10 CORONA-NORCO UNIFIED SCHOOL DISTRICT PRE CAL HONORS 1ST SEM FINAL EXAM REVIEW 1 (B.4 & CH. 1-5) 2008 - 2009 ANSWERS

1. 24 18. cos2 x 32. Domain = (, ) and 2. x + 2 2 Range = (, 3) 19. Domain = [3, ) 3 3. 33. 8.0542 Range = [0, ) 2 20. 34. 137.3653 4. Vertical shift 4 up; 3 35. 1,  p Vertical shrink (by 3) 21. horizontal shift left 4 36.  3 5. -2x2 + 8 x - 4 1 37. 6 22.  6. 1 2 67 38. x = 7. y=2( x + 1)2 - 5 23. – 1 9 3  39. Relative maximum at 8. 3x2  4x  24. 3x  2 4 (0.25,  2.88) 2 10 9. (x 1)(x  2)(x  3) 25. 40. $8963.38 3 10. 2  7i 41. 9 square meters 2  6 7 26 26. 42. 北3i , 4 i 11.  i 4 29 29 43. $9057.81 17 27.  12. -2 49 44. –4.0977 2 1 13.  ln x 28. Rises to the left, 45. 0.460 3 3 rises to the right 46.  51.6˚ 5 14. 29. –3, 3  36 47. 30. – 0.398 3 15. 105° 0.705 48.  28,394 feet 16. (0, 1) 10.693 49. 105˚ and 285˚ 17. Will vary. 31. y  x  7 50.

π 2π

Revised July 10