Download Precalculus S Final Review Chapters 3 and 4

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PreCalculus S Review for Final – Chapters 3 and 4
Directions: Find the answer that best completes the statement or answers the question.
Use the graph of f to describe the transformation that results in the graph of g. Then sketch the graphs of g and f.
1. f(x) =
; g(x) =
2. f(x) = ex; g(x) =
3. If the Laffite family deposits $8500 in a savings account at 6.75% interest, compounded continuously, how much will
be in the account after 25 years?
4. Find the amount of time required to double an amount at 5.84% if the interest is compounded continuously.
5. Among various populations of plants or animals, diseases spread exponentially. Use the function
to
model the spread of Common Corn Rust through a field of 8000 corn plants, with t equal to the number of days since the
first case of the disease. How many plants will be infected with Common Corn Rust after 10 days?
6. Jimmy invests $500 in an account with a 3% interest rate, making no other deposits or withdrawals. What will Jimmy’s
account balance be after 10 years if the interest is compounded 2 times each year?
7. A corporate jet originally cost $17,550,000. If its value depreciates by 5 percent per year, what will its value be after 10
years?
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Evaluate each expression.
8.
9.
10. Find ln 375. Round your answer to four decimal places.
Evaluate each expression.
11. log 3243
12. Evaluate the expression log 5
.
Evaluate each expression.
13.
14. log 75
Express each logarithm in terms of ln 3 and ln 5.
15. ln
Solve each equation.
16. 32x – 1 = 16x + 4
17. 4x + 7 = 5x – 3
18. Solve e–5x = 7.4 for x correct to four decimal places.
19. Solve log 6 x = 2
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Solve each equation.
20. log 7 (x2 + 11) = log 7 15
21. Find the values of the six trigonometric functions for angle θ , when PQ = 50 and QR = 64.
22. If sec θ =
, find cot θ.
23. If g = 19.2 and F = 61°, find h. Round to the nearest tenth.
24. If t = 26 and r = 5.7, find S. Round to the nearest tenth.
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25. Solve by using the measurements ∠PQR = 90°, ∠QRP = 75°, and r = 15. Round measures of sides to the nearest tenth
and measures of angles to the nearest degree.
26. Write
in degrees
27. Write –2160° in radians.
28. Find one positive and one negative angle coterminal with an angle of 166°.
29. Find the area of a sector with a central angle of 74° and a radius of 19.7 millimeters. Round to the nearest tenth.
(Hint: Convert degrees to RADIANS first!)
30. For a circle of radius 6 feet, find the arc length s subtended by a central angle of 24°.
(Hint: Convert degrees to RADIANS first!)
31. Find the least positive angle measurement that is coterminal with –230°.
32. Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and
. Find the exact
values of the five remaining trigonometric functions of θ.
33. Suppose θ is an angle in the standard position whose terminal side is in Quadrant III and
. Find the exact
values of the five remaining trigonometric functions of θ .
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34. Find the values of the six trigonometric functions of an angle in standard position if the point with coordinates (60, 11)
lies on its terminal side.
35. Find the exact value of csc (1140)°.
36. Find the reference angle for 366°.
37. Find the exact value of cos
.
38. Find the exact value of sin
39. Find the exact value of tan
.
.
40. Find the exact value of cos (–660)°.
41. Use the unit circle to find the value of cot (–180°).
42. Write an equation of the cosine function with amplitude 3 and period 8π.
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43. Find the amplitude, period, and phase shift of f(x) = –6sin (3x – 3).
44. Graph the function. Which choice gives the amplitude, period, phase shift, and vertical shift for the function?
a.
b.
3; ; –
;4
c.
3; ; –
; –4
3; ; –
;4
d.
3; ; –
;4
45. Graph the function. Which choice gives the amplitude, period, phase shift, and vertical shift for the function?
a.
b.
4; ; –
; –2
4; ; –
;2
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c.
d.
4; ; –
4; ; –
; –2
; –2
46. Graph the function. Which choice gives the amplitude, period, phase shift, and vertical shift for the function?
a.
b.
3;
;
;3
3;
c.
;
;3
d.
3;
;
; –3
3;
;
;3
47. Graph y =
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48. Graph
49. Graph
.
.
50. Graph y = 4
51. Find the value of
52. Evaluate
53. Given a triangle with b = 11, c = 10 , and A = 28°, what is the length of a? Round to the nearest tenth.
54. Determine whether
should be solved by using the Law of Sines or the Law of Cosines. Then solve the triangle.
A = 30°, b = 13, a = 15
55. Given a triangle with a = 6, A = 33°, and B = 30°, what is the length of c? Round to the nearest tenth.
56. Find the area of the triangle with a = 17.3, b = 15.6, and c = 18.5. Round to the nearest tenth.
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Answer Key
1. d
2. b
3. b
4. c
5. d
6. d
7. a
8. d
9. b
10. c
11. a
12. b
13. b
14. b
15. c
16. b
17. b
18. a
19. a
20. b
21. a
22. b
23. d
24. a
25. a
26. b
27. b
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28. a
29. c
30. b
31. d
32. b
33. a
34. c
35. c
36. c
37. c
38. b
39. b
40. c
41. b
42. c
43. d
44. c
45. a
46. a
47. a
48. a
49. c
50. c
51. b
52. d
53. a
54. b
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55. b
56. a
57. c
58. c
59. b
60. c
61. c
62. a
63. a
64. b
65. c
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