PreCalculus Semester 2Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 7. Use the graph to find the vector with initial point P and terminal point Q. Choose the correct answer from the following: a. b. c. d. 8. Given that u =<6, 3>, v =<–2, 1>, find 7 u – 4 v. a. 7u – 4v =<8, 2> b. 7u – 4v = <8, 17> c. 7u – 4v = <50, 17> d. 7u – 4v = <50, 2> 9. u = i + j, v = i – j, find 7 u – 2 v. a. 7u – 2v =<5, 9> b. 7u – 2v =<7, 2> c. 7u – 2v =<5, 7> d. 7u – 2v =<7, 9> 10. u = <10, –1>, v = <10, –4>, find |u – v|. a. |u – v| = 4 b. |u – v| = –5 c. |u – v| = –5 d. |u – v| = 3 11. Find the horizontal and vertical components of the vector v, where |v| = 34, . a. v = b. v = c. v = d. v = 12. Find the horizontal and vertical components of the vector v: |v| = 3, vectors i and j. . Write the vector in the form and write the vector in terms of the Select the correct answer (rounded to the nearest tenth): a. v = 2.1i + 3j b. v = 2.1i + 2.1j c. v = 3i + 3j d. v = 2.1i + –2.1j 13. Find the direction (in degrees) of the vector v = < 5, 3 >. a. 34 b. 30 c. 59 d. 31 14. A pilot heads his jet due east. The jet has a speed of 420 mi/h in still air. The wind is blowing due north with a speed of 37 mi/h. Find the true velocity of the jet as a vector. a. v = 37i – 420j b. v = 37i + 420j c. v = 420i – 37j d. v = 420i + 37j 15. A straight river flows east at a speed of 7 mi/h. A boater starts at the south shore of the river and heads in a direction a from the shore (see the figure). The motorboat has a speed of 20 mi/h in still water. The boater wants to arrive at a point on the north shore of the river directly opposite the starting point. In what direction should the boat be headed? a. a = 110 b. a = 7 c. a = 20 d. a = 90 16. The forces F 1, F 2, ..., F n acting at the same point P are said to be in equilibrium if the resultant force is zero, that is, if F 1 + F 2 + ... + F n = 0. F 1 = i + j, F 2 = i – j, F 3 = 9 i + 2 j Find the additional force required for the forces to be in equilibrium.P. a. F 4 = –11i + 2j b. F 4 = –11i – 2j c. F 4 = 2i – 11j d. F 4 = 11i + 2j 17. A 195-lb weight hangs from a string as shown in the figure. Find the tensions T 1 and T 2 in the string. a. b. c. d. T 1 = 110.2i + 63.6j, T 2 = –110.2i + 131.4j T 1 = –110.2i + 131.4j, T 2 = 110.2i + 63.6j T 1 = –107.2i + 50.6j, T 2 = 110.2i + 63.6j T 1 = –107.2i + 131.4j, T 2 = 110.2i + 50.6j 18. Evaluate the expression . a. 5,042 b. 210 c. 5,040.333333 d. 2,310 e. 216 19. Perform the matrix operation. a. b. c. The matrix operation is impossible. d. e. 20. Find A 2 if a. b. c. d. e. 21. Solve for x and y. a. x = 2, y = 3 b. x = 2, y = –3 c. x = 4, y = –5 d. x = 2, y = –5 e. x = 4, y = –3 22. Write the system of equations as a matrix equation. a. b. c. d. e. 23. Find the inverse of the matrix. a. b. c. d. 24. How many ways can 6 different mathematics books be placed next to each other on a shelf? a. 30 b. 6 c. 46,656 d. 720 e. 36 25. A true or false test contains 13 questions. How many different ways can this test be completed? a. 1,716 b. 26 c. 169 d. 8,192 e. 6,227,020,800 26. Four independent trials of a binomial experiment with probability of success are performed. Find the probability of no successes. and probability of failure a. b. c. d. e. 27. According to a ratings survey, of the households in a certain city tune in to the local evening TV news. If households are visited at random, what is the probability that of them will have their television tuned to the local news? a. b. c. d. e. 28. A drug used to prevent motion sickness is found to be effective about of the time. Eight friends, prone to seasickness, go on a sailing cruise, and all take the drug. Find the probability that exactly get seasick . a. 0.008197 b. 0.080773 c. 0.096928 d. 0.001463 e. 0.088851 29. Mike wins $7 if a coin toss shows heads and $2 if it shows tails. Find the expected value (or expectation) of the game. a. $4.50 b. $5.50 c. $5.00 d. $9.00 e. $14.00 30. A safe containing $1,000,000 is locked with a combination lock. You pay $3.00 for one guess at the six-digit combination. If you open the lock, you get to keep the million dollars. What is your expectation? a. $2.00 b. $5.00 c. $2.00 d. $3.00 e. $5.00 31. A government lottery operation sells scratch-off tickets. The player buys a ticket and then scratches off the coating to reveal which prize the player has won. For every 10,000 tickets printed, there are 2 thousand-dollar winners, 5 hundred-dollar winners, 30 ten-dollar winners, 200 five-dollar winners, and 500 one-dollar winners. The rest of the tickets are blanks, and the player wins nothing. Determine the "fair price" to pay for a ticket to play this game. The "fair price" is the price at which the player can be expected to break even if he plays the game many times, or in other words, the price at which his expectation is zero. a. b. c. d. e. $0.31 $0.33 $0.43 $0.59 $0.99 Numeric Response 33. Five independent trials of a binomial experiment with probability of success are performed. and probability of failure Find the probability of at least two successes. Give the answer to six decimal places, if necessary. __________ Short Answer 34. Find (a) (a) (b) and (b) the angle between u and v to the nearest degree. = __________ = __________ 35. Solve the system of equations by converting to a matrix equation and using the inverse of the coefficient matrix. Use the inverse of matrix. (x, y) = ( __________, __________ ) 36. Find the inverse of the matrix if it exists. 38. A cannon fires a cannonball as shown in the figure. The path of the cannonball is a parabola with vertex at the highest point of the path. If the cannonball lands 1600 ft from the cannon and the highest point it reaches is 4000 ft above the ground, find an equation for the path of the cannonball. Place the origin at the location of the cannon. PreCalculus Semester 2 Final Exam Study Guide Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: ANS: B A A D B D B C A D D D D D A B B B A E C D B D D C A B A C C PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: PTS: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 NUMERIC RESPONSE 32. ANS: 19 PTS: 1 33. ANS: 0.66304 PTS: 1 MSC: srca.10.04.11 MSC: MSC: MSC: MSC: MSC: MSC: MSC: MSC: srca.10.01.10m srca.10.01.23m srca.10.04.03m srca.10.04.15m srca.10.04.27m srca.10.05.01m srca.10.05.14m srca.10.05.20m SHORT ANSWER 34. ANS: ; 30 PTS: 1 35. ANS: –17; 17 PTS: 1 36. ANS: PTS: 1 37. ANS: PTS: 1 38. ANS: (x – 800)2 = –160(y – 4000) PTS: 1
