NAME DATE PERIOD REVIEW: End of Course Final algebra 2 Find the slope and y-intercept of each function described below. (lesson 2-3, 2-4) y = 1 2 x 3 y = 4x + 1 1 2 3 x y 4 0 1 2 3 4 5 6 7 5 4x 2y = 10 6 a line passing through the points (0, 3) and (-2, -1) Sketch a possible graph of a polynomial function with the given zeros. (lesson 6-1, 6-7) 7 x = 1, x = -4, x = 3 8 x = -3, x = 0, x = 2, x = 2 9 x = 4, x = 2, x = -2 Using its parent function (with any translation), match the polynomial function to its graph. (lesson 1-9, 5-1, 6-8, 9-3) 10 11 12 A f(x) = x 5 3 B f(x) = x 3-5 C f(x) = (x + 3) 2 + 5 Find the inverse of each function. (lesson 7-2, 9-5) 13 f(x) = ½x - 7 14 f(x) = 10 - x 2 15 y = 3x + 1 16 y = x - 7 6 2 Simplify each rational expression. (pg.331, lesson 8-2) 2x 3 6x x 2 + x 20 x 3 x 2 4x + 4 17 x 2 3x 18 x 4 19 x 2 x 6 20 x 2 2x 3 4x 6 x 2 4
Graph the piecewise functions. (lesson 9-2) 2 if x < 2 2x + 1 if x 0 21 f(x) = 22 f(x) = -½x + 3 if x 2 -x -3 if x > 0 Tell whether the function is exponential. If it is, state whether it shows growth or decay. (lesson 7-1) 23 f(x) = 1.5(0.2) x 24 f(x) = 25 f(x) = 1.1(x) 0.9 1 x 0.5 Answer the questions about the situation. (lesson 7-1) An initial population of 900 frogs decreases at a rate of 14% per year. 26 Write an equation to model the situation. 27 Write an equation if, instead of decreasing, the population increased by 5%. 28 Write an equation if the frog population started at 1,500 frogs and doubled every year. Match the function with its possible graph. (lesson 7-1, 7-3, 7-6) A B 29 y = e x 30 y = e -x 31 y =(½) -x 32 y =(½) x 33 y =(2) x 34 y =(2) -x Solve for x. (lesson 7-3, 7-4, 7-5) 35 log 36 6 = x 36 log 2 x = -3 37 38 8 (4 - x) = 16 log 1 = x 100 (2 - x)
39 4 2x - 8 = 32 x - 1 40 log 4 (3x - 2) = 2 41 log 5 (x + 7) = log 5 2x 42 log 2 (2x - 8) = log 2 (5x + 7) Express as a single logarithm and simplify, if possible. (lesson 7-4) 43 log 3 + log 4 44 log 5 100-2log 5 2 45 ln 14-3 ln 7 46 4 ln z - 2 ln x + y ln 5 47 log 25 log 5 Convert each measure from degrees to radians or from radians to degrees. (lesson 13-3) 2 48 60 49 51 50-150 3 10 For the right triangle show, solve for x. (p.928, lesson 13-1) 52 53 54 Write the equation to solve for θ. (lesson 13-4) 55 56 57 7 11 Write an equation to solve for the value. (lesson 13-1) 58 A boy begins to build a fort by leaning a plank against the wall making a 17 angle with the ground. The plank hits the wall 5 feet above the ground. Approximately how long is the plank? 59 A conveyor belt leads from the ground to a barn door 24 feet high. The angle between the belt and the ground is 32. What is the length of the conveyor belt to the nearest foot?
60 From a 200 foot building, a person sees a car driving. The angle of depression of the person at the top of the building is 15, as shown in the figure. How far is the car from the building? 61 A pilot of a helicopter measures the angle of depression to a landing spot to be 18.8. If the pilot's altitude is 1640 meters, what is the horizontal distance to the landing spot to the nearest meter? Evaluate. (lesson 13-3) 62 sin 3π 63 tan 7π 2 64 sec π 6 4 65 csc π Find the measure of a positive and negative angle that are coterminal with each given angle. (lesson 13-2) θ = 425 θ = -4 θ = 175 66 67 68 69 θ = 80 Use the trigonometric functions and trigonometric identities to answer. (lesson 14-3) 70 What is tan θ, if sin 1 and cos 15? 71 4 What is cot θ, if and? cos 3 5 4 7 sin 2 7 Determine the amplitude, period, phase shift and vertical shift of each function. (lesson 14-1, 14-2) 72 y = 3 cos (½x) 73 y = ¾ sin (2x - ) 74 y = tan (x + ) - 2 75 y = 2 sec ( x) + 1 Match the function with its graph. (lesson 14-1, 14-2) 76 y = ½ csc (2x) 77 y = sec (2x) 78 y = ½ cot (2x) 79 y = csc x 80 y = 2 sin (2x) 81 y = -2 sin (x) 82 y = tan ⅓x 83 y = sec (½x) A. B. C.
D. E. F. G. H. I. Match the definition to the vocabulary. (lesson 11-1, 11-2, 11-3) 84 Probability A. when the occurrence of one event does not affect the occurrence of the other 85 Outcome B. selection of a group of objects in which order is important 86 Permutation C. the probability of event B, given that event A has occurred 87 Combination D. each possible result of a probability experiment or situation 88 Conditional Probability E. ratio of the number of times that the event occurs to the number of trials 89 Experimental Probability F. product of the natural numbers less than or equal to the number 90 Independent Events G. a grouping of items in which order does not matter 91 Factorial H. measure of how likely an event will occur Write the formula used to solve each problem. (lesson 11-1) 92 In how many ways can 4 of 7 different kind of bushes be planted along one side of a house? 93 In how many ways can a team of 4 be selected from a group of 7 people? 94 A boy has 4 new books, but can only fit 3 on his bookshelf. How many ways can he arrange 3 books on the shelf? 95 How many ways can 3 desserts be choosen from a list of 7? Solve. (lesson 11-3) 96 Two cards are dealt from a standard deck of 52 cards. What is the probability of being dealt an Ace then a King? If only 1 card is dealt, what is the probability of being dealt an Ace OR a king? 97 Helen wrapped 7 gifts for her 7 cousins. If she gives them out randomly, what is the probability that every cousin gets the right present?
98 Using a coin and a six-sided number cube, what is the probability of tossing tails and rolling a multiple of 3? 99 What is the probability of filling a coin 4 times in a row and getting "tails" for all 4 consecutive coin flips? 100 A teacher writes MATHEMATICS on a piece of paper and then cuts out each letter and puts them all in a bag. What is the probability that she will select an M and then an A is she randomly draws 2 tiles? If only 1 tile is drawn, what is the probability she will choose an E or an A? 101 In one bowl, 5 out of the 9 chips are cheetos. In a second bowl, 2 out of the 20 chips are cheetos. If Chase chooses one chip from each bowl at random, what is the probability he will choose a cheeto from both bowls? Graph each conic section. (lesson 10-1, 10-2) 102 (x - 3) 2 + (y - 2) 2 = 9 103 (x - 1) 2 + (y + 4) 2 = 4