Pre-Calculus HonorsFinal Exam ReviewChapter 4Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. A tower that is 125 feet tall casts a shadow of 172 feet. Find the angle of elevation of the sun to the nearest
degree.
a. b. c. d. e.
2. If then
a. b. c. d. e.
3. The horizontal translation of the function is
a. exactly two units to the right b. exactly five units to the left
c. exactly 1.25 units to the rightd. exactly units to the left
e. exactly five units to the right
4. A student looks out a second-story school window and sees the top of the school flagpole at an angle of
elevation of 22o. The student is 18 ft. above the ground and 50 ft. from the flagpole. Find the height of the
flagpole.
a. 21.8b. 23.5c. 38.2d. 48.6e. 58.2
5. is equivalent to which of the following?
a. b. c. d. e.
6. Which of the following is an even function?
a. b. c. d. e.
7. An airplane flying at 490 mph has a bearing of . After flying for two hours how far north and how
far east has the plane traveled?
a. 444.9 mi. N, b. 873.2 mi. N, c. 436.6 mi. N, d. 222.5 mi. Ne. 237.1 mi. N,
873.2 mi. E 444.9 mi. E 222.5 mi. E 436.6 mi. E 452.8 mi. E
8. If then equals:
a. b. 45.58c. -45.88d. e.
9. If then equals:
a. b. c. d. e.
10. A 50 meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of
with the ground. What is the height of the balloon?
a. 16.3 mb. 47.3 mc. 145.2 md. 39.7 me. 24.8 m
11. Determine the exact value of given (7 , -10) on the terminal side of the angle in standard position.
a. b. c. d. e.
12. Determine the exact value of given (-4 , -10) on the terminal side of the angle in standard position.
a. b. c. d. e.
13. Determine the exact value of given (-2 , 3) on the terminal side of the angle in standard position.
a. b. c. d. e.
14. State the reference angle for .
a. b. c. d. e.
15. State the reference angle for .
a. b. c. d. e.
16. State the reference angle for .
a. b. c. d. e.
17. Determine the quadrant for .
a. Ib. IIc. IIId. IV
18. Determine the quadrant for .
a. Ib. IIc. IIId. IV
19. Determine the quadrant for .
a. Ib. IIc. IIId. IV
20. Determine the quadrant for .
a. Ib. IIc. IIId. IV
21. Determine the quadrant for .
a. Ib. IIc. IIId. IV
22. Find the complement and supplement for
a. b. c. d. e.
23. Express the angle in terms of degrees. Round if necessary.
a. b. c. d. e.
24. Express the angle in terms of degrees. Round if necessary.
a. b. c. d. e.
25. Express the angle in terms of degrees. Round if necessary.
a. b. c. d. e.
26. Express the angle -1.7 in terms of degrees. Round if necessary.
a. b. c. d. e.
27. Find the arc length given and .
a. 10b. 15.71c. 36d. 900e. 7.86
28. Find the arc length given and .
a. 4b. 45c. 180d. 3.14e. 5.18
29. Find the arc length given and .
a. 13.19b. 15.43c. 756d. 151.61e. 4.24
30. An airplane flying at 520 mph has a bearing of . After flying for 1.5 hours, how far south and how
far west has the plane traveled?
a. 661.5 mi. S, b. 275.6 mi. S, c. 441.0 mi. S, d. 413.3 mi. Se. 388.5 mi. S,
413.3 mi. W 441.0 mi.W 275.6 mi. W 661.5 mi. W 511.9 mi. W
31. At a point 150 feet from the base of a building, the angle of elevation to the top of the building is, and
the angle of elevation to the top of the flag pole that sits atop the building is.
Find the height of the flag pole.
a. 105.0 feetb. 86.0 feetc. 125.9 feetd. 16.4 feete. 20.8 feet
32. Given state the period.
a. b. 5c. d. 2e.
33. Given state the vertical shift.
a. 10b. 5c. -5d. 2e.
34. Given state the amplitude.
a. -5b. 10c. 5d. 2e.
35. Given state the period.
a. b. c. d. e.
36. Given state the period.
a. b. c. d. e.
37. Given state the period.
a. b. c. d. e. 8
38. Given state the phase shift.
a. b. 4c. d. e. -4
39. Given state the vertical shift.
a. 6b. -3c. -6d. 3e.
40. Simplify .
a. b. c. d. e.
41. Simplify .
a. b. c. d. e.
42. Simplify
a. b. c. d. e.
Pre-Calculus HonorsFinal Exam ReviewChapter 5Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. The graph represented by the equation has a maximum value of:
a. 2b. 3c. 5d. 8e. -3
2. The expression is equivalent to:
a. b. c. d. e.
3. If is measured in radians and , then we know that is:
a. b. c. d. e. 1
4. Determine given that .
a. b. c. d. e.
5. Find the exact value of the .
a. b. c. d. e. not possible
6. Given , A in quadrant II, find .
a. b. c. d. e.
7. Solve:
a. b. c. d. e.
8. is equivalent to which of the following?
a. b. c. d. e.
9. Solve:
a. b. c. d. e.
10. Which of the following equals ?
a. b. c. d. e. none of these
Pre-Calculus HonorsFinal Exam ReviewChapter 6Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. Two homes are located on opposite sides of a small hill at points P and Q. To measure the distance between
them, a surveyor walks the distance of 50 feet from house P to point R, uses a transit to measure ,
which is found to be , and then walks to house Q, a distance of 60 feet. How far apart are the houses?
a. 71.12 ftb. 72.11 ftc. 81.12 ft d. 82.11 ft e. 83.21 ft
2. In a triangle, suppose we know that b = 3 feet, c = 2 feet, and angle A = 140. According to the Law of
Cosines, the length of side a is approximately
a. 3.9 ftb. 4.2 ftc. 3.6ftd. 17.6 fte. 4.7 ft
3. Intriangle ABC , c = 2, B = 45oand a= 6. Find the area of triangle ABC.
a. 3.6b. 4.8c. 7.5d. 4.2e. 10.1
4. Find the value of x.
a. 3.4b. 7.4c. 8.4d. 10.7e. 12.6
5. Find the value of x.
a. 16.3b. 16.8c. 17.9d. 23.5e. 35.3
6. Given and , find the component form of the vector .
a. b. c. d. e.
7. Let and . Find .
a. b. c. d. e.
8. Find the angle between the vectors and to the nearest tenth of a degree.
a. 77.8° b. 175.6°c. 87.8° d. 185.6°e.
9. Given and , find the component form of the vector .
a. b. c. d. e.
10. Given and , find the magnitude of the vector .
a. b. c. d. e. 260
11. Let and . Find .
a. b. c. d. e.
12. Let and . Find .
a. 52b. c. d. 28e. -28
13. Let and find the unit vector in the direction of u.
a. b. c. d. e.
14. Find the angle between the vectors and to the nearest tenth of a degree.
a. 157.8° b. -157.8° c. 22.2°d. -22.2°e.
15. Which of the following would be the corresponding rectangular equation by eliminating the parameter given and.
a. b. c. d. e.
16. Convert the polar equation into a rectangular equation.
a. b. c. d. e.
17. Convert the polar equation into a rectangular equation.
a. b. c. d. e.
18. Convert the polar equation into a rectangular equation.
a. b. c. d. e.
19. Convert to rectangular coordinates.
a. b. c. d. e.
20. Convert to rectangular coordinates.
a. b. c. d. e.
21. Convert to rectangular coordinates.
a. b. c. d. e.
22. Convert to rectangular coordinates.
a. b. c. d. e.
23. Convert the rectangular coordinate to polar coordinates.
a.b. c. d. e.
24. Convert the rectangular coordinate to polar coordinates.
a.b. c. d. e.
25. Convert the rectangular coordinate to polar coordinates.
a.b. c. d. e.
26. Convert the rectangular equation to a polar equation.
a. b. c. d. e.
27. Convert the rectangular equation to a polar equation.
a. b. c. d. e.
28. Convert the rectangular equation to a polar equation.
a. b. c. d. e.
Pre-Calculus HonorsMidterm ReviewChapter 7 Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1. Solve the system
A. ( 0 , -5)B. (4 , 3)C. (0 , -5) and (4 , 3)D. (3 , 4)E. (3 , 4) and (0 , 5)
2. A small business has an initial investment of $5000. The unit cost of the product is $21.60 and the selling
price is $34.10. How many units must be sold to break even?
A. 90B. 200C. 147D. 400E. 231
3. The solution to a system of equations represents:
A. The zeros of each graph.
B. The minimum or maximum of each graph.
C. Where the graphs intersect.
D. The y-intercepts of the graphs.
E. Where the graphs have slopes of zero.
4. Two planes start from the same airport and fly in opposite directions. The second plane starts one half of an
hour after the first plane, but its speed is 80kilometers per hour faster. Find the airspeed of each plane if two
hours after the first plane departs the planes are 3200 kilometers apart.
A. 800 km/hr, 880 km/hr
B. 450 km/hr, 530 km/hr
C. 200 km/hr, 280 km/hr
D. 960 km/hr, 1040 km/hr
E. 880 km/hr, 960 km/hr
5. How many liters of an 80% acid solution must be added to 10 liters of a 20% acid solution to get a 30% acid
solution?
A. 1B. 2C. 3D. 4.5E. 8
6. Solve the system
A. (-1 , 3, 0)B. (1 , -1, 2)C. no solutionD. (1, -1, 3)E. (2, 1, 5)
7. Write the partial fraction decomposition for .
A. B. C. D. E.
8. A total of $1520 a year is received in interest from three investments. The interest rates for the three
investments are 5%, 7% and 8%. The 5% investment is half of the 7% investment and the 7% investment
is $1500 less than the 8% investment. Find the amount in each investment.
A. $3000 5%, $6000 at 7%, $7500 at 8%
B. $11,200 at 5%, $5600 at 7%, $4100 at 8%
C. $800 at 5%, $16000 at 7%, $17500 at 8%
D. $4000 at 5%, $8000 at 7%, $9500 at 8%
E. $10000 at 5%, $5000 at 7%, $6500 at 8%
9. Write the form of the partial fraction decomposition . Do not solve for the constants.
A. B. C.
D. E.
10. The first step in writing the partial fraction decomposition of .
A. factoring the numerator
B. writing it as
C. graphing to find all rational zeros
D. graphing to find all asymptotes
E. doing long division
Pre-Calculus HonorsFinal Exam ReviewChapter 10Multiple Choice Questions
Do NOT write on this sheet. All work must be done on a separate sheet of paper.
1.
a. 0b. -1c. 1d. 2e. does not exist
2.
a. b. c. d. 3e. does not exist
3.
a. 7b. 3c. 0d. e. does not exist
4.
a. b. 0c. d. e. does not exist
5.
a. 0b. c. d. e. does not exist
6.
a. 27b. 9c. -9d. 0e. does not exist
7.
a. -2b. 0c. d. e. does not exist
8.
a. 2b. 1c. 3d. -2e. does not exist
9.
a. b. c. d. e. does not exist
10.
a. b. -5c. d. e. does not exist
11.
a. b. -c. 4d. e. does not exist
12. Find the slope of the tangent line to at (2 , 5).
a. 6b. 14c. 2d. 5e. 3
13. Find the slope of the tangent line to at (2 , 1).
a. 2b. -2c. 1d. 5e. -1
14. Find the slope of the tangent line to at (-1 , 8).
a. -13b. -8c. -10d. -7e. 8
15. Find the slope of the tangent line to at (2 , 2).
a. -5b. 7c. 2d. 3e. –2
16. Find the derivative of .
a. b. c. d. e. -5
17. Find the derivative of .
a. b. c. d. e.
18. Find the derivative of .
a. b. c. d. e.
19. Find the derivative of .
a. b. c. d. e.
20. Find the difference quotient for .
a. b. c. d. e.
21. Find the difference quotient for .
a. b. c. d. e.
22.
a. does not existb. 0c. 1d. e. 8
23.
a. does not existb. 0c. 1d. 5e.
24.
a. does not existb. 0c. 1d. e. -5
25.
a. does not existb. 0c. -4d. 5e. 1
26.
a. does not existb. 0c. 11d. 8e. 3
27.
a. does not existb. 0c. -5d. -4e. 5
28. Find the limit of the sequence
a. does not existb. 0c. d. 1e. 5
29. Find the limit of the sequence
a. does not existb. 0c. d. 1e. 3
30.
a. 1b. -1c. 0d. e. does not exist