Algebra 2/Trigonometry Practice Test

Transcription

1 Algebra 2/Trigonometry Practice Test Part I Answer all 27 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [54] 8 1 Write the exponential expression x in radical form. 8 1) x 8 2) x ) x 8 4) 8 8 x 2 A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely as the number of people going on the trip. It will cost $0 per person if 44 people go on the trip. How much will it cost per person if 60 people go on the trip, to the nearest cent? 1) $ ) $40.91 ) $1, ) $21.29 Find the cosine and sine of 00º to the nearest hundredth. 1) 0.87, 0.5 2) 0.95, 0.55 ) 0.5, ) 0, 1 4 The expression 5 log b q + 2 log b y is equivalent to 1) log b (q 5 y 2 ) ) log b q 5 + y 2 2) log b q + y 4) log b qy Algebra 2/Trigonometry - Practice Exam [ 1 ]

2 5 The value of cot 11π to the nearest hundredth is 6 1) ) 0 ) 1.7 4) The sum of the reciprocals of two consecutive even integers is 11. Write an equation that can be used to find the 60 two integers. Find the two integers. 1) t + (t + 2) = ; 8 and 10 ) t + (t + 2) = ; 10 and ) + t t + 2 = ; 10 and 12 4) t t + 2 = 11 ; 8 and If f(x) = x + 9, find (f f 1 )(5). 1) 14 2) 5 ) 5 4) 25 8 Simplify: 128a 1 b 6 1) 4a 4 b 2 2a 2) 2a 4 b 2 4a ) 4a 4 b a 4) none of these 9 The accompanying diagram shows a circular dartboard. If darts thrown at the board are equally likely to land anywhere on the board, what is the probability that it will land in the shaded region? 1) 1 4 2) 1 16 π ) ) 16π Algebra 2/Trigonometry - Practice Exam [ 2 ]

3 10 What is the number of degrees in an angle whose radian measure is 7π 4? 1) 15π º 2) 7π º ) 15º 4) 5.5º The sales of lawn mowers t years after a new model is introduced is given by the function y = 5500 ln(9t + 4), where y is the number of mowers sold. How many mowers will be sold 5 years after a model is introduced, to the nearest whole number. 1) 42,96 mowers ) 21,405 mowers 2) 9,296 mowers 4) 20,940 mowers 12 In simplest form, 6 48 is equivalent to 1) 6 + i 48 ) 6 4i 2) 6 4i 4) 6 + 4i 1 Simplify: 6x 8 y 9 5x 2 y 4 1) x y 2 0y 5 ) 5x y 2 0y 2) 0x 10 y 1 5x 2 y 4 4) none of these 14 Write an explicit formula for the sequence a 1 =, r =. Find the fifth term in the sequence. 1) a n = ( ) n 1 ; 24 ) a n = () n ; 24 2) a n = () n 1 ; 24 4) a n = ( ) n ; For all values of d for which the expressions are defined, d 2 12d + 5 d 2 11d + 0 d 2 1d + 42 is equivalent to d 2 d 42 1) 2) 2d 2 78 (d 6)(d + 6) 1d 6 (d 6)(d + 6) ) 4) 2d d 6 2d d 78 (d 6)(d + 6) Algebra 2/Trigonometry - Practice Exam [ ]

4 16 A grocery store will only accept yellow onions that are at least in. in diameter. A grower has a crop of onions with diameters that are normally distributed, with a mean diameter of.25 in. and a standard deviation of 0.25 in. What percent of the onions will be accepted by the grocery store? 1) 4% 2) 97.5% ) 84% 4) 50% 17 A Ferris wheel has a radius of 80 feet. Two particular cars are located such that the central angle between them is 165º. To the nearest tenth, what is the measure of the intercepted arc between those two cars on the Ferris wheel? 1) 27.8 feet 2) 1,200.0 feet ) feet 4) 20.4 feet 18 Which graph represents the solution set of 2 x < 9? 1) ) 2) 4) 19 The value of the expression 5n is 8 n = 1) 125 2) 8 ) 210 4) Solve: x 4 4x 2 = 225 1) no solution ),, 5, 5 2), 5 4), 21 Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. Using the formula V = Pe rt, where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, that you will have in the account after 4 years? 1) $ ) $6, ) $10, ) $1,92.2 Algebra 2/Trigonometry - Practice Exam [ 4 ]

5 22 Which graph represents the equation y = 4 x? 1) ) 2) 4) 2 A survey of junior high school students found that 79% of students plan on attending college. If you pick three students at random, what are the chances that at least two plan on attending college, to the nearest percent? 1) 89% 2) 51% ) 11% 4) 9% 24 Expand and express in simplest form: (s 5v) 5 1) s 5 5s 4 v + 10s v 2 10s 2 v + 5sv 4 v 5 2) s s 4 v 1250s v s 2 v 15625sv v 5 ) s 5 25s 4 v + 250s v s 2 v + 125sv 4 125v 5 4) s 5 25s s 1250s s 125 Algebra 2/Trigonometry - Practice Exam [ 5 ]

6 25 Find the area of ABC to the nearest tenth. 1),847.1 m 2 2) 2,77.6 m 2 ) 1,250 m 2 4) 1,188.8 m 2 26 The expression 8a 6 2 is equivalent to a 1) 4 4 ) 1 4a 4 2) 4a 4 4) a The expression (2 5i) ( + 4i) is equivalent to 1) 1 + 9i ) 1 9i 2) 5 i 4) 10i Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 28 There are 6 people on the ballot for regional judges. Voters can vote for any 4. Voters can choose to vote for or 4 judges. In how many different ways can a person vote? 29 Solve the quadratic equation x x + 5 = 0 by completing the square. Algebra 2/Trigonometry - Practice Exam [ 6 ]

7 0 Using logarithms, solve the equation 5 4x = 2115 for x to the nearest hundredth. 1 If sin θ = 12 7 and 90 θ 180, find the exact value of cos θ 2. 2 Express x 7 2x 2 in simplest radical form. Is the relation {(, 5), ( 4, 5), ( 5, 0), (1, 1), (4, 0)} a function? Explain. 4 Use the definitions of the trigonometric ratios for a right triangle to derive a cofunction identity for tan(90 A). Show your steps. 5 Simplify: 5 2 Part III Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [12] 6 Applying the angle sum and difference formulas, find the exact value of cos 255 in simplest radical form. 7 A particular sound wave is modeled in the laboratory with the function y = sin 4 x π 2 a. Find the amplitude of the function. b. Find the period of the function. c. Describe any phase shift in the graph. d. Describe any vertical shift in the graph Algebra 2/Trigonometry - Practice Exam [ 7 ]

8 8 A plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 1,600 feet, and the angles of elevation are given. Find BC, the distance from Tower 2 to the plane, to the nearest foot. Find CD, the height of the plane from the ground, to the nearest foot. Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen. [6] 9 Students from two high schools went to a band competition. Each student gave a solo performance and was rated by the judges. The possible scores ranged from (one point from each judge) to 21 (seven points from each judge). The data show the scores of two groups of students. Westlake Student Scores: 8, 10, 15, 21,, 15, 10, 21, 15, 20 Northshore Student Scores: 5, 6, 19, 10, 12, 10, 12, 9, 20, 8 a. Find the mean and the range of the data for the Westlake High School students and for the Northshore High School students. b. Find the standard deviation for each set of data. Round to the nearest tenth. c. Use your results from parts a and b to compare the scores of the students from the two high schools. Algebra 2/Trigonometry - Practice Exam [ 8 ]

9 ID: A Algebra 2/Trigonometry Practice Test Answer Section 1 ANS: 1 STA: NY A2.A.10 2 ANS: 1 STA: NY A2.A.5 ANS: STA: NY A2.A.56 4 ANS: 1 STA: NY A2.A.19 5 ANS: 4 STA: NY A2.A.66 6 ANS: 2 STA: NY A2.A.2 7 ANS: 2 STA: NY A2.A.42 NY A2.A.44 8 ANS: 1 STA: NY A2.A.1 9 ANS: STA: NY A2.S.1 10 ANS: STA: NY A2.M.2 11 ANS: STA: NY A2.A ANS: 2 STA: NY A2.N.6 1 ANS: 1 STA: NY A2.A ANS: 1 STA: NY A2.A ANS: 4 STA: NY A2.A ANS: STA: NY A2.S.5 17 ANS: 4 STA: NY A2.A ANS: 2 STA: NY A2.A.1 19 ANS: 4 STA: NY A2.N ANS: STA: NY A2.A ANS: 4 STA: NY A2.A ANS: 4 STA: NY A2.A.5 2 ANS: 1 STA: NY A2.S ANS: STA: NY A2.A.6 25 ANS: 4 STA: NY A2.A ANS: 1 STA: NY A2.A.8 27 ANS: STA: NY A2.N.9 28 ANS: ANS: 5 ± i 10 0 ANS: 1.19 STA: NY A2.S.11 STA: NY A2.A.24 STA: NY A2.A.27 Algebra 2/Trigonometry - Practice Exam [ 1 ]

10 ID: A 1 ANS: ANS: x 6 STA: NY A2.A.77 STA: NY A2.N.2 ANS: Yes; for each element in the domain there is exactly one element in the range. STA: NY A2.A.7 4 ANS: In a right triangle, the acute angles are complementary. So A + B = 90 and B = 90 A, where A and B are the measures of the acute angles. tan(90 A) = tan B A and B are complementary angles. = b definition of tangent in a right triangle a = cot A definition of cotangent in a right triangle 5 ANS: ANS: PTS: 4 7 ANS: a. b. 1 2 π STA: NY A2.A.58 STA: NY A2.A.14 STA: NY A2.A.76 c. phase shift is π units to the right 2 d. vertical shift is 2 units up PTS: 4 8 ANS: 2,4; 1,25 PTS: 4 STA: NY A2.A.69 STA: NY A2.A.7 Algebra 2/Trigonometry - Practice Exam [ 2 ]

11 ID: A 9 ANS: a. Westlake mean = 1.8, range = 18 Northshore mean = 11.1, range = 15 b. Westlake standard deviation = 5.7 Northshore standard deviation = 4.7 c. Answers may vary. Sample: The Westlake students had a higher mean score and a larger amount of variation in the scores, as shown by the larger range and standard deviation. The Northshore students had a lower mean score and less variation. PTS: 6 STA: NY A2.S.4 Algebra 2/Trigonometry - Practice Exam [ ]