PRACTICE REGENTS EXAMINATION 010 ALGEBRA /TRIGONOMETRY Prepared by J. Boeshore and L. LaSpina Bethpage High School GENERAL DIRECTIONS TO THE STUDENT Answer all 39 questions in this examination. Write your answers to the Part I multiple-choice questions on the separate answer sheet. No partial credit will be allowed on the multiple-choice section. For Parts II, III, and IV, clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in these parts, a correct numerical answer with no work shown will receive only 1 credit. A reference sheet that you may need to answer some questions in this examination is included. Scrap paper is not permitted for any part of this examination, but you may use the blank spaces in this examination as scrap paper. Scrap graph paper is provided at the end of this examination for any question for which graphing may be helpful but is not required. Any work done on this sheet of scrap graph paper will not be scored. Write all your work in pen, except graphs and drawings, which should be done in pencil. Note: A graphing calculator and a straightedge (ruler) must be available for you to use while taking this examination.
Part I Answer all 7 questions in this part. Each correct answer will receive 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] 1 The expression ( 6i) is equivalent to [A] 4 + 36i [C] 3 + 4i [B] 3 4i [D] 4 36i If f ( x) = 5x and g( x) = x, what is the value of f(g(8))? [A] 8 10 [C] 80 [B] 16 [D] 1, 80 3 How many distinct triangles can be formed if m A = 30, side b = 1, and side a = 8? [A] [B] 0 [C] 3 [D] 1 4 A survey completed at a large university asked 5,000 students to estimate the average number of hours they spend studying each week. Every tenth student entering the library was surveyed. The data showed that the mean number of hours that students spend studying was 1.8 per week. Which characteristic of the survey could create a bias in the results? [A] the size of the sample [B] the size of the population [C] the method of analyzing the data [D] the method of choosing the students who were surveyed
5 Which graph is not a function? [A] [B] [C] [D] 6 If log 5 x = what is the value of x? [A] 5 [B] 5 [C] 5 [D] 5 7 The expression cos 40 cos 10 + sin 40 sin10 is equivalent to [A] sin 50 [B] sin 60 [C] sin 30 [D] cos 50 m 1 8 What is the value of ( m + 1)? 3 m= 1 [A] 15 [B] 55 [C] 57 [D] 45 9 The center of a circle represented by the equation (x ) + ( y + 3) = 100 is located in Quadrant [A] III [B] IV [C] I [D] II 10 If sinθ is negative and cotθ = 3, in which quadrant does the terminal side of θ lie? [A] I [B] II [C] III [D] IV 3
11 The accompanying diagram shows a section of a sound wave as displayed on an oscilloscope. Which equation could represent this graph? [A] y = cos x [B] y = 1 sin π x [C] y = 1 cos x [D] y = sin x 1 Which set of ordered pairs is not a function? [A] {(4,1), (5,1), (6,1), (7,1)} [B] {(1,), (3,4), (4,5), (5,6)} [C] {(3,1), (,1), (1,), (3,)} [D] {(0,0), (1,1), (,), (3,3)} 13 The expression n+ 1 3 ( b ) is equivalent to n 4n+ 3 b b [A] n 3n 1 b b + [B] [C] 3n b [D] n b 14 On a standardized test, the distribution of scores is normal, the mean of the scores is 75, and the standard deviation is 5.8. If a student scored 83, the student's score ranks [A] below the 75th percentile [B] between the 84th percentile and the 97 th percentile [C] above the 97th percentile [D] between the 75th percentile and the 84 th percentile 4
15 What is the inverse of the function y = log 4 x? [A] 4 x = y [B] x 4 = y [C] 4 y = x [D] y 4 = x 16 Factored completely, the expression 6x x 4 x 3 is equivalent to [A] x (x + 3)(x ) [B] x (x 3)(x + ) [C] x (x 3)(x + ) [D] x (x + 3)(x ) 17 The expression 3 4 6 4 16a b is equivalent to [A] b a [B] 4a b [C] a b [D] 4b a 3 18 If sin 6A = cos 9A, then m A is equal to [A] 6 [B] 1 1 [C] 36 [D] 54 19 What is the third term in the expansion of (cos x +3) 5? [A] 60cos 3 x [B] 90cos 3 x [C] 70cos x [D] 90cos x 0 If the length of a rectangular garden is represented by expression represents the area of the garden? x + x and its width is represented by x 6 x + x 15 x + 4, which x [A] x + 5 [B] x [C] x + 5 [D] x + x ( x + 5) 1 What is the domain of h(x) = x 4x 5? [A] {x 5 or x 1} [B] {x 1 or x 5} [C] { 5 x 1} [D] { 1 x 5} In the equation log x 4 + log x 9 =, x is equal to [A] 13 [B] 6 [C] 18 [D] 65 5
3 A clock has a diameter of 8 inches and a minute hand with length 4. In inches, what is the arc traced by the tip of the minute hand as it travels through an angle at 45? [A] π [B] π [C] 3 [D] 180 4 The infinite series 686 + 98+ 14 + + 7 [A] undefined [B] 800 7 + evaluates to [C] 1000 [D] 401 3 5 If x is an acute angle and sin x = 1 then cosx equals 13 [A] 5 169 [B] 119 169 [C] 119 169 [D] 5 169 6 Which graph represents the solution set for the expression x + 3 > 7? 7 Rhombus ABCD has side length 10 and an area of 85. Determine the measure of the acute angle ABC to the nearest tenth. [A] 11.8 [B] 58. [C]59.3 [D]57.8 6
Part II Answer all 8 questions in this part. Each correct answer will receive 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. [16] 8 In a certain school district, the ages of all new teachers hired during the last 5 years are normally distributed. Within this curve, 95.4% of the ages, centered about the mean, are between 4.6 and 37.4 years. Find the mean age and the standard deviation of the data. 9 The quadratic equation 3x + bx + c = 0, where b and c are integers, has i as a root. Find the value of b. 30 Solve algebraically for x: 7 x+1 = 9 4x 7
31 The price per person to rent a limousine for a prom varies inversely as the number of passengers. If five people rent the limousine, the cost is $70 each. How many people are renting the limousine when the cost per couple is $87.50? 3 The cost of a long-distance telephone call is determined by a flat fee for the first 5 minutes and a fixed amount for each additional minute. If a 15-minute telephone call costs $3.5 and a 3-minute call costs $5.17, find the cost of a 30-minute call. 8
33 Solve for all values of q that satisfy the equation 3q + 7 = q + 3 34 A landscape designer is designing a triangular garden with two sides that are 4 feet and 6 feet, respectively. The angle opposite the 4- foot side is 30. How many distinct triangular gardens can the designer make using these measurements? 9
35 If the sine of an angle is 3 5 and the angle is not in Quadrant I, what is the value of the cosine of the angle? Part III Answer all 3 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. [1] 36 Solve for x and express your answer in simplest radical form: 4 3 = 7 x x + 1 10
37 In the accompanying diagram of ΔABC, m A = 65, m B = 70, and the side opposite vertex B is 7. Find the length of the side opposite vertex A, and find the area of ΔABC. 11
38 The height of a projectile is modeled by the equation y = x + 38x +10, where x is time, in seconds, and y is height, in feet. During what interval of time, to the nearest tenth of a second, is the projectile at least 15 feet above ground? [The use of the accompanying grid is optional.] 1
Part IV Answer the question in this part. The 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. [6] 39 Two tow trucks try to pull a car out of a ditch. One tow truck applies a force of 1,500 pounds while the other truck applies a force of,000 pounds. The resultant force is 3,000 pounds. Find the measure, to the nearest degree, of the angle formed between the resultant and the larger force. Find the angle between the two applied forces, rounded to the nearest degree. 13