HONORS ALGEBRA 2



PRECALCULUS FINAL EXAM REVIEW

**** This packet is intended to be used as supplemental review and practice of problems that reflect the topics

which will be covered on the final exam. It should NOT be used as your only review.

Chapter 3 Exponential and Logarithmic functions

Graph the exponential function. 1. [pic] 2. [pic]

Write each equation in exponential form 3. [pic] 4. [pic]

Write each equation in logarithmic form. 5. [pic] 6. [pic]

Evaluate each expression, without a calculator. 7. [pic] 8. [pic] 9. [pic] 10. [pic]

11. [pic] 12 [pic] 13. [pic] 14. [pic] 15. [pic] 16. [pic] 17. [pic]

Graph each logarithmic function. 18. [pic] 19. [pic]

Find the domain of the logarithmic function. 20. [pic] 21. [pic]

Expand each expression as much as possible. 22. [pic] 23. [pic] 24. [pic]

Write each expression as a single logarithm. 25. [pic] 26. [pic] 27. [pic]

28 [pic]

Solve: 29. [pic] 30. [pic] 31. [pic] 32. [pic]

33. [pic]

34. Using compound interest formulas, find the missing values.

Principle Interest Rate Compounded Time Amount

a) $1500 10% monthly 12 yrs ?

b) ? 8% quarterly 10 yrs $20,000

c) $5000 5% continuously ? $10,000

d) $1000 ? semiannually 4 yes $1435.77

35. Using exponential the decay model, find missing values:

Initial Amount Half-Life Time Amount .

a) 300 mg 140 days ? 200 mg

b) 22 mg 1600 yrs 4000 yrs ?

c) ? 30 yrs 80 yr 1.6 g

Chapter 4 Trigonometric Functions

1. In which quadrant is the terminal side of a) [pic] b) [pic].

2. A bicycle wheel with a radius of 13 inches makes 2.1 revolutions pr second. What is the speed of the bicycle?

3. A point on the rim of a wheel has a linear speed of 14 cm/s. If the radius of the wheel is 20 cm, what is the

angular speed of the wheel in radians per second?

4. The needle of the scale in a bulk food section of a supermarket is 28 cm long. Find the distance the tip of the

needle travels if it rotates [pic]

5. Find the coordinates of the point of intersection of a [pic] and the unit circle.

6. Evaluate: a) [pic] b) [pic] c) [pic]

7. If [pic] find [pic].

8. Find the exact values of the sine and cosine functions for the angle[pic] shown in the figure 1

[pic]

[pic]

9. Use the fundamental identities to simplify: [pic]

0. If [pic] is an acute angle, find the indicated trigonometric function: a) if [pic] find [pic]

b) if [pic] find [pic]

11. A 12-foot ladder makes an angle of [pic] with the ground as it leans against a house. How far up the house does

the ladder reach?

12. The cable supporting a ski lift rises 3 feet for each 8 feet of horizontal length. The top of the cable is fastened

675 feet above the cable’s lowest point. Find the lengths b and c, and find the measure of angle [pic]

c

675

[pic]

b

13. To find the height of a pole, a surveyor moves 100 feet away from the base of the pole and then, from an eye-

level height of 6.5 feet, measures the angle of elevation to the top of the pole to be [pic]. Find the height of the

pole to the nearest foot.

14. Find the quadrant the terminal side of [pic] lies if [pic] and [pic]

15. Given: [pic] and [pic], find [pic].

16. The point [pic] lies on the terminal side of an angle in standard position. Determine the exact value of [pic]

17. Find the reference angle: a) [pic] b) [pic] c) [pic]

18. Find the exact value of [pic]

19. Find the five key points for the graph of [pic] on the interval [pic]

20. Find the amplitude and period: a) [pic] b) [pic]

21. Find a cosine function that has an amplitude of [pic] and a period of [pic]

22. Graph: a) [pic] b) [pic] c) [pic] d) [pic] e) [pic]

f) [pic] g) [pic] h) [pic] i) [pic]

23. Evaluate: a) [pic] b) [pic] c) [pic]

24. An airplane is flying east at a constant altitude of 28,000 meters. When first seen to the east of an observer, the

angle of elevation to the airplane is [pic]. After 73 seconds, the angle of elevation is [pic]. Find the speed of

the airplane.

25. At a distance 56 feet from the base of a flagpole, the angle of elevation to the top of a flag that is 3.1 feet tall is

[pic]. The angle of elevation to the bottom of the flag is [pic]. The pole extends 1 foot above the flag. Find

the height of the pole.

26. An energy company uses one wellhead to drill several exploratory wells at different angles. They strike oil when

they have drilled 2879 feet along an angle of depression of [pic]. Find the depth of the oil deposit.

27. A hiker travels 3.9 miles per hour at a heading of S[pic]E from a ranger station. After 3.5 hours, how far south and

how far east is the hiker from the ranger station?

28. A ship leaves port at 20 miles per hour, with a heading of S[pic]W. There is a warning buoy 5 miles directly north

of port. What is the bearing of the warning buoy as seen from the ship after 5.5 hours?

Chapter 6 Additional Topics in Trigonometry

C

1. Find c [pic] 40

A

c [pic]

B

2. Find c if [pic]

3. Solve the triangle: [pic]

4. Find the area of the triangle: a) [pic] b) [pic]

5. A pole 85 feet tall is situated at the bottom of a hill that slopes up at an angle of [pic]. A guy wire from

the top of the pole to the hillside forms an angle of [pic] with the top of the pole. Find the distance from

the base of the pole to the guy wire’s point of attachment.

6. A loading dock ramp that is 18 feet ling rises at an angel of [pic]from the horizon. Due to new design

specifications, a longer ramp is to be used, so that the angle is reduced to [pic]. How much farther out from the

dock will that put the foot of the ramp?

7. Two Coast Guard stations located 75 miles apart on a north-south line each receive a radio signal from a ship at

sea. From the northernmost station, the ship’s bearing is S[pic]E. From the other station, the ship’s bearing is

N[pic]E. How far is the ship from the northernmost station?

8. Find the third side of the triangle.

9

[pic]

9

72. Use the law of cosines to solve triangle ABC given: [pic]

10. Use the law of cosines to solve triangle ABC given: [pic]

11. Two ships leave a port at the same time. When ship A is Ship B

200 miles due west of the port, ship B is 185 miles from

the port and 250 miles from ship , in the direction shown

at the right What is ship B’s bearing?

Ship A Port

12. A plane travels 170 miles at a heading of N[pic]W. It then changes direction and travels 165 miles at a

heading of N[pic]W. How far is the plane from its original position?

13. Find the area of the triangle: a) equilateral triangle with perimeter of 29.4 b) [pic]

Chapter 5 Analytic Trigonometry

1. Find an expression that completes the fundamental trig identity: a) [pic]____ b) [pic]____

c) [pic]____

2. Factor the expression and use identities to simplify [pic]

3. Find the remaining trig functions given [pic]

4. Verify the identity: a) [pic] b) [pic]

5. Find solutions for each equation in the interval [pic]: a) [pic] b) [pic]

c) [pic] d) [pic] e) [pic] f) [pic]

g) [pic]

6. Find all solutions: [pic]

7. Find the exact value of sine, cosine, and tangent of the angle [pic]

8. Find the exact value of [pic].

9. Find [pic] given [pic]

10. Find the exact value of [pic] given [pic]

11. Find the exact values of [pic] given [pic]

12. Find the exact value of [pic] given [pic] and [pic] is in quadrant I

13. Find the exact value of [pic] given [pic]

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