Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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 1 2. f x 2 Graph the exponential function. 1. f x 3 1 x 1 log 49 7 2 Write each equation in exponential form 3. Write each equation in logarithmic form. 5. 63 216 Evaluate each expression, without a calculator. 11. log17 17 12 log3 38 13. ln e5 7. log 4 64 14. ln 1 e2 4. 3 log 4 x 6. b 4 625 8. log5 1 25 9. log3 9 15. log3 log8 8 Graph each logarithmic function. 18. f x log 2 x 2 Find the domain of the logarithmic function. x 16. ln e6 x 10. log16 4 17. eln 19. f x 1 log 2 x 21. f x ln x 1 20. f x log8 x 5 2 xy 2 x 23. log 2 24. ln 3 e 64 1 25. ln x 2ln x 1 26. 27. 3log 2 x 1 log z 5 Expand each expression as much as possible. 22. log 6 36x3 Write each expression as a single logarithm. 28 Solve: 1 1 log a x 3 log a x 3 2 3 29. 24 x 2 64 31. log 4 3x 5 3 30. 9 x 2 27 x 32. ln x 4 ln x 1 ln x 33. log 4 2 x 1 log 4 x 3 log 4 x 5 34. Using compound interest formulas, find the missing values. a) b) c) d) Principle $1500 ? $5000 $1000 Interest Rate 10% 8% 5% ? Compounded monthly quarterly continuously semiannually Time 12 yrs 10 yrs ? 4 yes 35. Using exponential the decay model, find missing values: a) b) c) Initial Amount 300 mg 22 mg ? 5 Half-Life 140 days 1600 yrs 30 yrs Time ? 4000 yrs 80 yr Amount . 200 mg ? 1.6 g Amount ? $20,000 $10,000 $1435.77 Chapter 4 Trigonometric Functions 9 b) 105 . 10 2. A bicycle wheel with a radius of 13 inches makes 2.1 revolutions pr second. What is the speed of the bicycle? 1. In which quadrant is the terminal side of a) 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 174. 5. Find the coordinates of the point of intersection of a 150 and the unit circle. 6. Evaluate: a) cos 9 4 3 b) tan 4 7 c) csc 6 4 , find sin t 2 . 19 8. Find the exact values of the sine and cosine functions for the angle shown in the figure 7. If sin t 1 3 tan 9. Use the fundamental identities to simplify: sin 15 , find csc 17 b) if csc 26 find cot 0. If is an acute angle, find the indicated trigonometric function: a) if sin 11. A 12-foot ladder makes an angle of 50 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 c 675 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 eyelevel height of 6.5 feet, measures the angle of elevation to the top of the pole to be 40 . Find the height of the pole to the nearest foot. 14. Find the quadrant the terminal side of lies if tan 0 and cos 0 12 15. Given: tan and sin 0 , find cos . 35 16. The point 9, 40 lies on the terminal side of an angle in standard position. Determine the exact value of sin 17. Find the reference angle: a) 3.5 b) 5 3 c) 159 18. Find the exact value of cos150 19. Find the five key points for the graph of y 2sin x on the interval 0, 2 20. Find the amplitude and period: a) y 2.5cos x 2 21. Find a cosine function that has an amplitude of 3 x 2 7x f) y cot 4 22. Graph: a) y sin 23. Evaluate: a) arctan 1 b) y 1.5cos 2x 3 1 and a period of 8 2 x 3x 2x b) y 3cos 2.5 c) y 4sin x d) y tan e) y tan 2 2 2 3 5x 5x 3x 3 g) y cot h) y 2sec i) y 1.5csc 8 4 3 2 2 1 4 b) cot arctan c) csc cos x 5 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 71.5 . After 73 seconds, the angle of elevation is 51.6 . 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 25.6 . The angle of elevation to the bottom of the flag is 22.9 . 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 44 . Find the depth of the oil deposit. 27. A hiker travels 3.9 miles per hour at a heading of S 21 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 44 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 92 40 A c 35 2. Find c if A 31, a 11, and b 13 B 3. Solve the triangle: B 32, C 25, and a 18 4. Find the area of the triangle: a) A 39, a 13.3, and b 13.3 b) B 6511', a 5 and c 2 5. A pole 85 feet tall is situated at the bottom of a hill that slopes up at an angle of 17.8 . A guy wire from the top of the pole to the hillside forms an angle of 24 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 17.8 from the horizon. Due to new design specifications, a longer ramp is to be used, so that the angle is reduced to 8 . 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 65 E. From the other station, the ship’s bearing is N 20 E. How far is the ship from the northernmost station? 8. Find the third side of the triangle. 9 51 9 72. Use the law of cosines to solve triangle ABC given: a 11, b 16, c 15 10. Use the law of cosines to solve triangle ABC given: A 42, b 3, c 9 11. Two ships leave a port at the same time. When ship A is 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 B Ship A Port 12. A plane travels 170 miles at a heading of N 41 W. It then changes direction and travels 165 miles at a heading of N 70 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) a 23.5, b 23.5, and c 26.4 Chapter 5 Analytic Trigonometry 1. Find an expression that completes the fundamental trig identity: a) tan x ____ b) cos x ____ c) cot ____ 2 2 2 2 2. Factor the expression and use identities to simplify cos x sin x cos x 1 4 1 cos sin b) 2csc sin 1 cos 3. Find the remaining trig functions given csc x 17 and tan x 4. Verify the identity: a) sin 2 x 1 sec x 1 cos x sec x 5. Find solutions for each equation in the interval 0,2 : a) 3cot 2 x 9 0 c) 10cos x 5 2 0 d) tan 2 x sec x 1 e) tan 2 3 6 2 0 2 7. Find the exact value of sine, cosine, and tangent of the angle 8. Find the exact value of cos345 . 3 7 12 5 3 A ; and B 8 2 2 9. Find cos A B given sin A ; cos B ; x 2 x 2 f) 3sec2 4sec 4 0 g) 4cos3x 2 3 0 6. Find all solutions: sin 2 x b) 9tan x 8 3 17tan x 1 3 ; x 11 2 6 3 11. Find the exact values of sin 2 and cos 2 given sin , and 2 11 2 27 12. Find the exact value of tan given sin and is in quadrant I 2 45 10. Find the exact value of sin 2x given sin x 13. Find the exact value of sin 2 given tan 48 3 and 55 2