JMAP REGENTS BY TYPE The NY Algebra 2/Trigonometry Regents Exam Questions from Spring 2009 to January 2016 www.jmap.org Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org Algebra 2/Trigonometry Multiple Choice Regents Exam Questions 5 What is the period of the function f(θ) = −2cos 3θ ? 1) π 2π 2) 3 3π 3) 2 4) 2π 1 The expression cos 4x cos 3x + sin4x sin 3x is equivalent to 1) sinx 2) sin 7x 3) cos x 4) cos 7x 2 What is the range of f(x) = (x + 4) 2 + 7? 1) y ≥ −4 2) y ≥ 4 3) y = 7 4) y ≥ 7 6 In the diagram below of right triangle JTM, JT = 12, JM = 6, and m∠JMT = 90. 3 A market research firm needs to collect data on viewer preferences for local news programming in Buffalo. Which method of data collection is most appropriate? 1) census 2) survey 3) observation 4) controlled experiment What is the value of cot J ? 3 3 1) 2) 3) 4 Brian correctly used a method of completing the square to solve the equation x 2 + 7x − 11 = 0. Brian’s first step was to rewrite the equation as x 2 + 7x = 11 . He then added a number to both sides of the equation. Which number did he add? 7 1) 2 49 2) 4 49 3) 2 4) 49 4) 2 3 2 3 3 7 The conjugate of 7 − 5i is 1) −7 − 5i 2) −7 + 5i 3) 7 − 5i 4) 7 + 5i 1 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 12 The expression 2i 2 + 3i 3 is equivalent to 1) −2 − 3i 2) 2 − 3i 3) −2 + 3i 4) 2 + 3i 8 Which function is one-to-one? 1) k(x) = x 2 + 2 2) 3) 4) g(x) = x 3 + 2 f(x) = |x | + 2 j(x) = x 4 + 2 13 The product of (3 + 9 Which angle does not terminate in Quadrant IV when drawn on a unit circle in standard position? 1) −300° 2) −50° 3) 280° 4) 1030° 1) 2) 3) 4) The range of y = sin −1 x is [−1,1]. 3) A domain of y = cos −1 x is (−∞,∞). 4) The range of y = cos −1 x is [0, π ]. 5) is 4−6 5 14 − 6 5 14 4 14 What is the fifteenth term of the sequence 5,−10,20,−40,80,. . .? 1) −163,840 2) −81,920 3) 81,920 4) 327,680 10 Which statement regarding the inverse function is true? 1) A domain of y = sin −1 x is [0,2π ]. 2) 5) and (3 − 15 Four points on the graph of the function f(x) are shown below. {(0,1),(1,2),(2,4),(3,8)} Which equation represents f(x)? 11 A school cafeteria has five different lunch periods. The cafeteria staff wants to find out which items on the menu are most popular, so they give every student in the first lunch period a list of questions to answer in order to collect data to represent the school. Which type of study does this represent? 1) observation 2) controlled experiment 3) population survey 4) sample survey 1) 2) 3) 4) 2 f(x) = 2 x f(x) = 2x f(x) = x + 1 f(x) = log 2 x Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 16 What is the number of degrees in an angle whose 11π ? radian measure is 12 1) 150 2) 165 3) 330 4) 518 20 Which equation has real, rational, and unequal roots? 1) x 2 + 10x + 25 = 0 2) x 2 − 5x + 4 = 0 3) x 2 − 3x + 1 = 0 4) x 2 − 2x + 5 = 0 17 Which statement about the graph of the equation y = e x is not true? 1) It is asymptotic to the x-axis. 2) The domain is the set of all real numbers. 3) It lies in Quadrants I and II. 4) It passes through the point (e,1). 21 Which values of x are solutions of the equation x 3 + x 2 − 2x = 0? 1) 0,1,2 2) 0,1,−2 3) 0,−1,2 4) 0,−1,−2 18 If f(x) = x 2 − 5 and g(x) = 6x, then g(f(x)) is equal to 1) 6x 3 − 30x 2) 6x 2 − 30 3) 36x 2 − 5 4) x 2 + 6x − 5 22 Which survey is least likely to contain bias? 1) surveying a sample of people leaving a movie theater to determine which flavor of ice cream is the most popular 2) surveying the members of a football team to determine the most watched TV sport 3) surveying a sample of people leaving a library to determine the average number of books a person reads in a year 4) surveying a sample of people leaving a gym to determine the average number of hours a person exercises per week 19 If f x = 1) 2) 3) 4) x , what is the value of f(−10)? x − 16 2 5 2 5 − 42 5 58 5 18 − 2 23 The value of the expression 2 ∑ (n n =0 1) 2) 3) 4) 3 12 22 24 26 2 + 2 n ) is Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 24 An investment is earning 5% interest compounded quarterly. The equation represents the total amount of money, A, where P is the original investment, r is the interest rate, t is the number of years, and n represents the number of times per year the money earns interest. Which graph could represent this investment over at least 50 years? 26 Which statement regarding correlation is not true? 1) The closer the absolute value of the correlation coefficient is to one, the closer the data conform to a line. 2) A correlation coefficient measures the strength of the linear relationship between two variables. 3) A negative correlation coefficient indicates that there is a weak relationship between two variables. 4) A relation for which most of the data fall close to a line is considered strong. 1) 27 Which summation represents 5 + 7 + 9 + 11 +. . .+ 43? 43 1) ∑n n=5 2) 20 2) ∑ (2n + 3) n=1 24 3) ∑ (2n − 3) n=4 23 3) 4) ∑ (3n − 4) n=3 28 Which step can be used when solving x 2 − 6x − 25 = 0 by completing the square? 1) x 2 − 6x + 9 = 25 + 9 2) x 2 − 6x − 9 = 25 − 9 3) x 2 − 6x + 36 = 25 + 36 4) x 2 − 6x − 36 = 25 − 36 4) 25 The value of x in the equation 4 2x + 5 = 8 3x is 1) 1 2) 2 3) 5 4) −10 4 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 33 In KLM , KL = 20 , LM = 13, and m∠K = 40 . The measure of ∠M ? 1) must be between 0° and 90° 2) must equal 90° 3) must be between 90° and 180° 4) is ambiguous 29 What is the period of the function 1 x y = sin − π ? 2 3 1) 2) 3) 4) 1 2 1 3 2 π 3 6π 34 Which formula can be used to determine the total number of different eight-letter arrangements that can be formed using the letters in the word DEADLINE? 1) 8! 8! 2) 4! 8! 3) 2!+ 2! 8! 4) 2!⋅ 2! 30 Ms. Bell's mathematics class consists of 4 sophomores, 10 juniors, and 5 seniors. How many different ways can Ms. Bell create a four-member committee of juniors if each junior has an equal chance of being selected? 1) 210 2) 3,876 3) 5,040 4) 93,024 35 An amateur bowler calculated his bowling average for the season. If the data are normally distributed, about how many of his 50 games were within one standard deviation of the mean? 1) 14 2) 17 3) 34 4) 48 31 The solution set of the inequality x 2 − 3x > 10 is 1) {x | − 2 < x < 5} 2) {x | 0 < x < 3} 3) {x | x < − 2 or x > 5} 4) {x | x < − 5 or x > 2} 32 The expression 4ab is equivalent to 1) 2ab 6b 2) 3) 4) 16ab 2b −5ab + 7ab 6b −5ab 2b + 7ab 2b − 3a 18b 3 + 7ab 36 What is the solution of the equation 2 log 4 (5x) = 3? 1) 6.4 2) 2.56 9 3) 5 8 4) 5 6b 6b 5 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 41 Six people met at a dinner party, and each person shook hands once with everyone there. Which expression represents the total number of handshakes? 1) 6! 2) 6!⋅ 2! 6! 3) 2! 6! 4) 4!⋅ 2! x 1 − 4 x 37 Written in simplest form, the expression is 1 1 + 2x 4 equivalent to 1) x − 1 2) x − 2 x−2 3) 2 2 x −4 4) x+2 42 The principal would like to assemble a committee of 8 students from the 15-member student council. How many different committees can be chosen? 1) 120 2) 6,435 3) 32,432,400 4) 259,459,200 38 What is a formula for the nth term of sequence B shown below? B = 10,12,14,16,. . . 1) b n = 8 + 2n 2) b n = 10 + 2n 3) b n = 10(2) n 4) b n = 10(2) n − 1 43 The expression 39 Given ABC with a = 9, b = 10, and m∠B = 70, what type of triangle can be drawn? 1) an acute triangle, only 2) an obtuse triangle, only 3) both an acute triangle and an obtuse triangle 4) neither an acute triangle nor an obtuse triangle 1) 2) 3) 4) 40 Factored completely, the expression 12x 4 + 10x 3 − 12x 2 is equivalent to 1) x 2 (4x + 6)(3x − 2) 2) 3) 4) a 2 b −3 is equivalent to a −4 b 2 a6 b5 b5 a6 a2 b a −2 b −1 44 In MNP , m = 6 and n = 10. Two distinct triangles can be constructed if the measure of angle M is 1) 35 2) 40 3) 45 4) 50 2(2x 2 + 3x)(3x 2 − 2x) 2x 2 (2x − 3)(3x + 2) 2x 2 (2x + 3)(3x − 2) 6 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 45 The lengths of 100 pipes have a normal distribution with a mean of 102.4 inches and a standard deviation of 0.2 inch. If one of the pipes measures exactly 102.1 inches, its length lies 1) below the 16th percentile 2) between the 50th and 84th percentiles 3) between the 16th and 50th percentiles 4) above the 84th percentile 49 The expression 1) 2) 3) 4) 46 Which equation represents a circle with its center at (2,−3) and that passes through the point (6,2)? 1) (x − 2) 2 + (y + 3) 2 = 2) (x + 2) + (y − 3) = 41 (x − 2) 2 + (y + 3) 2 = 41 (x + 2) 2 + (y − 3) 2 = 41 3) 4) 2 4 5− 13 is equivalent to 4 13 5 13 − 13 4(5 − 13) 38 5+ 13 3 4(5 + 13) 38 41 2 50 The roots of the equation 4(x 2 − 1) = −3x are 1) imaginary 2) real, rational, equal 3) real, rational, unequal 4) real, irrational, unequal 47 In which interval of f(x) = cos(x) is the inverse also a function? 1) 2) 3) 4) − − π 2 <x< π π 51 Theresa is comparing the graphs of y = 2 x and 2 y = 5 x . Which statement is true? 1) The y-intercept of y = 2 x is (0,2), and the y-intercept of y = 5 x is (0,5). 2) Both graphs have a y-intercept of (0,1), and y = 2 x is steeper for x > 0. 3) Both graphs have a y-intercept of (0,1), and y = 5 x is steeper for x > 0. 4) Neither graph has a y-intercept. π ≤x≤ 2 2 0≤x≤π π 3π ≤x≤ 2 2 48 The roots of the equation 2x 2 + 7x − 3 = 0 are 1 1) − and −3 2 1 2) and 3 2 3) 4) 52 When the inverse of tan θ is sketched, its domain is 1) −1 ≤ θ ≤ 1 −7 ± 73 4 7± 2) 73 3) 4) 4 7 π π ≤θ≤ 2 2 0≤θ≤π −∞ < θ < ∞ − Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 53 An angle, P, drawn in standard position, terminates in Quadrant II if 1) cos P < 0 and csc P < 0 2) sinP > 0 and cos P > 0 3) csc P > 0 and cot P < 0 4) tanP < 0 and sec P > 0 57 Which equation represents a graph that has a period of 4π ? 1 1) y = 3 sin x 2 2) y = 3 sin2x 1 3) y = 3 sin x 4 4) y = 3 sin4x 54 When x −1 − 1 is divided by x − 1, the quotient is 1) −1 1 2) − x 1 3) x2 1 4) (x − 1) 2 55 The expression 3 58 In ABC , a = 15, b = 14, and c = 13, as shown in the diagram below. What is the m∠C , to the nearest degree? 27a −6 b 3 c 2 is equivalent to 2 3 1) 2) 3) 4) 3bc a2 3b 9 c 6 a 18 3b 6 c 5 a3 3b 3 1) 2) 3) 4) 3c 2 53 59 67 127 a2 59 In simplest form, 56 The expression (3 − 7i) 2 is equivalent to 1) −40 + 0i 2) −40 − 42i 3) 58 + 0i 4) 58 − 42i 1) 2) 3) 4) 8 3i 5i 10i 12i 10 12 3 5 −300 is equivalent to Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 60 Which equation is represented by the graph below? 62 What is the formula for the nth term of the sequence 54,18,6,. . .? 1 n 1) a n = 6 3 2) 1 n − 1 a n = 6 3 3) 1 n a n = 54 3 4) 1) 2) 3) 4) 63 If angles A and B are complementary, then sec B equals 1) csc(90° − B) 2) csc(B − 90°) 3) cos(B − 90°) 4) cos(90° − B) y=5 y = 0.5 x y = 5 −x y = 0.5−x x 61 Which equation is sketched in the diagram below? 1) 2) 3) 4) 1 n − 1 a n = 54 3 64 The solution set of 4 x 1) {1,3} 2) {−1,3} 3) {−1,−3} 4) {1,−3} 2 + 4x = 2 −6 is 65 A circle has a radius of 4 inches. In inches, what is the length of the arc intercepted by a central angle of 2 radians? 1) 2π 2) 2 3) 8π 4) 8 y = csc x y = sec x y = cot x y = tanx 9 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 68 In ABC , m∠A = 74, a = 59.2, and c = 60.3. What are the two possible values for m∠C , to the nearest tenth? 1) 73.7 and 106.3 2) 73.7 and 163.7 3) 78.3 and 101.7 4) 78.3 and 168.3 66 Which problem involves evaluating 6 P 4 ? 1) How many different four-digit ID numbers can be formed using 1, 2, 3, 4, 5, and 6 without repetition? 2) How many different subcommittees of four can be chosen from a committee having six members? 3) How many different outfits can be made using six shirts and four pairs of pants? 4) How many different ways can one boy and one girl be selected from a group of four boys and six girls? 69 If a = 3 and b = −2, what is the value of the a −2 expression −3 ? b 9 1) − 8 2) −1 8 3) − 9 8 4) 9 67 Which equation represents the circle shown in the graph below that passes through the point (0,−1)? 70 Which function is one-to-one? 1) f(x) = |x | 2) 3) 4) 1) 2) 3) 4) (x − 3) 2 + (y + 4) 2 (x − 3) 2 + (y + 4) 2 (x + 3) 2 + (y − 4) 2 (x + 3) 2 + (y − 4) 2 f(x) = 2 x f(x) = x 2 f(x) = sinx 71 An auditorium has 21 rows of seats. The first row has 18 seats, and each succeeding row has two more seats than the previous row. How many seats are in the auditorium? 1) 540 2) 567 3) 760 4) 798 = 16 = 18 = 16 = 18 10 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 72 How many distinct triangles can be formed if m∠A = 35, a = 10, and b = 13? 1) 1 2) 2 3) 3 4) 0 A2 B , then log r can be represented by C 1 1 log A + log B − log C 6 3 2 3(log A + log B − logC) 1 log(A 2 + B) − C 3 1 1 2 log A + log B − log C 3 3 3 75 If r = 1) 2) 3) 4) 3 ? 73 What is the principal value of cos −1 − 2 1) −30° 2) 60° 3) 150° 4) 240° 3 76 The table below shows the first-quarter averages for Mr. Harper’s statistics class. 74 Which diagram represents a relation that is both one-to-one and onto? 1) 2) 3) What is the population variance for this set of data? 1) 8.2 2) 8.3 3) 67.3 4) 69.3 4) 11 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 77 In the diagram below, the spinner is divided into eight equal regions. 80 The expression (x − 1) 2 1) 3 (x 2 − 1) 2 1 3 (x 2 − 1) 2 2) 3) 4) Which expression represents the probability of the spinner landing on B exactly three times in five spins? 1 3 4 5 1) 8 C 3 5 5 2) 3) 4) − 2 3 is equivalent to (x 2 − 1) 3 1 (x 2 − 1) 3 81 Which trigonometric expression does not simplify to 1? 1) sin 2 x(1 + cot 2 x) 5 3 1 4 C 8 3 5 5 1 2 7 3 C 5 3 8 8 2) 3) 4) sec 2 x(1 − sin 2 x) cos 2 x(tan 2 x − 1) cot 2 x(sec 2 x − 1) 1 3 7 2 5 C3 8 8 82 What is the coefficient of the fourth term in the expansion of (a − 4b) 9 ? 1) −5,376 2) −336 3) 336 4) 5,376 78 The minimum point on the graph of the equation y = f(x) is (−1,−3). What is the minimum point on the graph of the equation y = f(x) + 5 ? 1) (−1,2) 2) (−1,−8) 3) (4,−3) 4) (−6,−3) 83 What is the equation of a circle with its center at (0,−2) and passing through the point (3,−5)? 1) 2) 79 In ABC , m∠A = 120 , b = 10, and c = 18. What is the area of ABC to the nearest square inch? 1) 52 2) 78 3) 90 4) 156 3) 4) 12 x 2 + (y + 2) 2 (x + 2) 2 + y 2 x 2 + (y + 2) 2 (x + 2) 2 + y 2 =9 =9 = 18 = 18 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 84 The graph of y = x 3 − 4x 2 + x + 6 is shown below. − 87 The expression x 1) − x5 2) − x2 1 3) 4) 2 5 is equivalent to 2 5 2 x5 1 5 x2 88 Which relation does not represent a function? What is the product of the roots of the equation x 3 − 4x 2 + x + 6 = 0? 1) −36 2) −6 3) 6 4) 4 1) 2) 85 What is the domain of the function f(x) = x − 2 + 3? 1) (−∞,∞) 2) (2,∞) 3) [2,∞) 4) [3,∞) 3) 86 What is the fourth term in the expansion of (3x − 2) 5 ? 1) 2) 3) 4) −720x 2 −240x 720x 2 1,080x 3 4) 13 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 89 Which is a graph of y = cot x ? 91 The solutions of the equation y 2 − 3y = 9 are 1) 1) 3 ± 3i 3 2 2) 3 ± 3i 5 2 3) −3 ± 3 5 2 4) 3±3 5 2 92 The number of possible different 12-letter arrangements of the letters in the word “TRIGONOMETRY” is represented by 12! 1) 3! 12! 2) 6! 12 P 12 3) 8 P 12 12 4) 6! 2) 3) 93 What is the common ratio of the geometric sequence whose first term is 27 and fourth term is 64? 3 1) 4 64 2) 81 4 3) 3 37 4) 3 4) 90 The relationship between t, a student’s test scores, and d, the student’s success in college, is modeled by the equation d = 0.48t + 75.2. Based on this linear regression model, the correlation coefficient could be 1) between −1 and 0 2) between 0 and 1 3) equal to −1 4) equal to 0 14 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 94 If n is a negative integer, then which statement is always true? 1) 6n −2 < 4n −1 n > −6n −1 2) 4 3) 6n −1 < 4n −1 4) 4n −1 > (6n) −1 98 For which equation does the sum of the roots equal 3 and the product of the roots equal −2? 4 1) 4x 2 − 8x + 3 = 0 2) 4x 2 + 8x + 3 = 0 3) 4x 2 − 3x − 8 = 0 4) 4x 2 + 3x − 2 = 0 95 What is the equation of the circle passing through the point (6,5) and centered at (3,−4)? 99 If sin A = 1) 2) 3) 4) (x − 6) 2 + (y − 5) 2 (x − 6) 2 + (y − 5) 2 (x − 3) 2 + (y + 4) 2 (x − 3) 2 + (y + 4) 2 = 82 = 90 = 82 = 90 2 where 0° < A < 90°, what is the value 3 of sin2A? 96 Which statement about the equation 3x 2 + 9x − 12 = 0 is true? 1) The product of the roots is −12. 2) The product of the roots is −4. 3) The sum of the roots is 3. 4) The sum of the roots is −9. 1) 2 5 3 2) 2 5 9 3) 4 5 9 4) − 4 5 9 100 What is the radian measure of the smaller angle formed by the hands of a clock at 7 o’clock? 1) 97 A survey is to be conducted in a small upstate village to determine whether or not local residents should fund construction of a skateboard park by raising taxes. Which segment of the population would provide the most unbiased responses? 1) a club of local skateboard enthusiasts 2) senior citizens living on fixed incomes 3) a group opposed to any increase in taxes 4) every tenth person 18 years of age or older walking down Main St. 2) 3) 4) 15 π 2 2π 3 5π 6 7π 6 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 101 Given the relation {(8,2),(3,6),(7,5),(k,4)}, which value of k will result in the relation not being a function? 1) 1 2) 2 3) 3 4) 4 105 Samantha constructs the scatter plot below from a set of data. 102 The value of tan126°43′ to the nearest ten-thousandth is 1) −1.3407 2) −1.3408 3) −1.3548 4) −1.3549 Based on her scatter plot, which regression model would be most appropriate? 1) exponential 2) linear 3) logarithmic 4) power 103 Which expression is equivalent to the sum of the sequence 6,12,20,30? 7 ∑2 1) n − 10 n=4 6 ∑ 2n3 2) 2 106 A study finds that 80% of the local high school students text while doing homework. Ten students are selected at random from the local high school. Which expression would be part of the process used to determine the probability that, at most, 7 of the 10 students text while doing homework? 4 6 1 4 1) 10 C 6 5 5 n=3 5 ∑ 5n − 4 3) n=2 5 ∑n 4) 2 +n n =2 104 If x = 12x − 7 is solved by completing the square, one of the steps in the process is 1) (x − 6) 2 = −43 2) 4 10 1 7 10 C 7 5 5 3) 7 10 3 2 10 C 8 10 10 4) 7 9 3 1 10 C 9 10 10 2 2) 3) 4) (x + 6) 2 = −43 (x − 6) 2 = 29 (x + 6) 2 = 29 16 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 110 Factored completely, the expression 6x − x 3 − x 2 is equivalent to 1) x(x + 3)(x − 2) 2) x(x − 3)(x + 2) 3) −x(x − 3)(x + 2) 4) −x(x + 3)(x − 2) 1 x − 3 and g(x) = 2x + 5, what is the value 2 of (g f)(4)? 1) −13 2) 3.5 3) 3 4) 6 107 If f(x) = 111 Which sketch shows the inverse of y = a x , where a > 1? 108 The yearbook staff has designed a survey to learn student opinions on how the yearbook could be improved for this year. If they want to distribute this survey to 100 students and obtain the most reliable data, they should survey 1) every third student sent to the office 2) every third student to enter the library 3) every third student to enter the gym for the basketball game 4) every third student arriving at school in the morning 1) 109 The expression 2logx − (3log y + log z) is equivalent to x2 1) log 3 y z 2) 3) 4) 2) x2z y3 2x log 3yz 2xz log 3y log 3) 4) 17 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 112 If a function is defined by the equation f(x) = 4 x , which graph represents the inverse of this function? 113 The roots of the equation 2x 2 + 4 = 9x are 1) real, rational, and equal 2) real, rational, and unequal 3) real, irrational, and unequal 4) imaginary 114 What is the solution set of the equation |4a + 6| − 4a = −10? 1) ∅ 2) 0 1 3) 2 1 4) 0, 2 1) 2) 115 Which list of ordered pairs does not represent a one-to-one function? 1) (1,−1),(2,0),(3,1),(4,2) 2) (1,2),(2,3),(3,4),(4,6) 3) (1,3),(2,4),(3,3),(4,1) 4) (1,5),(2,4),(3,1),(4,0) 3) 116 Twenty different cameras will be assigned to several boxes. Three cameras will be randomly selected and assigned to box A. Which expression can be used to calculate the number of ways that three cameras can be assigned to box A? 1) 20! 20! 2) 3! 3) 20 C 3 4) 20 P 3 4) 18 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 117 Which graph represents one complete cycle of the equation y = sin3π x ? 119 What is the value of x in the equation 9 3x + 1 = 27 x + 2 ? 1) 1 1 2) 3 1 3) 2 4 4) 3 1) 120 What are the domain and the range of the function shown in the graph below? 2) 3) 1) 2) 3) 4) 4) 118 For which equation does the sum of the roots equal −3 and the product of the roots equal 2? 1) x 2 + 2x − 3 = 0 2) x 2 − 3x + 2 = 0 3) 2x 2 + 6x + 4 = 0 4) 2x 2 − 6x + 4 = 0 {x | x > −4}; {y | y > 2} {x | x ≥ −4}; {y | y ≥ 2} {x | x > 2}; {y | y > −4} {x | x ≥ 2}; {y | y ≥ −4} 121 The expression log 8 64 is equivalent to 1) 8 2) 2 1 3) 2 1 4) 8 19 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 125 Which statement is true about the graphs of f and g shown below? 122 The product of i 7 and i 5 is equivalent to 1) 1 2) −1 3) i 4) −i 123 Which calculator output shows the strongest linear relationship between x and y? 1) 1) 2) 3) 4) 2) f is a relation and g is a function. f is a function and g is a relation. Both f and g are functions. Neither f nor g is a function. 3) 126 Which value of r represents data with a strong positive linear correlation between two variables? 1) 0.89 2) 0.34 3) 1.04 4) 0.01 4) 124 Which expression represents the total number of different 11-letter arrangements that can be made using the letters in the word “MATHEMATICS”? 11! 1) 3! 11! 2) 2!+ 2!+ 2! 11! 3) 8! 11! 4) 2!⋅ 2!⋅ 2! 5 127 The value of the expression ∑ (−r r =3 1) 2) 3) 4) 20 −38 −12 26 62 2 + r) is Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 128 The expression cos 2 θ − cos 2θ is equivalent to 1) sin 2 θ 2) −sin 2 θ 3) cos 2 θ + 1 4) −cos 2 θ − 1 129 In 1) 2) 3) 4) ABC , a = 3, b = 5, and c = 7. What is m∠C ? 22 38 60 120 130 In PQR, p equals r sinP sinQ r sinP sinR r sinR sinP q sinR sinQ 1) 2) 3) 4) 131 The expression 1) 2) 3) 4) 132 The graph below shows the function f(x). Which graph represents the function f(x + 2)? 1) 2) sin 2 θ + cos 2 θ is equivalent to 1 − sin 2 θ 3) cos 2 θ sin 2 θ sec 2 θ csc 2 θ 4) 21 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 133 Which graph represents the function log 2 x = y ? 134 In the diagram below of a unit circle, the ordered 2 2 represents the point where the ,− pair − 2 2 terminal side of θ intersects the unit circle. 1) 2) What is m∠θ ? 1) 45 2) 135 3) 225 4) 240 3) 135 The solution set of 1) {−3,4} 2) {−4,3} 3) {3} 4) {−4} 3x + 16 = x + 2 is 4) 136 If m = {(−1,1),(1,1),(−2,4),(2,4),(−3,9),(3,9)}, which statement is true? 1) m and its inverse are both functions. 2) m is a function and its inverse is not a function. 3) m is not a function and its inverse is a function. 4) Neither m nor its inverse is a function. 22 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 137 In the diagram below of right triangle KTW, KW = 6, KT = 5, and m∠KTW = 90. 140 Which expression is equivalent to What is the measure of ∠K , to the nearest minute? 1) 33°33' 2) 33°34' 3) 33°55' 4) 33°56' 1) − 14 + 5 3 11 2) − 17 + 5 3 11 3) 14 + 5 3 14 4) 17 + 5 3 14 3 +5 3 −5 ? 141 A dartboard is shown in the diagram below. The two lines intersect at the center of the circle, and 2π . the central angle in sector 2 measures 3 138 What is the common difference of the arithmetic sequence 5,8,11,14? 8 1) 5 2) −3 3) 3 4) 9 1 139 The expression log 5 is equivalent to 25 1 1) 2 2) 2 1 3) − 2 4) −2 If darts thrown at this board are equally likely to land anywhere on the board, what is the probability that a dart that hits the board will land in either sector 1 or sector 3? 1 1) 6 1 2) 3 1 3) 2 2 4) 3 23 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 142 What is the radian measure of an angle whose measure is −420°? 7π 1) − 3 7π 2) − 6 7π 3) 6 7π 4) 3 143 The expression 1) 2) 3) 4) 1 2 5 4 1 2 4 5 3x y 3x y 9xy 9xy 4 145 Which values of x are in the solution set of the following system of equations? y = 3x − 6 y = x2 − x − 6 1) 2) 3) 4) 146 What are the values of θ in the interval 0° ≤ θ < 360° that satisfy the equation tan θ − 3 = 0? 1) 60º, 240º 2) 72º, 252º 3) 72º, 108º, 252º, 288º 4) 60º, 120º, 240º, 300º 81x 2 y 5 is equivalent to 5 2 2 5 147 The number of minutes students took to complete a quiz is summarized in the table below. 144 Three marbles are to be drawn at random, without replacement, from a bag containing 15 red marbles, 10 blue marbles, and 5 white marbles. Which expression can be used to calculate the probability of drawing 2 red marbles and 1 white marble from the bag? 15 C 2 ⋅5 C 1 1) 30 C 3 2) 3) 4) 15 15 15 0, − 4 0, 4 6, − 2 −6, 2 If the mean number of minutes was 17, which equation could be used to calculate the value of x? 119 + x 1) 17 = x 119 + 16x 2) 17 = x 446 + x 3) 17 = 26 + x 446 + 16x 4) 17 = 26 + x P 2 ⋅5 P 1 30 C 3 C 2 ⋅5 C 1 30 P 3 P 2 ⋅5 P 1 30 P 3 24 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 148 Which equation is represented by the graph below? −5 w 150 When simplified, the expression −9 w equivalent to 1) w −7 2) w 2 3) w 7 4) w 14 1 2 is 3 2 1 x − x − 4 is subtracted from 4 2 5 2 3 x − x + 1, the difference is 4 2 1 1) −x 2 + x − 5 2 1 2) x 2 − x + 5 2 2 3) −x − x − 3 4) x 2 − x − 3 151 When 1) 2) 3) 4) y = cot x y = csc x y = sec x y = tanx 152 What is the conjugate of −2 + 3i? 1) −3 + 2i 2) −2 − 3i 3) 2 − 3i 4) 3 + 2i 149 Expressed with a rational denominator and in x is simplest form, x− x 1) 2) x2 + x x x2 − x − x 3) x+ x 1−x 4) x+ x x−1 153 Expressed as a function of a positive acute angle, sin230° is equal to 1) −sin 40° 2) −sin 50° 3) sin 40° 4) sin 50° 25 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 157 The graph of y = f(x) is shown below. 1 2 mile on day 1, and mile on day 2, 3 3 1 2 and 1 miles on day 3, and 2 miles on day 4, and 3 3 this pattern continued for 3 more days. Which expression represents the total distance the jogger ran? 154 A jogger ran 7 1) ∑ 13 (2) d−1 d=1 7 2) ∑ 13 (2) d d=1 7 3) d−1 ∑ 2 13 1 d ∑ 2 3 d=1 d=1 7 4) Which set lists all the real solutions of f(x) = 0? 1) {−3,2} 2) {−2,3} 3) {−3,0,2} 4) {−2,0,3} 155 A four-digit serial number is to be created from the digits 0 through 9. How many of these serial numbers can be created if 0 can not be the first digit, no digit may be repeated, and the last digit must be 5? 1) 448 2) 504 3) 2,240 4) 2,520 158 Akeem invests $25,000 in an account that pays 4.75% annual interest compounded continuously. Using the formula A = Pe rt , where A = the amount in the account after t years, P = principal invested, and r = the annual interest rate, how many years, to the nearest tenth, will it take for Akeem’s investment to triple? 1) 10.0 2) 14.6 3) 23.1 4) 24.0 156 What is the fifteenth term of the geometric sequence − 5, 10 ,−2 5 ,. . .? 1) 2) 3) 4) −128 5 128 10 −16384 5 16384 10 26 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 159 Which relation is both one-to-one and onto? 162 Which expression, when rounded to three decimal places, is equal to −1.155? 5π 1) sec 6 2) 1) 3) 4) tan(49°20 ′) 3π sin − 5 csc(−118°) 2) 163 The solution set of the equation 1) {1} 2) {0} 3) {1,6} 4) {2,3} 3) x + 3 = 3 − x is 4) 164 What is the value of x in the equation log 5 x = 4? 1) 1.16 2) 20 3) 625 4) 1,024 160 Which two functions are inverse functions of each other? 1) f(x) = sinx and g(x) = cos(x) 2) f(x) = 3 + 8x and g(x) = 3 − 8x 3) f(x) = e x and g(x) = lnx 4) 1 f(x) = 2x − 4 and g(x) = − x + 4 2 165 The equation log a x = y where x > 0 and a > 1 is equivalent to 161 The discriminant of a quadratic equation is 24. The roots are 1) imaginary 2) real, rational, and equal 3) real, rational, and unequal 4) real, irrational, and unequal 27 y 1) 2) x =a ya = x 3) 4) a =x ax = y y Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 166 The roots of 3x 2 + x = 14 are 1) imaginary 2) real, rational, and equal 3) real, rational, and unequal 4) real, irrational, and unequal 170 Which graph represents the solution set of |6x − 7| ≤ 5? 1) 2) 3) 167 Which expression always equals 1? 1) cos 2 x − sin 2 x 2) cos 2 x + sin 2 x 3) cos x − sinx 4) cos x + sinx 4) 171 Which graph represents a function? 168 Which value is in the domain of the function graphed below, but is not in its range? 1) 2) 1) 2) 3) 4) 0 2 3 7 3) 169 For which value of k will the roots of the equation 2x 2 − 5x + k = 0 be real and rational numbers? 1) 1 2) −5 3) 0 4) 4 4) 28 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org Algebra 2/Trigonometry Multiple Choice Regents Exam Questions 172 A circle with center O and passing through the origin is graphed below. 174 What are the sum and product of the roots of the equation 6x 2 − 4x − 12 = 0? 2 1) sum = − ; product = −2 3 2 2) sum = ; product = −2 3 2 3) sum = −2; product = 3 2 4) sum = −2; product = − 3 175 What is the conjugate of What is the equation of circle O? 1) x 2 + y 2 = 2 5 1) 2) x 2 + y 2 = 20 2) 3) (x + 4) 2 + (y − 2) 2 = 2 5 (x + 4) 2 + (y − 2) 2 = 20 3) 4) 4) 173 Mrs. Hill asked her students to express the sum 1 + 3 + 5 + 7 + 9 +. . .+ 39 using sigma notation. Four different student answers were given. Which student answer is correct? 1) ∑ (2k − 1) k=1 2) 40 2) ∑ (k − 1) 3) k=2 37 3) ∑ (k + 2) 4) k = −1 39 4) 1 3 − + i 2 2 1 3 − i 2 2 3 1 + i 2 2 1 3 − − i 2 2 176 Which expression is equivalent to (5 −2 a 3 b −4 ) −1 ? 20 1) 1 3 + i? 2 2 ∑ (2k − 1) k=1 29 10b 4 a3 25b 4 a3 a3 25b 4 a2 125b 5 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 177 Expressed as a function of a positive acute angle, cos(−305°) is equal to 1) −cos 55° 2) cos 55° 3) −sin 55° 4) sin 55° 181 Which graph does not represent a function? 1) 178 How many distinct triangles can be constructed if m∠A = 30, side a = 34 , and side b = 12? 1) one acute triangle 2) one obtuse triangle 3) two triangles 4) none 2) 3) 179 In FGH , f = 6, g = 9 , and m∠H = 57. Which statement can be used to determine the numerical value of h? 1) h 2 = 6 2 + 9 2 − 2(9)(h) cos 57° 2) 3) 4) h 2 = 6 2 + 9 2 − 2(6)(9) cos 57° 6 2 = 9 2 + h 2 − 2(9)(h) cos 57° 9 2 = 6 2 + h 2 − 2(6)(h) cos 57° 4) 182 If sin θ < 0 and cot θ > 0, in which quadrant does the terminal side of angle θ lie? 1) I 2) II 3) III 4) IV 180 Which graph represents the solution set of | 4x − 5 | | > 1? | | 3 | 1) 2) 3) 183 Which value of r represents data with a strong negative linear correlation between two variables? 1) −1.07 2) −0.89 3) −0.14 4) 0.92 4) 30 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 184 The expression 1) 2) 3) 4) given m(x) = sinx , n(x) = 3x , and p(x) = x 2 ? −6x 4 5 −6x 8 5 6x 4 i 5 6x 8 i 5 185 The expression 1) 2) 3) 4) 188 Which expression is equivalent to (n m p)(x), −180x 16 is equivalent to 1) 2) 3) 4) cot x is equivalent to csc x sin(3x) 2 3sinx 2 sin 2 (3x) 3sin 2 x 189 There are eight people in a tennis club. Which expression can be used to find the number of different ways they can place first, second, and third in a tournament? 1) 8 P 3 2) 8 C 3 3) 8 P 5 4) 8 C 5 sinx cos x tanx sec x 186 What is the common difference of the arithmetic sequence below? −7x,−4x,−x,2x,5x,. . . 1) −3 2) −3x 3) 3 4) 3x 190 If the terminal side of angle θ passes through point (−3,−4), what is the value of sec θ ? 5 1) 3 5 2) − 3 5 3) 4 5 4) − 4 1 187 If sin A = , what is the value of cos 2A? 3 2 1) − 3 2 2) 3 7 3) − 9 7 4) 9 191 If logx = 2log a + log b , then x equals 1) 2) 3) 4) 31 a2b 2ab a2 + b 2a + b Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 1 3 9 195 The common ratio of the sequence − , ,− is 2 4 8 3 1) − 2 2 2) − 3 1 3) − 2 1 4) − 4 192 In a circle with a diameter of 24 cm, a central angle 4π radians intercepts an arc. The length of the of 3 arc, in centimeters, is 1) 8π 2) 9π 3) 16π 4) 32π 193 If the amount of time students work in any given week is normally distributed with a mean of 10 hours per week and a standard deviation of 2 hours, what is the probability a student works between 8 and 11 hours per week? 1) 34.1% 2) 38.2% 3) 53.2% 4) 68.2% 196 The expression 1) 2) 3) 194 Circle O has a radius of 2 units. An angle with a measure of π 4) radians is in standard position. If 6 the terminal side of the angle intersects the circle at point B, what are the coordinates of B? 3 1 , 1) 2 2 2) 3,1 1 3 3) , 2 2 4) 1, 3 3− 8 3 is equivalent to 3 −2 6 3 − 3+ 3− 2 3 6 24 3 3− 2 3 6 197 Which ordered pair is in the solution set of the system of equations shown below? y 2 − x 2 + 32 = 0 3y − x = 0 1) 2) 3) 4) 32 (2,6) (3,1) (−1,−3) (−6,−2) Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 198 If m∠θ = −50 , which diagram represents θ drawn in standard position? 200 The roots of the equation 9x 2 + 3x − 4 = 0 are 1) imaginary 2) real, rational, and equal 3) real, rational, and unequal 4) real, irrational, and unequal 4 1) 201 Which expression is equivalent to ∑ (a − n) ? 2 n=1 1) 2) 3) 4) 2a + 17 4a 2 + 30 2a 2 − 10a + 17 4a 2 − 20a + 30 2 2) 202 Yusef deposits $50 into a savings account that pays 3.25% interest compounded quarterly. The amount, A, in his account can be determined by the nt r formula A = P 1 + , where P is the initial n amount invested, r is the interest rate, n is the number of times per year the money is compounded, and t is the number of years for which the money is invested. What will his investment be worth in 12 years if he makes no other deposits or withdrawals? 1) $55.10 2) $73.73 3) $232.11 4) $619.74 3) 4) 203 How many negative solutions to the equation 2x 3 − 4x 2 + 3x − 1 = 0 exist? 1) 1 2) 2 3) 3 4) 0 199 In the interval 0° ≤ x < 360°, tanx is undefined when x equals 1) 0º and 90º 2) 90º and 180º 3) 180º and 270º 4) 90º and 270º 33 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 5 204 If sin −1 = A, then 8 5 1) sin A = 8 8 2) sin A = 5 5 3) cos A = 8 8 4) cos A = 5 206 The expression to 1) 2) 3) 4) x 2 + 9x − 22 ÷ (2 − x) is equivalent x 2 − 121 x − 11 1 x − 11 11 − x 1 11 − x 207 If f x = 2x 2 − 3x + 4, then f x + 3 is equal to 205 Which graph does not represent a function? 1) 2) 3) 4) 2x 2 − 3x + 7 2x 2 − 3x + 13 2x 2 + 9x + 13 2x 2 + 9x + 25 1) 208 The graph below shows the average price of gasoline, in dollars, for the years 1997 to 2007. 2) 3) What is the approximate range of this graph? 1) 1997 ≤ x ≤ 2007 2) 1999 ≤ x ≤ 2007 3) 0.97 ≤ y ≤ 2.38 4) 1.27 ≤ y ≤ 2.38 4) 34 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 213 What is the inverse of the function f(x) = log 4 x? 209 The amount of money in an account can be determined by the formula A = Pe rt , where P is the initial investment, r is the annual interest rate, and t is the number of years the money was invested. What is the value of a $5000 investment after 18 years, if it was invested at 4% interest compounded continuously? 1) $9367.30 2) $9869.39 3) $10,129.08 4) $10,272.17 12x 3 2x 3) 6x 2x 2 6x 2 3 2 4) 1) 2) 3) 4) 1 2 4 1 215 What is a positive value of tan x , when 2 sin x = 0.8? 1) 0.5 2) 0.4 3) 0.33 4) 0.25 16x 2 y 7 is equivalent to 7 4 2x y 2x 8 y 28 1 2 f −1 (x) = −log x 4 214 If order does not matter, which selection of students would produce the most possible committees? 1) 5 out of 15 2) 5 out of 25 3) 20 out of 25 4) 15 out of 25 3 211 The expression 4) 2) 3 3 210 The expression 27x 2 16x 4 is equivalent to 1) 12x 2 3 2 2) 3) f −1 (x) = x 4 f −1 (x) = 4 x f −1 (x) = log x 4 1) 3 216 The points (2,3), 4, , and (6,d) lie on the graph 4 of a function. If y is inversely proportional to the square of x, what is the value of d? 1) 1 1 2) 3 3) 3 4) 27 7 4 4x y 4x 8 y 28 212 The sum of the first eight terms of the series 3 − 12 + 48 − 192 + . . . is 1) −13,107 2) −21,845 3) −39,321 4) −65,535 35 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 217 A scholarship committee rewards the school's top math students. The amount of money each winner receives is inversely proportional to the number of scholarship recipients. If there are three winners, they each receive $400. If there are eight winners, how much money will each winner receive? 1) $1067 2) $400 3) $240 4) $150 221 What is the product of the roots of 4x 2 − 5x = 3? 3 1) 4 5 2) 4 3 3) − 4 5 4) − 4 218 The expression x 2 (x + 2) − (x + 2) is equivalent to 222 Liz has applied to a college that requires students to score in the top 6.7% on the mathematics portion of an aptitude test. The scores on the test are approximately normally distributed with a mean score of 576 and a standard deviation of 104. What is the minimum score Liz must earn to meet this requirement? 1) 680 2) 732 3) 740 4) 784 1) 2) 3) 4) x2 x2 − 1 x 3 + 2x 2 − x + 2 (x + 1)(x − 1)(x + 2) 219 What is the range of f(x) = |x − 3 | + 2? 1) {x | x ≥ 3} 2) {y | y ≥ 2} 3) {x | x ∈ real numbers} 4) {y | y ∈ real numbers} 223 What is the common ratio of the sequence 1 5 3 3 3 4 9 a b ,− a b , ab 5 ,. . .? 64 32 16 3b 1) − 2 2a 6b 2) − 2 a 220 What is the solution set for the equation 5x + 29 = x + 3? 1) {4} 2) {−5} 3) {4,5} 4) {−5,4} 3) 4) 36 3a 2 b 6a 2 − b − Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 224 Which graph is the solution to the inequality 4 |2x + 6| − 5 < 27? 228 The table below displays the number of siblings of each of the 20 students in a class. 1) 2) 3) 4) 225 The expression (2a) 1) 2) 3) 4) −4 What is the population standard deviation, to the nearest hundredth, for this group? 1) 1.11 2) 1.12 3) 1.14 4) 1.15 is equivalent to −8a 16 a4 2 − 4 a 1 16a 4 4 3 229 The sum of 6a 4 b 2 and simplest radical form, is 226 What is the number of degrees in an angle whose 8π ? radian measure is 5 1) 576 2) 288 3) 225 4) 113 6 2) 2a 2 b 3) 4a 6ab 2 10a 2 b 3 8 4) 162a 4 b 2 , expressed in 168a 8 b 4 3 21a 2 b 3 230 A customer will select three different toppings for a supreme pizza. If there are nine different toppings to choose from, how many different supreme pizzas can be made? 1) 12 2) 27 3) 84 4) 504 227 What is the third term in the expansion of (2x − 3) 5 ? 1) 2) 3) 4) 1) 3 720x 3 180x 3 −540x 2 −1080x 2 37 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 231 If f x = 4x 2 − x + 1, then f(a + 1) equals 1) 2) 3) 4) 235 The expression 1) 6ab 2 2) 6ab 4 3) 12ab 2 4) 12ab 4 4a − a + 6 4a 2 − a + 4 4a 2 + 7a + 6 4a 2 + 7a + 4 2 232 A population of rabbits doubles every 60 days according to the formula P = 10(2) , where P is the population of rabbits on day t. What is the value of t when the population is 320? 1) 240 2) 300 3) 660 4) 960 233 Which value of k satisfies the equation 8 3k + 4 = 4 2k − 1 ? 1) −1 9 2) − 4 3) −2 14 4) − 5 1) 2) 3) 4) 1) amplitude: −3; period: π 2) 3 amplitude: −3; period: 6π 3) amplitude: 3; period: 4) 3 4 16b 8 is equivalent to {−3,−1,2} {3,1,−2} {4,−8} {−6} 237 If d varies inversely as t, and d = 20 when t = 2, what is the value of t when d = −5? 1) 8 2) 2 3) −8 4) −2 234 What are the amplitude and the period of the graph θ 27a 3 ⋅ 236 What are the zeros of the polynomial function graphed below? t 60 represented by the equation y = −3 cos 3 ? π 3 amplitude: 3; period: 6π 38 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 239 Which values of x in the interval 0° ≤ x < 360° satisfy the equation 2sin 2 x + sin x − 1 = 0? 1) {30°,270°} 2) {30°,150°,270°} 3) {90°,210°,330°} 4) {90°,210°,270°,330°} 238 Which graph best represents the inequality y + 6 ≥ x2 − x? 240 What is the period of the graph of the equation 1 y = sin2x ? 3 1 1) 3 2) 2 3) π 4) 6π 1) 2) 241 What is the product of 1) 2) 3) 4) 3) 3 4a 2 b 4 and 3 16a 3 b 2 ? 3 4ab 2 a 2 4a 2 b 3 3 a 3 8ab 2 a 2 8a 2 b 3 3 a 242 What is the fourth term in the binomial expansion (x − 2) 8 ? 1) 2) 3) 4) 4) 39 448x 5 448x 4 −448x 5 −448x 4 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 243 What is the product of the roots of the quadratic equation 2x 2 − 7x = 5? 1) 5 5 2) 2 3) −5 5 4) − 2 246 Which arithmetic sequence has a common difference of 4? 1) {0,4n,8n,12n,. . . } 2) {n,4n,16n,64n,. . . } 3) {n + 1,n + 5,n + 9,n + 13,. . . } 4) {n + 4,n + 16,n + 64,n + 256,. . . } 247 The first four terms of the sequence defined by 1 a 1 = and a n + 1 = 1 − a n are 2 1 1 1 1 , , , 1) 2 2 2 2 1 1 ,1,1 ,2 2) 2 2 1 1 1 1 , , , 3) 2 4 8 16 1 1 1 1 ,1 ,2 ,3 4) 2 2 2 2 244 A cliff diver on a Caribbean island jumps from a height of 105 feet, with an initial upward velocity of 5 feet per second. An equation that models the height, h(t) , above the water, in feet, of the diver in time elapsed, t, in seconds, is h(t) = −16t 2 + 5t + 105. How many seconds, to the nearest hundredth, does it take the diver to fall 45 feet below his starting point? 1) 1.45 2) 1.84 3) 2.10 4) 2.72 248 What is the range of the function shown below? 2 3 245 What is the product of x − y 2 and 4 5 2 x + 3 y 2 ? 5 4 1) 2) 3) 4) 4 2 9 4 x − y 16 25 4 9 2 x− y 25 16 2 2 3 4 x − y 4 5 4 x 5 1) 2) 3) 4) 40 x≤0 x≥0 y≤0 y≥0 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 249 Which expression is equivalent to 1) 2) 3) 4) y 2x −2 y −2 4y −5 3 252 If sin A = , what is the value of cos 2A? 8 9 1) − 64 1 2) 4 23 3) 32 55 4) 64 ? 3 2x 2 2y 3 x2 2x 2 y3 x2 2y 3 253 What is the solution set of the equation 3x 5 − 48x = 0? 1) {0,±2} 2) {0,±2,3} 3) {0,±2,±2i} 4) {±2,±2i} 7 and ∠A terminates in Quadrant IV, 25 tan A equals 7 1) − 25 7 2) − 24 24 3) − 7 24 4) − 25 250 If sin A = − 254 What is the total number of points of intersection of the graphs of the equations 2x 2 − y 2 = 8 and y = x + 2? 1) 1 2) 2 3) 3 4) 0 251 Which task is not a component of an observational study? 1) The researcher decides who will make up the sample. 2) The researcher analyzes the data received from the sample. 3) The researcher gathers data from the sample, using surveys or taking measurements. 4) The researcher divides the sample into two groups, with one group acting as a control group. 3 3 2 3 255 The expression x + 1 x − 1 − x − 1 is 2 2 2 equivalent to 1) 0 2) −3x 3 x−2 3) 4 4) 3x − 2 41 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 256 What is the middle term in the expansion of x 6 − 2y ? 2 1) 2) 3) 4) 260 What is the total number of different nine-letter arrangements that can be formed using the letters in the word “TENNESSEE”? 1) 3,780 2) 15,120 3) 45,360 4) 362,880 20x 3 y 3 15 − x4y2 4 −20x 3 y 3 15 4 2 x y 4 261 Which equation represents the graph below? 1 7 2 3 5 x − x is subtracted from x 2 − x + 2, 4 4 8 8 the difference is 1 1) − x 2 − x + 2 4 1 2 x −x+2 2) 4 1 1 3) − x 2 + x + 2 4 2 1 2 1 x − x−2 4) 2 4 257 When 1) 2) 3) 4) y = −2sin 2x 1 y = −2 sin x 2 y = −2 cos 2x 1 y = −2 cos x 2 258 The scores on a standardized exam have a mean of 82 and a standard deviation of 3.6. Assuming a normal distribution, a student's score of 91 would rank 1) below the 75th percentile 2) between the 75th and 85th percentiles 3) between the 85th and 95th percentiles 4) above the 95th percentile 262 Which function is not one-to-one? 1) {(0,1),(1,2),(2,3),(3,4)} 2) {(0,0),(1,1),(2,2),(3,3)} 3) {(0,1),(1,0),(2,3),(3,2)} 4) {(0,1),(1,0),(2,0),(3,2)} 259 Which relation is not a function? 1) (x − 2) 2 + y 2 = 4 263 The equation y − 2 sin θ = 3 may be rewritten as 1) f(y) = 2 sinx + 3 2) f(y) = 2sin θ + 3 3) f(x) = 2sin θ + 3 4) f(θ) = 2sin θ + 3 2) 3) 4) x 2 + 4x + y = 4 x+y = 4 xy = 4 42 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 264 Which expression represents the third term in the expansion of (2x 4 − y) 3 ? 1) 2) 3) 4) 268 A circle is drawn to represent a pizza with a 12 inch diameter. The circle is cut into eight congruent pieces. What is the length of the outer edge of any one piece of this circle? 3π 1) 4 2) π 3π 3) 2 4) 3π −y 3 −6x 4 y 2 6x 4 y 2 2x 4 y 2 265 The ninth term of the expansion of (3x + 2y) 15 is 1) 15 C 9 (3x) 6 (2y) 9 2) 15 C 9 (3x) 9 (2y) 6 7 C 8 (3x) (2y) 269 Which equation has roots with the sum equal to 8 3) 15 4) 8 7 15 C 8 (3x) (2y) and the product equal to 1) 2) 3) 4) 266 What is the third term of the recursive sequence below? a 1 = −6 an = 1) 2) 3) 4) 1 a −n 2 n−1 1) 2) 3) 4) 267 The legs of a right triangle are represented by x + 2 and x − 2 . The length of the hypotenuse of the right triangle is represented by 2x 2 + 4 2x 2 + 4 x 2 +2 4) x2 − 2 4x 2 + 9x + 3 = 0 4x 2 + 9x − 3 = 0 4x 2 − 9x + 3 = 0 4x 2 − 9x − 3 = 0 270 If ∠A is acute and tanA = 11 − 2 5 − 2 1 − 2 −4 1) 2) 3) 3 ? 4 43 2 3 1 cot A = 3 cot A = 2 3 1 cot(90° − A) = 3 cot(90° − A) = 2 , then 3 9 4 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 275 What is the area of a parallelogram that has sides measuring 8 cm and 12 cm and includes an angle of 120°? 1) 24 3 5 271 The expression 4 + ∑ 3(k − x) is equal to k=2 1) 2) 3) 4) 58 − 4x 46 − 4x 58 − 12x 46 − 12x 2) 3) 4) 272 If f(x) = 4x − x 2 and g(x) = 1 1 , then (f g) is x 2 276 What is the solution of the inequality 9 − x 2 < 0? 1) {x | − 3 < x < 3} 2) {x | x > 3 or x < −3} 3) {x | x > 3} 4) {x | x < −3} equal to 4 1) 7 2) −2 7 3) 2 4) 4 277 What is the solution set of |x − 2| =3x + 10? 1) { } 2) −2 3) {−6} 4) {−2,−6} 273 The scores of 1000 students on a standardized test were normally distributed with a mean of 50 and a standard deviation of 5. What is the expected number of students who had scores greater than 60? 1) 1.7 2) 23 3) 46 4) 304 278 The expression 1) 2) 3) 274 Which ordered pair is a solution of the system of equations shown below? x + y = 5 4) (x + 3) + (y − 3) = 53 2 1) 2) 3) 4) 48 3 83 3 96 3 2 (2,3) (5,0) (−5,10) (−4,9) 44 4+ 11 20 + 5 11 27 4 − 11 20 − 5 11 27 5 4− 11 is equivalent to Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 279 When x 2 + 3x − 4 is subtracted from x 3 + 3x 2 − 2x , the difference is 1) x 3 + 2x 2 − 5x + 4 2) x 3 + 2x 2 + x − 4 3) −x 3 + 4x 2 + x − 4 4) −x 3 − 2x 2 + 5x + 4 1− 283 The simplest form of 1) 2) 3) 280 The equation x + y − 2x + 6y + 3 = 0 is equivalent to 1) (x − 1) 2 + (y + 3) 2 = −3 2 2) 3) 4) 2 4) (x − 1) 2 + (y + 3) 2 = 7 (x + 1) 2 + (y + 3) 2 = 7 (x + 1) 2 + (y + 3) 2 = 10 1− 4 x 2 8 − x x2 is 1 2 x x+2 x 3 x − x−2 1 284 If log b x = 3log b p − 2 log b t + log b r , then the 2 value of x is p3 1) t2 r 15 281 What is the value of tan Arc cos ? 17 8 1) 15 8 2) 17 15 3) 8 17 4) 8 2) 3) 4) 3 2 p t r 1 2 p 3 t2 r p3 t2 r 285 A doctor wants to test the effectiveness of a new drug on her patients. She separates her sample of patients into two groups and administers the drug to only one of these groups. She then compares the results. Which type of study best describes this situation? 1) census 2) survey 3) observation 4) controlled experiment 282 The quantities p and q vary inversely. If p = 20 when q = −2, and p = x when q = −2x + 2, then x equals 1) −4 and 5 20 2) 19 3) −5 and 4 1 4) − 4 45 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 286 Given the sequence: x,(x + y),(x + 2y),. . . Which expression can be used to determine the common difference of this sequence? 1) x − (x + y) 2) (x + 2y) − (x + y) x 3) (x + y) (x + 2y) 4) (x + y) 289 Which graph represents a relation that is not a function? 1) 287 The expression 1) 2) 3) 4) 7+ 1 7− 11 is equivalent to 11 38 7− 11 2) 38 7+ 11 60 7− 11 60 3) 288 If $5000 is invested at a rate of 3% interest compounded quarterly, what is the value of the investment in 5 years? (Use the formula nt r A = P 1 + , where A is the amount accrued, P n is the principal, r is the interest rate, n is the number of times per year the money is compounded, and t is the length of time, in years.) 1) $5190.33 2) $5796.37 3) $5805.92 4) $5808.08 4) 46 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 290 In which graph is θ coterminal with an angle of −70°? 292 Max solves a quadratic equation by completing the square. He shows a correct step: (x + 2) 2 = −9 What are the solutions to his equation? 1) 2 ± 3i 2) −2 ± 3i 3) 3 ± 2i 4) −3 ± 2i 1) 293 If f(x) = 2x 2 − 3x + 1 and g(x) = x + 5, what is f(g(x))? 1) 2) 3) 4) 2) 2x 2 + 17x + 36 2x 2 + 17x + 66 2x 2 − 3x + 6 2x 2 − 3x + 36 294 The roots of the equation x 2 − 10x + 25 = 0 are 1) imaginary 2) real and irrational 3) real, rational, and equal 4) real, rational, and unequal 3) 295 A population, p(x) , of wild turkeys in a certain area is represented by the function p(x) = 17(1.15) 2x , where x is the number of years since 2010. How many more turkeys will be in the population for the year 2015 than 2010? 1) 46 2) 49 3) 51 4) 68 4) 291 The domain of f(x) = − 3 is the set of all real 2−x numbers 1) greater than 2 2) less than 2 3) except 2 4) between −2 and 2 47 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 300 A video-streaming service can choose from six half-hour shows and four one-hour shows. Which expression could be used to calculate the number of different ways the service can choose four half-hour shows and two one-hour shows? 1) 6 P 4 ⋅4 P 2 2) 6 P 4 + 4 P 2 3) 6 C 4 ⋅4 C 2 4) 6 C 4 + 4 C 2 3 296 What is the value of ∑ cos n2π ? n=1 1) 2) 3) 4) 1 −1 0 1 − 2 297 A wheel has a radius of 18 inches. Which distance, to the nearest inch, does the wheel travel when it 2π radians? rotates through an angle of 5 1) 45 2) 23 3) 13 4) 11 301 What is the sum of the first 19 terms of the sequence 3,10,17,24,31,. . .? 1) 1188 2) 1197 3) 1254 4) 1292 3 302 If p varies inversely as q, and p = 10 when q = , 2 3 what is the value of p when q = ? 5 1) 25 2) 15 3) 9 4) 4 298 How many different ways can teams of four members be formed from a class of 20 students? 1) 5 2) 80 3) 4,845 4) 116,280 299 In DEF , d = 5, e = 8, and m∠D = 32. How many distinct triangles can be drawn given these measurements? 1) 1 2) 2 3) 3 4) 0 303 When x −1 + 1 is divided by x + 1, the quotient equals 1) 1 1 2) x 3) x 1 4) − x 48 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 304 The table below displays the results of a survey regarding the number of pets each student in a class has. The average number of pets per student in this class is 2. 307 Which expression is equivalent to 1) 2) 3) What is the value of k for this table? 1) 9 2) 2 3) 8 4) 4 4) x −1 y 4 3x −5 y −1 x4 y5 3 5 4 x y 3 3x 4 y 5 y4 3x 5 308 The expression log4m2 is equivalent to 1) 2(log4 + logm) 2) 2log4 + log m 3) log4 + 2logm 4) log16 + 2logm 305 Which equation could be used to solve 2 5 − = 1? x−3 x 1) x 2 − 6x − 3 = 0 2) x 2 − 6x + 3 = 0 3) x 2 − 6x − 6 = 0 4) x 2 − 6x + 6 = 0 2 309 What is the value of ∑ (3 − 2a) ? x x=0 1) 2) 3) 4) 306 The formula to determine continuously compounded interest is A = Pe rt , where A is the amount of money in the account, P is the initial investment, r is the interest rate, and t is the time, in years. Which equation could be used to determine the value of an account with an $18,000 initial investment, at an interest rate of 1.25% for 24 months? 1) A = 18,000e 1.25 • 2 2) A = 18,000e 1.25 • 24 3) A = 18,000e 0.0125 • 2 4) A = 18,000e 0.0125 • 24 4a − 2a + 12 4a 2 − 2a + 13 4a 2 − 14a + 12 4a 2 − 14a + 13 2 310 When factored completely, the expression x 3 − 2x 2 − 9x + 18 is equivalent to 1) (x 2 − 9)(x − 2) 2) (x − 2)(x − 3)(x + 3) 3) 4) 49 (x − 2) 2 (x − 3)(x + 3) (x − 3) 2 (x − 2) ? Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 311 Which value of k will make x 2 − 1 x + k a perfect 4 1 3 + x y 315 The expression is equivalent to 2 xy square trinomial? 1 1) 64 1 2) 16 1 3) 8 1 4) 4 1) 2) 3) 4) 312 What is the domain of the function g x = 3 x -1? 1) (−∞,3] 2) (−∞,3) 3) (−∞,∞) 4) (−1,∞) 3 2 3x + y 2xy 3xy 2 3x + y 2 316 The fraction 3 is equivalent to 3a 2 b 1) −1 313 Which expression is equivalent to 3x 2 ? 1 1) 3x 2 2) −3x 2 1 3) 9x 2 4) −9x 2 1 a b 2) b ab 3) 3b ab 4) 3 a 317 Expressed in simplest form, equivalent to −6y 2 + 36y − 54 1) (2y − 6)(6 − 2y) 3y − 9 2) 2y − 6 3 3) 2 3 4) − 2 314 What is the solution set for 2cos θ − 1 = 0 in the interval 0° ≤ θ < 360°? 1) {30°,150°} 2) {60°,120°} 3) {30°,330°} 4) {60°,300°} 50 3y 9 + is 2y − 6 6 − 2y Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 318 What is the solution set of the equation − 2 sec x = 2 when 0° ≤ x < 360°? 1) {45°,135°,225°,315°} 2) {45°,315°} 3) {135°,225°} 4) {225°,315°} 322 Which equation is graphed in the diagram below? 319 The sides of a parallelogram measure 10 cm and 18 cm. One angle of the parallelogram measures 46 degrees. What is the area of the parallelogram, to the nearest square centimeter? 1) 65 2) 125 3) 129 4) 162 1) 2) 3) 4) 320 What is the number of degrees in an angle whose measure is 2 radians? 360 1) 2) 3) 4) π π π y = 3 cos x + 8 30 π y = 3 cos x + 5 15 π y = −3 cos x + 8 30 π y = −3 cos x + 5 15 323 What is the solution set of the equation 5 30 ? +1= 2 x − 3 x −9 1) {2,3} 2) {2} 3) {3} 4) { } 360 360 90 321 The conjugate of the complex expression −5x + 4i is 1) 5x − 4i 2) 5x + 4i 3) −5x − 4i 4) −5x + 4i 324 What is the sum of the roots of the equation −3x 2 + 6x − 2 = 0? 2 1) 3 2) 2 2 3) − 3 4) −2 51 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 328 An arithmetic sequence has a first term of 10 and a sixth term of 40. What is the 20th term of this sequence? 1) 105 2) 110 3) 124 4) 130 325 By law, a wheelchair service ramp may be inclined no more than 4.76°. If the base of a ramp begins 15 feet from the base of a public building, which equation could be used to determine the maximum height, h, of the ramp where it reaches the building’s entrance? h 1) sin 4.76° = 15 15 2) sin 4.76° = h h 3) tan4.76° = 15 15 4) tan4.76° = h 329 If sin x = siny = a and cos x = cos y = b , then cos(x − y) is 1) 2) 3) 4) 326 What are the coordinates of the center of a circle whose equation is x 2 + y 2 − 16x + 6y + 53 = 0 ? 1) (−8,−3) 2) (−8,3) 3) (8,−3) 4) (8,3) b2 − a2 b2 + a2 2b − 2a 2b + 2a 330 The expression sin(θ + 90)° is equivalent to 1) −sin θ 2) −cos θ 3) sin θ 4) cos θ 327 A survey completed at a large university asked 2,000 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 15.7 per week. Which characteristic of the survey could create a bias in the results? 1) the size of the sample 2) the size of the population 3) the method of analyzing the data 4) the method of choosing the students who were surveyed 2 331 The expression 2 − 3 x is equivalent to 1) 4 − 9x 2) 4 − 3x 3) 4 − 12 x + 9x 4) 52 4 − 12 x + 6x Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 332 If x 2 + 2 = 6x is solved by completing the square, an intermediate step would be 1) (x + 3) 2 = 7 2) 3) 4) 336 When factored completely, x 3 + 3x 2 − 4x − 12 equals 1) (x + 2)(x − 2)(x − 3) 2) (x + 2)(x − 2)(x + 3) (x − 3) 2 = 7 (x − 3) 2 = 11 (x − 6) 2 = 34 3) 4) 337 Which transformation of y = f(x) moves the graph 7 units to the left and 3 units down? 1) y = f(x + 7) − 3 2) y = f(x + 7) + 3 3) y = f(x − 7) − 3 4) y = f(x − 7) + 3 333 If f(x) = 9 − x 2 , what are its domain and range? 1) domain: {x | − 3 ≤ x ≤ 3}; range: {y | 0 ≤ y ≤ 3} 2) domain: {x | x ≠ ±3}; range: {y | 0 ≤ y ≤ 3} 3) domain: {x | x ≤ −3 or x ≥ 3}; range: {y | y ≠ 0} 4) domain: {x | x ≠ 3}; range: {y | y ≥ 0} 334 Given angle A in Quadrant I with sin A = 12 and 13 338 A school math team consists of three juniors and five seniors. How many different groups can be formed that consist of one junior and two seniors? 1) 13 2) 15 3) 30 4) 60 3 angle B in Quadrant II with cos B = − , what is the 5 value of cos(A − B)? 33 1) 65 33 2) − 65 63 3) 65 63 4) − 65 335 The solution set of the equation 1) {−2,−4} 2) {2,4} 3) {4} 4) { } (x 2 − 4)(x + 3) (x 2 − 4)(x − 3) 339 When −3 − 2i is multiplied by its conjugate, the result is 1) −13 2) −5 3) 5 4) 13 2x − 4 = x − 2 is 53 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 340 On January 1, a share of a certain stock cost $180. Each month thereafter, the cost of a share of this stock decreased by one-third. If x represents the time, in months, and y represents the cost of the stock, in dollars, which graph best represents the cost of a share over the following 5 months? 341 Approximately how many degrees does five radians equal? 1) 286 2) 900 3) 4) π 36 5π 342 A math club has 30 boys and 20 girls. Which expression represents the total number of different 5-member teams, consisting of 3 boys and 2 girls, that can be formed? 1) 30 P 3 ⋅20 P 2 2) 30 C 3 ⋅20 C 2 3) 30 P 3 + 20 P 2 4) 30 C 3 + 20 C 2 1) 2) 343 What is the domain of the function shown below? 3) 4) 1) 2) 3) 4) 54 −1 ≤ x ≤ 6 −1 ≤ y ≤ 6 −2 ≤ x ≤ 5 −2 ≤ y ≤ 5 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 346 Which graph represents a one-to-one function? 10x 2 , then logT is equivalent to y (1 + 2logx) − logy log(1 + 2x) − logy (1 − 2logx) + logy 2(1 − logx) + logy 344 If T = 1) 2) 3) 4) 1) 345 Which graph represents the equation y = cos −1 x ? 2) 1) 3) 2) 4) 347 In parallelogram BFLO, OL = 3.8, LF = 7.4, and m∠O = 126. If diagonal BL is drawn, what is the area of BLF ? 1) 11.4 2) 14.1 3) 22.7 4) 28.1 3) 4) 55 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 348 Which expression is equivalent to 1) x y2 2) x3 y6 3) 4) 352 Which graph shows y = cos −1 x ? x −1 y 2 x2y ? −4 y2 x y6 1) x3 349 A study compared the number of years of education a person received and that person's average yearly salary. It was determined that the relationship between these two quantities was linear and the correlation coefficient was 0.91. Which conclusion can be made based on the findings of this study? 1) There was a weak relationship. 2) There was a strong relationship. 3) There was no relationship. 4) There was an unpredictable relationship. 350 The expression 1) 8a 4 2) 8a 8 3) 4a 5 3 a 4) 4a 3 3 2) 3) 64a 16 is equivalent to a5 4) 351 The expression (x + i) 2 − (x − i) 2 is equivalent to 1) 0 2) −2 3) −2 + 4xi 4) 4xi 56 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 353 What is the common difference in the sequence 2a + 1, 4a + 4, 6a + 7, 8a + 10, . . .? 1) 2a + 3 2) −2a − 3 3) 2a + 5 4) −2a + 5 357 As shown in the table below, a person’s target heart rate during exercise changes as the person gets older. 354 If x = 3i , y = 2i , and z = m + i, the expression xy 2 z equals 1) −12 − 12mi 2) −6 − 6mi 3) 12 − 12mi 4) 6 − 6mi 1 2 355 What is the value of 4x + x + x 1 1) 7 2 1 2) 9 2 1 3) 16 2 1 4) 17 2 0 − 1 4 Which value represents the linear correlation coefficient, rounded to the nearest thousandth, between a person’s age, in years, and that person’s target heart rate, in beats per minute? 1) −0.999 2) −0.664 3) 0.998 4) 1.503 when x = 16? 358 The table of values below can be modeled by which equation? 356 What is the graph of the solution set of |2x − 1| > 5? 1) 2) 3) 4) 1) 2) 3) 4) 57 f(x) = f(x) = f(y) = f(y) = |x + 3 | |x | + 3 | y + 3| |y| + 3 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 3 3 = , then k is 361 If tan Arc cos k 3 1) 1 2) 2 3) 2 4) 3 2 359 In the diagram below, the length of which line segment is equal to the exact value of sin θ ? 1) 2) 3) 4) 362 How many distinct ways can the eleven letters in the word "TALLAHASSEE" be arranged? 1) 831,600 2) 1,663,200 3) 3,326,400 4) 5,702,400 TO TS OR OS 3 , what are the domain and range? x−4 {x | x > 4} and {y | y > 0} {x | x ≥ 4} and {y | y > 0} {x | x > 4} and {y | y ≥ 0} {x | x ≥ 4} and {y | y ≥ 0} 363 For y = 1) 2) 3) 4) 360 The table below shows five numbers and their frequency of occurrence. 364 Two sides of a triangular-shaped sandbox measure 22 feet and 13 feet. If the angle between these two sides measures 55°, what is the area of the sandbox, to the nearest square foot? 1) 82 2) 117 3) 143 4) 234 The interquartile range for these data is 1) 7 2) 5 3) 7 to 12 4) 6 to 13 58 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 365 Expressed in simplest form, 1) 2) 3) 4) − −7 −i 7i −18 − −32 is 369 What is the equation of the graph shown below? 2 2 2 2 366 How many different 11-letter arrangements are possible using the letters in the word “ARRANGEMENT”? 1) 2,494,800 2) 4,989,600 3) 19,958,400 4) 39,916,800 2) y = 2x y = 2 −x 3) x=2 y 4) x=2 −y 1) 367 A spinner is divided into eight equal sections. Five sections are red and three are green. If the spinner is spun three times, what is the probability that it lands on red exactly twice? 25 1) 64 45 2) 512 75 3) 512 225 4) 512 x 1 − expressed as a single x − 1 2 − 2x fraction? x+1 1) x−1 2x − 1 2) 2 − 2x 2x + 1 3) 2(x − 1) 2x − 1 4) 2(x − 1) 370 What is 368 When factored completely, the expression 3x 3 − 5x 2 − 48x + 80 is equivalent to 1) (x 2 − 16)(3x − 5) 2) 3) 4) (x 2 + 16)(3x − 5)(3x + 5) (x + 4)(x − 4)(3x − 5) (x + 4)(x − 4)(3x − 5)(3x − 5) 371 The value of sin(180 + x) is equivalent to 1) −sinx 2) −sin(90 − x) 3) sinx 4) sin(90 − x) 59 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 372 The expression 1) 2) 3) 4) 1 + cos 2A is equivalent to sin2A cot A tanA sec A 1 + cot 2A 373 What is the period of the graph y = 1) 2) 3) 4) 376 Susie invests $500 in an account that is compounded continuously at an annual interest rate of 5%, according to the formula A = Pe rt , where A is the amount accrued, P is the principal, r is the rate of interest, and t is the time, in years. Approximately how many years will it take for Susie’s money to double? 1) 1.4 2) 6.0 3) 13.9 4) 14.7 π 1 sin6x ? 2 6 π 377 The area of triangle ABC is 42. If AB = 8 and m∠B = 61, the length of BC is approximately 1) 5.1 2) 9.2 3) 12.0 4) 21.7 3 π 2 6π 374 What is the fourth term of the sequence defined by a 1 = 3xy 5 378 The value of csc 138°23′ rounded to four decimal places is 1) −1.3376 2) −1.3408 3) 1.5012 4) 1.5057 2x a n = a n − 1 ? y 1) 2) 3) 4) 12x 3 y 3 24x 2 y 4 24x 4 y 2 48x 5 y 379 Given y varies inversely as x, when y is multiplied 1 by , then x is multiplied by 2 1 1) 2 2) 2 1 3) − 2 4) −2 375 A theater has 35 seats in the first row. Each row has four more seats than the row before it. Which expression represents the number of seats in the nth row? 1) 35 + (n + 4) 2) 35 + (4n) 3) 35 + (n + 1)(4) 4) 35 + (n − 1)(4) 60 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 380 The expression x(3i 2 ) 3 + 2xi 12 is equivalent to 1) 2x + 27xi 2) −7x 3) −25x 4) −29x 383 In a certain high school, a survey revealed the mean amount of bottled water consumed by students each day was 153 bottles with a standard deviation of 22 bottles. Assuming the survey represented a normal distribution, what is the range of the number of bottled waters that approximately 68.2% of the students drink? 1) 131 − 164 2) 131 − 175 3) 142 − 164 4) 142 − 175 381 Which equation is represented by the graph below? 384 The terminal side of an angle measuring 4π 5 radians lies in Quadrant 1) I 2) II 3) III 4) IV 1) 2) 3) 4) (x − 3) 2 + (y + 1) 2 (x + 3) 2 + (y − 1) 2 (x − 1) 2 + (y + 3) 2 (x + 3) 2 + (y − 1) 2 =5 =5 = 13 = 13 1 − 385 Which expression is equivalent to 9x 2 y 6 2 ? 1 1) 3xy 3 2) 3) 382 If log x − log 2a = log3a , then logx expressed in terms of loga is equivalent to 1 log 5a 1) 2 1 log 6 + log a 2) 2 3) log6 + loga 4) log6 + 2loga 2 4) 3xy 3 3 xy 3 xy 3 3 386 How many full cycles of the function y = 3 sin2x appear in radians? 1) 1 2) 2 3) 3 4) 4 61 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 387 If 2x 3 = y, then logy equals 1) log(2x) + log3 2) 3log(2x) 3) 3log2 + 3 logx 4) log2 + 3logx 391 If f(x) = 2x 2 + 1 and g(x) = 3x − 2, what is the value of f(g( − 2))? 1) −127 2) −23 3) 25 4) 129 x 1 x 1 388 What is the product of − and + ? 4 3 4 3 x2 1 − 1) 8 9 2) 3) 4) b c is equivalent to 392 The expression b d− c c+1 1) d−1 a +b 2) d −b ac + b 3) cd − b ac + 1 4) cd − 1 a+ x2 1 − 16 9 x2 x 1 − − 8 6 9 x2 x 1 − − 16 6 9 389 In the right triangle shown below, what is the measure of angle S, to the nearest minute? 1) 2) 3) 4) 393 Which equation is represented by the graph below? 28°1' 28°4' 61°56' 61°93' 1) 2) 390 What is the product of the roots of x 2 − 4x + k = 0 if one of the roots is 7? 1) 21 2) −11 3) −21 4) −77 3) 4) 62 y = 2 cos 3x y = 2 sin3x 2π y = 2 cos x 3 2π y = 2 sin x 3 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 394 Which graph represents the solution set of x + 16 ≤ 7? x−2 398 What is the common ratio of the geometric sequence shown below? −2,4,−8,16,. . . 1 1) − 2 2) 2 3) −2 4) −6 1) 2) 3) 4) 399 The exact value of csc 120° is 395 Angle θ is in standard position and (−4,0) is a point on the terminal side of θ . What is the value of sec θ ? 1) −4 2) −1 3) 0 4) undefined 1) 2) 3) 4) 1) 1) 2) 3) 4) 2 3 3 −2 − 400 Which ratio represents csc A in the diagram below? 396 How many different six-letter arrangements can be made using the letters of the word “TATTOO”? 1) 60 2) 90 3) 120 4) 720 397 If cos θ = 2 3 3 2 3 , then what is cos 2θ ? 4 2) 1 8 9 16 1 − 8 3 2 3) 4) 63 25 24 25 7 24 7 7 24 Algebra 2/Trigonometry Multiple Choice Regents Exam Questions www.jmap.org 401 The function f(x) = tanx is defined in such a way 1 1 x + 8 and h(x) = x − 2, what is the 2 2 value of g(h( − 8))? 1) 0 2) 9 3) 5 4) 4 404 If g(x) = −1 that f (x) is a function. What can be the domain of f(x)? 1) {x | 0 ≤ x ≤ π } 2) {x | 0 ≤ x ≤ 2π } π π 3) x | − < x < 2 2 π 3π 4) x | − < x < 2 2 402 If log2 = a and log3 = b , the expression log 405 A sequence has the following terms: a 1 = 4, a 2 = 10, a 3 = 25, a 4 = 62.5. Which formula represents the nth term in the sequence? 1) a n = 4 + 2.5n 2) a n = 4 + 2.5(n − 1) 9 is 20 equivalent to 1) 2b − a + 1 2) 2b − a − 1 3) b 2 − a + 10 2b 4) a+1 403 The expression 1) 2) 3) 4) 2x + 4 is equivalent to x+2 (2x + 4) x − 2 x−2 (2x + 4) x − 2 x−4 2 x−2 2 x+2 64 3) a n = 4(2.5) n 4) a n = 4(2.5) n − 1 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org Algebra 2/Trigonometry 2 Point Regents Exam Questions 412 Express xi 8 − yi 6 in simplest form. 406 Find, to the nearest tenth of a square foot, the area of a rhombus that has a side of 6 feet and an angle of 50°. 413 If x is a real number, express 2xi(i − 4i 2 ) in simplest a + bi form. 3 407 Evaluate: ∑ (−n 4 − n) n=1 414 The graph below represents the function y = f(x) . 408 The probability of Ashley being the catcher in a 2 softball game is . Calculate the exact probability 5 that she will be the catcher in exactly five of the next six games. 409 Find the solution of the inequality x 2 − 4x > 5, algebraically. 410 Find the total number of different twelve-letter arrangements that can be formed using the letters in the word PENNSYLVANIA. State the domain and range of this function. 415 Express the sum 7 + 14 + 21 + 28 +. . .+ 105 using sigma notation. 411 A committee of 5 members is to be randomly selected from a group of 9 teachers and 20 students. Determine how many different committees can be formed if 2 members must be teachers and 3 members must be students. 416 Prove that the equation shown below is an identity for all values for which the functions are defined: csc θ ⋅ sin 2 θ ⋅ cot θ = cos θ 65 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 422 Solve the equation 2tan C − 3 = 3tan C − 4 algebraically for all values of C in the interval 0° ≤ C < 360°. 417 Solve algebraically for x: 5 4x = 125 x − 1 418 Write an equation of the circle shown in the graph below. 423 Howard collected fish eggs from a pond behind his house so he could determine whether sunlight had an effect on how many of the eggs hatched. After he collected the eggs, he divided them into two tanks. He put both tanks outside near the pond, and he covered one of the tanks with a box to block out all sunlight. State whether Howard's investigation was an example of a controlled experiment, an observation, or a survey. Justify your response. 424 Express in simplest form: 3 a6b9 −64 425 Find the number of possible different 10-letter arrangements using the letters of the word “STATISTICS.” 419 Find the third term in the recursive sequence a k + 1 = 2a k − 1, where a 1 = 3. 420 Use the discriminant to determine all values of k that would result in the equation x 2 − kx + 4 = 0 having equal roots. 426 The following is a list of the individual points scored by all twelve members of the Webster High School basketball team at a recent game: 2 2 3 4 6 7 9 10 10 11 12 14 Find the interquartile range for this set of data. 421 If f(x) = x 2 − 6, find f −1 (x). 427 Solve algebraically for x: 66 2x + 1 + 4 = 8 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 1 1 3 428 Express the product of y 2 − y and 12y + 3 5 2 as a trinomial. 434 Solve sec x − 2 = 0 algebraically for all values of x in 0° ≤ x < 360°. 5 435 Evaluate: 10 + 429 Determine, to the nearest minute, the degree 5 π radians. measure of an angle of 11 ∑ (n 3 − 1) n=1 436 The table below shows the concentration of ozone in Earth’s atmosphere at different altitudes. Write the exponential regression equation that models these data, rounding all values to the nearest thousandth. 430 Show that sec θ sin θ cot θ = 1 is an identity. 431 Solve |−4x + 5| < 13 algebraically for x. 432 Find, to the nearest tenth of a degree, the angle whose measure is 2.5 radians. 433 A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a 10-minute period. 437 The area of a parallelogram is 594, and the lengths of its sides are 32 and 46. Determine, to the nearest tenth of a degree, the measure of the acute angle of the parallelogram. cot x sin x as a single trigonometric sec x function, in simplest form, for all values of x for which it is defined. 438 Express Write an exponential regression equation for the data, rounding all values to the nearest thousandth. 67 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 439 Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of 83°50'. 442 Express the product of cos 30° and sin 45° in simplest radical form. 443 On the axes below, for −2 ≤ x ≤ 2, graph y = 2x + 1 − 3. 440 On the unit circle shown in the diagram below, sketch an angle, in standard position, whose degree measure is 240 and find the exact value of sin240°. 444 The formula for continuously compounded interest is A = Pe rt , where A is the amount of money in the account, P is the initial investment, r is the interest rate, and t is the time in years. Using the formula, determine, to the nearest dollar, the amount in the account after 8 years if $750 is invested at an annual rate of 3%. 445 Solve algebraically for the exact value of x: log 8 16 = x + 1 441 In a circle, an arc length of 6.6 is intercepted by a 2 central angle of radians. Determine the length of 3 the radius. 68 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 452 Given the equation 3x 2 + 2x + k = 0, state the sum and product of the roots. 446 Find, to the nearest tenth, the radian measure of 216º. 2 . 3 Determine the probability, expressed as a fraction, of winning exactly four games if seven games are played. 447 The probability of winning a game is 453 Express 5 with a rational denominator, in 3− 2 simplest radical form. 454 Multiply x + yi by its conjugate, and express the product in simplest form. 448 Find, algebraically, the measure of the obtuse angle, to the nearest degree, that satisfies the equation 5csc θ = 8. 455 Express 108x 5 y 8 in simplest radical form. 6xy 5 449 Determine the sum of the first twenty terms of the sequence whose first five terms are 5, 14, 23, 32, 41. 456 If sec(a + 15)° =csc(2a)°, find the smallest positive value of a, in degrees. 450 In a study of 82 video game players, the researchers found that the ages of these players were normally distributed, with a mean age of 17 years and a standard deviation of 3 years. Determine if there were 15 video game players in this study over the age of 20. Justify your answer. 457 Solve algebraically for x: 4 − 2x − 5 = 1 458 The number of bacteria present in a Petri dish can be modeled by the function N = 50e 3t , where N is the number of bacteria present in the Petri dish after t hours. Using this model, determine, to the nearest hundredth, the number of hours it will take for N to reach 30,700. 451 On a test that has a normal distribution of scores, a score of 57 falls one standard deviation below the mean, and a score of 81 is two standard deviations above the mean. Determine the mean score of this test. 69 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 464 If f(x) = x 2 − x and g(x) = x + 1, determine f(g(x)) in simplest form. 459 The scores of one class on the Unit 2 mathematics test are shown in the table below. 2 2 465 Express x − 1 as a trinomial. 3 466 The function f(x) is graphed on the set of axes below. On the same set of axes, graph f(x + 1) + 2. Find the population standard deviation of these scores, to the nearest tenth. 460 Matt places $1,200 in an investment account earning an annual rate of 6.5%, 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 Matt will have in the account after 10 years. 461 Determine the sum and the product of the roots of the equation 12x 2 + x − 6 = 0. 467 Find, to the nearest minute, the angle whose measure is 3.45 radians. 462 Express the exact value of csc 60°, with a rational denominator. 468 Solve algebraically for the exact values of x: 5x 1 x = + x 4 2 463 Solve |2x − 3| > 5 algebraically. 70 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 469 Factor the expression 12t 8 − 75t 4 completely. 474 Convert 2.5 radians to degrees, and express the answer to the nearest minute. 470 Determine which set of data given below has the stronger linear relationship between x and y. Justify your choice. 475 If g(x) = ax form. 2 1 − x , express g(10) in simplest 476 The two sides and included angle of a parallelogram are 18, 22, and 60°. Find its exact area in simplest form. 471 Write an equation of the circle shown in the diagram below. 477 Express 4xi + 5yi 8 + 6xi 3 + 2yi 4 in simplest a + bi form. 478 If f(x) = x 2 − 6 and g(x) = 2 x − 1, determine the value of (g f)(−3). 479 Determine the area, to the nearest integer, of SRO shown below. 472 Assume that the ages of first-year college students are normally distributed with a mean of 19 years and standard deviation of 1 year. To the nearest integer, find the percentage of first-year college students who are between the ages of 18 years and 20 years, inclusive. To the nearest integer, find the percentage of first-year college students who are 20 years old or older. 480 Convert 3 radians to degrees and express the answer to the nearest minute. 473 If log x + 1 64 = 3, find the value of x. 71 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 4 3 5 2 7 x − x + x is 8 9 3 3 2 subtracted from 2x 3 + x 2 − . 4 9 488 Solve algebraically for x: log5x − 1 4 = 481 Find the difference when 1 3 489 Write an equation for the graph of the trigonometric function shown below. 482 Show that sec 2 x − 1 is equivalent to sin 2 x. 2 sec x 483 Solve the equation 6x 2 − 2x − 3 = 0 and express the answer in simplest radical form. 36 − x 2 (x + 6) 2 484 Express in simplest form: x−3 2 x + 3x − 18 490 Determine the sum and the product of the roots of 3x 2 = 11x − 6. 485 Determine how many eleven-letter arrangements can be formed from the word "CATTARAUGUS." 491 For a given set of rectangles, the length is inversely proportional to the width. In one of these rectangles, the length is 12 and the width is 6. For this set of rectangles, calculate the width of a rectangle whose length is 9. 486 The probability that Kay and Joseph Dowling will have a redheaded child is 1 out of 4. If the Dowlings plan to have three children, what is the exact probability that only one child will have red hair? 492 Factor completely: x 3 + 3x 2 + 2x + 6 493 Determine, to the nearest minute, the number of degrees in an angle whose measure is 2.5 radians. 487 Starting with sin 2 A + cos 2 A = 1, derive the formula tan 2 A + 1 = sec 2 A . 72 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 494 The graph of the equation y = 1 x has an 2 498 Solve algebraically for x: log 27 (2x − 1) = asymptote. On the grid below, sketch the graph of 1 x y = and write the equation of this asymptote. 2 499 Simplify the expression 4 3 3x −4 y 5 and write the (2x 3 y −7 ) −2 answer using only positive exponents. 500 Two sides of a parallelogram are 24 feet and 30 feet. The measure of the angle between these sides is 57°. Find the area of the parallelogram, to the nearest square foot. 501 Factor completely: 10ax 2 − 23ax − 5a 502 Determine algebraically the x-coordinate of all points where the graphs of xy = 10 and y = x + 3 intersect. 495 Express 5 3x 3 − 2 27x 3 in simplest radical form. 503 In an arithmetic sequence, a 4 = 19 and a 7 = 31. Determine a formula for a n , the n th term of this sequence. 496 A blood bank needs twenty people to help with a blood drive. Twenty-five people have volunteered. Find how many different groups of twenty can be formed from the twenty-five volunteers. 504 Solve for x: 497 Express cos θ(sec θ − cos θ), in terms of sin θ . 73 1 = 2 3x − 1 16 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 505 In a certain school, the heights of the population of girls are normally distributed, with a mean of 63 inches and a standard deviation of 2 inches. If there are 450 girls in the school, determine how many of the girls are shorter than 60 inches. Round the answer to the nearest integer. 510 If p and q vary inversely and p is 25 when q is 6, determine q when p is equal to 30. 511 Express −130° in radian measure, to the nearest hundredth. 506 Determine the value of n in simplest form: i 13 + i 18 + i 31 + n = 0 507 Solve for x: 512 Solve algebraically for x: 16 2x + 3 = 64 x + 2 12 4x = 2+ x −3 x−3 513 On a multiple-choice test, Abby randomly guesses on all seven questions. Each question has four choices. Find the probability, to the nearest thousandth, that Abby gets exactly three questions correct. 508 A circle shown in the diagram below has a center of (−5,3) and passes through point (−1,7). 514 Solve e 4x = 12 algebraically for x, rounded to the nearest hundredth. 515 Find the first four terms of the recursive sequence defined below. a 1 = −3 a n = a (n − 1) − n 1 4 − 2 d 516 Express in simplest form: 3 1 + d 2d Write an equation that represents the circle. 509 Factor completely: x 3 − 6x 2 − 25x + 150 74 Algebra 2/Trigonometry 2 Point Regents Exam Questions www.jmap.org 517 The table below shows the number of new stores in a coffee shop chain that opened during the years 1986 through 1994. 4 521 Simplify: ∑ x − a a=1 2 . 522 If θ is an angle in standard position and its terminal side passes through the point (−3,2), find the exact value of csc θ . 523 Find the sum and product of the roots of the equation 5x 2 + 11x − 3 = 0. Using x = 1 to represent the year 1986 and y to represent the number of new stores, write the exponential regression equation for these data. Round all values to the nearest thousandth. 524 The heights, in inches, of 10 high school varsity basketball players are 78, 79, 79, 72, 75, 71, 74, 74, 83, and 71. Find the interquartile range of this data set. 525 Determine the solution of the inequality |3 − 2x| ≥ 7. [The use of the grid below is optional.] 518 In triangle ABC, determine the number of distinct triangles that can be formed if m∠A = 85, side a = 8, and side c = 2. Justify your answer. 519 Write a quadratic equation such that the sum of its roots is 6 and the product of its roots is −27. 520 Evaluate e x ln y when x = 3 and y = 2 . 75 Algebra 2/Trigonometry 4 Point Regents Exam Questions www.jmap.org Algebra 2/Trigonometry 4 Point Regents Exam Questions 526 Solve x 3 + 5x 2 = 4x + 20 algebraically. 531 Solve algebraically for all values of x: log (x + 4) (17x − 4) = 2 527 Express as a single fraction the exact value of sin75°. 3 532 If log 4 x = 2.5 and log y 125 = − , find the numerical 2 x value of , in simplest form. y 528 Solve algebraically for all exact values of x in the interval 0 ≤ x < 2π : 2sin2 x + 5sinx = 3 533 The probability that the Stormville Sluggers will 2 win a baseball game is . Determine the 3 probability, to the nearest thousandth, that the Stormville Sluggers will win at least 6 of their next 8 games. 529 The data collected by a biologist showing the growth of a colony of bacteria at the end of each hour are displayed in the table below. 534 The periodic graph below can be represented by the trigonometric equation y = a cos bx + c where a, b, and c are real numbers. Write an exponential regression equation to model these data. Round all values to the nearest thousandth. Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of bacteria in the colony at the end of 7 hours. State the values of a, b, and c, and write an equation for the graph. 530 Solve the equation 8x 3 + 4x 2 − 18x − 9 = 0 algebraically for all values of x. 76 Algebra 2/Trigonometry 4 Point Regents Exam Questions www.jmap.org 535 Solve the equation cos 2x = cos x algebraically for all values of x in the interval 0° ≤ x < 360°. 539 Solve algebraically for x: 536 A ranch in the Australian Outback is shaped like triangle ACE, with m∠A = 42, m∠E = 103 , and AC = 15 miles. Find the area of the ranch, to the nearest square mile. 540 Solve the equation below algebraically, and express the result in simplest radical form: 13 = 10 − x x 537 Find the exact roots of x 2 + 10x − 8 = 0 by completing the square. 541 The letters of any word can be rearranged. Carol believes that the number of different 9-letter arrangements of the word “TENNESSEE” is greater than the number of different 7-letter arrangements of the word “VERMONT.” Is she correct? Justify your answer. 538 A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The number of organisms at a given time is recorded in the table below. x 2 3 + = − x+2 x x+2 542 In ABC , m∠A = 32, a = 12, and b = 10. Find the measures of the missing angles and side of ABC . Round each measure to the nearest tenth. 543 The table below shows the results of an experiment involving the growth of bacteria. Write a power regression equation for this set of data, rounding all values to three decimal places. Using this equation, predict the bacteria’s growth, to the nearest integer, after 15 minutes. Determine the exponential regression equation model for these data, rounding all values to the nearest ten-thousandth. Using this equation, predict the number of single-celled organisms, to the nearest whole number, at the end of the 18th hour. 77 Algebra 2/Trigonometry 4 Point Regents Exam Questions www.jmap.org 544 Solve 2x 2 − 12x + 4 = 0 by completing the square, expressing the result in simplest radical form. 549 During a particular month, a local company surveyed all its employees to determine their travel times to work, in minutes. The data for all 15 employees are shown below. 25 55 40 65 29 45 59 35 25 37 52 30 8 40 55 3 1+ x 545 Express in simplest terms: 5 24 1− − 2 x x 546 Solve algebraically for x: Determine the number of employees whose travel time is within one standard deviation of the mean. 1 2 4 − = x + 3 3 − x x2 − 9 550 Use the recursive sequence defined below to express the next three terms as fractions reduced to lowest terms. a1 = 2 −2 a n = 3 a n − 1 547 As shown in the diagram below, fire-tracking station A is 100 miles due west of fire-tracking station B. A forest fire is spotted at F, on a bearing 47° northeast of station A and 15° northeast of station B. Determine, to the nearest tenth of a mile, the distance the fire is from both station A and station B. [N represents due north.] 551 The diagram below shows the plans for a cell phone tower. A guy wire attached to the top of the tower makes an angle of 65 degrees with the ground. From a point on the ground 100 feet from the end of the guy wire, the angle of elevation to the top of the tower is 32 degrees. Find the height of the tower, to the nearest foot. 548 Whenever Sara rents a movie, the probability that it is a horror movie is 0.57. Of the next five movies she rents, determine the probability, to the nearest hundredth, that no more than two of these rentals are horror movies. 552 Solve algebraically for x: |3x − 5| − x < 17 78 Algebra 2/Trigonometry 4 Point Regents Exam Questions www.jmap.org 553 Circle O shown below has a radius of 12 centimeters. To the nearest tenth of a centimeter, determine the length of the arc, x, subtended by an angle of 83°50'. 557 Find the measure of the smallest angle, to the nearest degree, of a triangle whose sides measure 28, 47, and 34. 5 and angles A and B 41 are in Quadrant I, find the value of tan(A + B) . 558 If tanA = 2 and sin B = 3 559 Write the binomial expansion of (2x − 1) 5 as a polynomial in simplest form. 554 Solve the inequality −3 |6 − x| < −15 for x. Graph the solution on the line below. 560 The members of a men’s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 60%. If there are 10 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black? 555 Because Sam’s backyard gets very little sunlight, the probability that a geranium planted there will flower is 0.28. Sam planted five geraniums. Determine the probability, to the nearest thousandth, that at least four geraniums will flower. 561 The table below gives the relationship between x and y. Use exponential regression to find an equation for y as a function of x, rounding all values to the nearest hundredth. Using this equation, predict the value of x if y is 426.21, rounding to the nearest tenth. [Only an algebraic solution can receive full credit.] 556 In a triangle, two sides that measure 8 centimeters and 11 centimeters form an angle that measures 82°. To the nearest tenth of a degree, determine the measure of the smallest angle in the triangle. 79 Algebra 2/Trigonometry 4 Point Regents Exam Questions www.jmap.org 562 Ten teams competed in a cheerleading competition at a local high school. Their scores were 29, 28, 39, 37, 45, 40, 41, 38, 37, and 48. How many scores are within one population standard deviation from the mean? For these data, what is the interquartile range? 567 The measures of the angles between the resultant and two applied forces are 60° and 45°, and the magnitude of the resultant is 27 pounds. Find, to the nearest pound, the magnitude of each applied force. 568 The table below shows the final examination scores for Mr. Spear’s class last year. 563 A study shows that 35% of the fish caught in a local lake had high levels of mercury. Suppose that 10 fish were caught from this lake. Find, to the nearest tenth of a percent, the probability that at least 8 of the 10 fish caught did not contain high levels of mercury. 564 The table below shows the amount of a decaying radioactive substance that remained for selected years after 1990. Find the population standard deviation based on these data, to the nearest hundredth. Determine the number of students whose scores are within one population standard deviation of the mean. Write an exponential regression equation for this set of data, rounding all values to the nearest thousandth. Using this equation, determine the amount of the substance that remained in 2002, to the nearest integer. 4 − x2 x 2 + 7x + 12 569 Express in simplest form: 2x − 4 x+3 565 Solve the equation 2x 3 − x 2 − 8x + 4 = 0 algebraically for all values of x. 570 Find all values of θ in the interval 0° ≤ θ < 360° that satisfy the equation sin2θ = sin θ . 566 The probability that a professional baseball player 1 will get a hit is . Calculate the exact probability 3 that he will get at least 3 hits in 5 attempts. 80 Algebra 2/Trigonometry 6 Point Regents Exam Questions www.jmap.org Algebra 2/Trigonometry 6 Point Regents Exam Questions 571 Solve algebraically for all values of x: 81 x 3 + 2x 2 = 27 576 Solve algebraically for all values of x: log (x + 3) (2x + 3) + log (x + 3) (x + 5) = 2 5x 3 577 The temperature, T, of a given cup of hot chocolate after it has been cooling for t minutes can best be modeled by the function below, where T 0 is the temperature of the room and k is a constant. ln(T − T 0 ) = −kt + 4.718 A cup of hot chocolate is placed in a room that has a temperature of 68°. After 3 minutes, the temperature of the hot chocolate is 150°. Compute the value of k to the nearest thousandth. [Only an algebraic solution can receive full credit.] Using this value of k, find the temperature, T, of this cup of hot chocolate if it has been sitting in this room for a total of 10 minutes. Express your answer to the nearest degree. [Only an algebraic solution can receive full credit.] 572 Two forces of 40 pounds and 28 pounds act on an object. The angle between the two forces is 65°. Find the magnitude of the resultant force, to the nearest pound. Using this answer, find the measure of the angle formed between the resultant and the smaller force, to the nearest degree. 573 In a triangle, two sides that measure 6 cm and 10 cm form an angle that measures 80°. Find, to the nearest degree, the measure of the smallest angle in the triangle. 574 A homeowner wants to increase the size of a rectangular deck that now measures 14 feet by 22 feet. The building code allows for a deck to have a maximum area of 800 square feet. If the length and width are increased by the same number of feet, find the maximum number of whole feet each dimension can be increased and not exceed the building code. [Only an algebraic solution can receive full credit.] 578 Solve algebraically for x: x 2 + x − 1 + 11x = 7x + 3 579 Solve algebraically for all values of x: x 4 + 4x 3 + 4x 2 = −16x 575 Solve algebraically, to the nearest hundredth, for all values of x: log 2 (x 2 − 7x + 12) − log 2 (2x − 10) = 3 580 Two forces of 25 newtons and 85 newtons acting on a body form an angle of 55°. Find the magnitude of the resultant force, to the nearest hundredth of a newton. Find the measure, to the nearest degree, of the angle formed between the resultant and the larger force. 81 Algebra 2/Trigonometry 6 Point Regents Exam Questions www.jmap.org 584 In the interval 0° ≤ θ < 360°, solve the equation 5cos θ = 2sec θ − 3 algebraically for all values of θ , to the nearest tenth of a degree. 581 Given: DC = 10, AG = 15, BE = 6 , FE = 10 , m∠ABG = 40, m∠GBD = 90, m∠C < 90 , BE ≅ ED , and GF ≅ FB 585 Solve algebraically for x: log x + 3 Find m∠A to the nearest tenth. Find BC to the nearest tenth. 582 Solve the following systems of equations algebraically: 5 = y − x 4x 2 = −17x + y + 4 583 Perform the indicated operations and simplify completely: x 2 + 2x − 8 x 3 − 3x 2 + 6x − 18 2x − 4 ⋅ ÷ x 4 − 3x 3 x 2 − 4x 16 − x 2 82 x3 + x − 2 =2 x ID: A Algebra 2/Trigonometry Multiple Choice Regents Exam Questions Answer Section 1 ANS: TOP: 2 ANS: TOP: 3 ANS: TOP: 4 ANS: TOP: 5 ANS: 2π = b 3 PTS: 2 REF: Angle Sum and Difference Identities 4 PTS: 2 REF: Domain and Range KEY: 2 PTS: 2 REF: Analysis of Data 2 PTS: 2 REF: Solving Quadratics KEY: 2 2π 3 fall0910a2 STA: A2.A.76 KEY: simplifying 061112a2 STA: A2.A.39 real domain, quadratic 061301a2 STA: A2.S.1 061122a2 STA: A2.A.24 completing the square PTS: 2 REF: 061111a2 STA: A2.A.69 TOP: Properties of Graphs of Trigonometric Functions 6 ANS: 1 12 2 − 6 2 = 108 = 36 3 = 6 3 . cot J = A 6 = ⋅ O 6 3 PTS: 2 REF: 011120a2 STA: A2.A.55 7 ANS: 4 PTS: 2 REF: 011111a2 TOP: Conjugates of Complex Numbers 8 ANS: 2 PTS: 2 REF: 061218a2 TOP: Defining Functions 9 ANS: 1 −300° + 360° =60°, which terminates in Quadrant I. PTS: 2 REF: 011602a2 10 ANS: 4 PTS: 2 TOP: Domain and Range 11 ANS: 4 PTS: 2 TOP: Analysis of Data 12 ANS: 1 2i 2 + 3i 3 = 2(−1) + 3(−i) = −2 − 3i PTS: 2 13 ANS: 4 (3 + 5)(3 − REF: 081004a2 5) = 9 − KEY: period 3 3 = 3 3 TOP: Trigonometric Ratios STA: A2.N.8 STA: A2.A.43 STA: A2.A.60 REF: 061427a2 TOP: Unit Circle STA: A2.A.63 REF: 011406a2 STA: A2.S.1 STA: A2.N.7 TOP: Imaginary Numbers STA: A2.N.4 TOP: Operations with Irrational Expressions 25 = 4 PTS: 2 REF: 081001a2 KEY: without variables | index = 2 1 ID: A 14 ANS: 3 a n = 5(−2) n − 1 a 15 = 5(−2) 15 − 1 = 81,920 PTS: 2 REF: 011105a2 STA: A2.A.32 15 ANS: 1 PTS: 2 REF: 061004a2 TOP: Identifying the Equation of a Graph 16 ANS: 2 11π 180 ⋅ = 165 12 π TOP: Sequences STA: A2.A.52 PTS: 2 REF: 061002a2 STA: A2.M.2 KEY: degrees 17 ANS: 4 PTS: 2 REF: 011219a2 TOP: Properties of Graphs of Functions and Relations 18 ANS: 2 6(x 2 − 5) = 6x 2 − 30 TOP: Radian Measure STA: A2.A.52 PTS: 2 REF: 011109a2 KEY: variables 19 ANS: 2 −10 −10 5 f 10 = = =− 2 84 42 (−10) − 16 STA: A2.A.42 TOP: Compositions of Functions PTS: 2 20 ANS: 2 (−5) 2 − 4(1)(4) = 9 REF: 061102a2 STA: A2.A.41 TOP: Functional Notation PTS: 2 21 ANS: 2 x 3 + x 2 − 2x = 0 REF: 011506a2 STA: A2.A.2 TOP: Using the Discriminant STA: A2.A.26 REF: 061401a2 TOP: Solving Polynomial Equations STA: A2.S.2 x(x 2 + x − 2) = 0 x(x + 2)(x − 1) = 0 x = 0,−2,1 PTS: 2 REF: 011103a2 22 ANS: 1 PTS: 2 TOP: Analysis of Data 2 ID: A 23 ANS: 3 n 2 n + 2n Σ 0 1 2 0 2 2 2 2 0 + 2 = 1 1 + 2 = 3 2 + 2 = 8 12 2 2 × 12 = 24 PTS: 2 REF: fall0911a2 KEY: basic 24 ANS: 1 PTS: 2 TOP: Graphing Exponential Functions 25 ANS: 2 4 2x + 5 = 8 3x . STA: A2.N.10 TOP: Sigma Notation REF: 011505a2 STA: A2.A.53 STA: A2.A.27 TOP: Exponential Equations REF: 011616a2 STA: A2.S.8 REF: 061205a2 STA: A2.A.34 2x + 5 3x 2 2 = 2 3 2 4x + 10 = 2 9x 4x + 10 = 9x 10 = 5x 2=x 26 27 28 29 PTS: KEY: ANS: TOP: ANS: TOP: ANS: TOP: ANS: 2π = b 2 REF: 061105a2 common base not shown 3 PTS: 2 Correlation Coefficient 2 PTS: 2 Sigma Notation 1 PTS: 2 Solving Quadratics 4 2π = 6π 1 3 REF: 061408a2 STA: A2.A.24 KEY: completing the square PTS: 2 REF: 061027a2 STA: A2.A.69 TOP: Properties of Graphs of Trigonometric Functions 30 ANS: 1 10 C 4 = 210 PTS: 2 REF: 061113a2 STA: A2.S.11 3 KEY: period TOP: Combinations ID: A 31 ANS: 3 x 2 − 3x − 10 > 0 or (x − 5)(x + 2) > 0 x − 5 < 0 and x + 2 < 0 x − 5 > 0 and x + 2 > 0 x < 5 and x < −2 x > 5 and x > −2 x < −2 x>5 PTS: 2 KEY: one variable 32 ANS: 4 4ab 2b − 3a PTS: KEY: 33 ANS: 13 sin40 9b 2 REF: 011115a2 2b + 7ab STA: A2.A.4 6b = 4ab 2b − 9ab TOP: Quadratic Inequalities 2b + 7ab 2 REF: fall0918a2 STA: A2.A.14 with variables | index = 2 4 20 = . 81 + 40 < 180. (180 − 81) + 40 < 180 sinM 6b = −5ab 2b + 7ab 6b TOP: Operations with Radicals M ≈ 81 PTS: 2 REF: 061327a2 34 ANS: 4 PTS: 2 TOP: Permutations 35 ANS: 3 68% × 50 = 34 STA: A2.A.75 REF: fall0925a2 TOP: Law of Sines - The Ambiguous Case STA: A2.S.10 PTS: 2 KEY: predict 36 ANS: 4 2 log 4 (5x) = 3 REF: 081013a2 STA: A2.S.5 TOP: Normal Distributions REF: fall0921a2 STA: A2.A.28 TOP: Logarithmic Equations log 4 (5x) = 3 2 5x = 4 3 2 5x = 8 x= 8 5 PTS: 2 KEY: advanced 4 ID: A 37 ANS: 2 x 1 x2 − 4 − (x + 2)(x − 2) 4 x 4x 8x = = × = x−2 1 1 2x + 4 4x 2(x + 2) + 2x 4 8x PTS: 2 REF: fall0920a2 38 ANS: 1 common difference is 2. b n = x + 2n STA: A2.A.17 TOP: Complex Fractions 10 = x + 2(1) 8=x PTS: 2 REF: 081014a2 STA: A2.A.29 TOP: Sequences 39 ANS: 1 10 9 . 58° + 70° is possible. 122° + 70° is not possible. = sinA sin 70 A ≈ 58 PTS: 2 REF: 011210a2 STA: A2.A.75 40 ANS: 4 12x 4 + 10x 3 − 12x 2 = 2x 2 (6x 2 + 5x − 6) = 2x 2 (2x + 3)(3x − 2) TOP: Law of Sines - The Ambiguous Case PTS: 2 REF: 061008a2 STA: A2.A.7 KEY: single variable 41 ANS: 4 PTS: 2 REF: 081526a2 TOP: Differentiating Permutations and Combinations 42 ANS: 2 15 C 8 = 6,435 TOP: Factoring Polynomials PTS: 43 ANS: TOP: 44 ANS: 2 REF: 081012a2 STA: A2.S.11 1 PTS: 2 REF: fall0914a2 Negative and Fractional Exponents 1 6 10 = sin 35 sin N STA: A2.S.9 TOP: Combinations STA: A2.A.9 N ≈ 73 73 + 35 < 180 (180 − 73) + 35 < 180 PTS: 2 REF: 061226a2 STA: A2.A.75 5 TOP: Law of Sines - The Ambiguous Case ID: A 45 ANS: 1 PTS: 2 KEY: interval 46 ANS: 3 REF: fall0915a2 (6 − 2) 2 + (2 − −3) 2 = r= PTS: 47 ANS: TOP: 48 ANS: −7 ± 16 + 25 = 2 REF: 081516a2 3 PTS: 2 Domain and Range 3 TOP: Normal Distributions 41 STA: A2.A.48 REF: 061224a2 TOP: Equations of Circles STA: A2.A.63 STA: A2.A.25 TOP: Solving Quadratics 7 2 − 4(2)(−3) −7 ± 73 = 2(2) 4 PTS: 2 REF: 081009a2 KEY: quadratic formula 49 ANS: 3 5+ 13 13 5 + 13 4 5− STA: A2.S.5 ⋅ = 4(5 + 13) 5 + 13 = 3 25 − 13 PTS: 2 REF: 061116a2 STA: A2.N.5 50 ANS: 4 4x 2 + 3x − 4 = 0 b 2 − 4ac = 3 2 − 4(4)(−4) = 9 + 64 = 73 TOP: Rationalizing Denominators PTS: 2 REF: 011618a2 STA: A2.A.2 TOP: Using the Discriminant KEY: determine nature of roots given equation 51 ANS: 3 As originally written, alternatives (2) and (3) had no domain restriction, so that both were correct. PTS: 2 REF: 061405a2 STA: A2.A.52 TOP: Properties of Graphs of Functions and Relations 52 ANS: 4 PTS: 2 REF: 011622a2 TOP: Domain and Range 53 ANS: 3 If csc P > 0, sinP > 0. If cot P < 0 and sinP > 0, cos P < 0 PTS: 2 REF: 061320a2 STA: A2.A.60 6 STA: A2.A.63 TOP: Finding the Terminal Side of an Angle ID: A 54 ANS: 2 −(x − 1) 1 1−x −1 x x x x −1 1 = = = = − x−1 x−1 x−1 x−1 x −1 PTS: 2 55 ANS: 1 3 REF: 081018a2 27a −6 b 3 c 2 = 3a −2 bc 2 3 = 3bc a2 STA: A2.A.9 TOP: Negative Exponents 2 3 PTS: 2 REF: 011606a2 STA: A2.A.11 56 ANS: 2 (3 − 7i)(3 − 7i) = 9 − 21i − 21i + 49i 2 = 9 − 42i − 49 = −40 − 42i TOP: Radicals as Fractional Exponents PTS: 2 REF: fall0901a2 STA: A2.N.9 TOP: Multiplication and Division of Complex Numbers 57 ANS: 1 2π = 4π b b= 1 2 PTS: 2 REF: 011425a2 STA: A2.A.69 TOP: Properties of Graphs of Trigonometric Functions 58 ANS: 1 13 2 = 15 2 + 14 2 − 2(15)(14) cos C KEY: period 169 = 421 − 420 cos C −252 = −420 cos C 252 = cos C 420 53 ≈ C PTS: 2 REF: 061110a2 KEY: find angle 59 ANS: 3 −300 = 100 −1 3 STA: A2.A.73 TOP: Law of Cosines PTS: 2 REF: 061006a2 60 ANS: 2 PTS: 2 TOP: Families of Functions STA: A2.N.6 REF: 061108a2 TOP: Square Roots of Negative Numbers STA: A2.A.52 7 ID: A 61 ANS: 1 PTS: 2 REF: 011123a2 STA: A2.A.71 62 ANS: 4 PTS: 2 REF: 061026a2 TOP: Sequences 63 ANS: 3 Cofunctions secant and cosecant are complementary TOP: Graphing Trigonometric Functions STA: A2.A.29 PTS: 2 64 ANS: 3 STA: A2.A.58 TOP: Cofunction Trigonometric Relationships STA: A2.A.27 TOP: Exponential Equations 4x (2 2 ) 2 2 + 4x 2 x + 4x 2 2x + 8x REF: 011625a2 = 2 −6 . = 2 −6 =2 −6 2x 2 + 8x = −6 2x 2 + 8x + 6 = 0 x 2 + 4x + 3 = 0 (x + 3)(x + 1) = 0 x = −3 x = −1 PTS: 2 REF: 061015a2 KEY: common base shown 65 ANS: 4 s = θ r = 2⋅4 = 8 PTS: KEY: 66 ANS: TOP: 67 ANS: TOP: 68 ANS: 59.2 sin74 2 REF: fall0922a2 STA: A2.A.61 arc length 1 PTS: 2 REF: 061317a2 Differentiating Permutations and Combinations 2 PTS: 2 REF: 011126a2 Equations of Circles 3 60.3 = 180 − 78.3 = 101.7 sinC TOP: Arc Length STA: A2.S.9 STA: A2.A.49 C ≈ 78.3 PTS: 2 REF: 081006a2 STA: A2.A.75 8 TOP: Law of Sines - The Ambiguous Case ID: A 69 ANS: 3 1 9 8 3 −2 = = − −3 9 1 (−2) − 8 PTS: 2 REF: 061003a2 STA: A2.N.1 70 ANS: 2 PTS: 2 REF: 011225a2 TOP: Defining Functions 71 ANS: 4 n 21 S n = [2a + (n − 1)d] = [2(18) + (21 − 1)2] = 798 2 2 TOP: Negative and Fractional Exponents STA: A2.A.43 PTS: KEY: 72 ANS: 10 sin 35 TOP: Series 2 REF: 061103a2 arithmetic 2 13 = . 35 + 48 < 180 sinB 35 + 132 < 180 B ≈ 48,132 PTS: 73 ANS: TOP: 74 ANS: TOP: 75 ANS: TOP: 76 ANS: STA: A2.A.35 2 REF: 011113a2 STA: 3 PTS: 2 REF: Using Inverse Trigonometric Functions 4 PTS: 2 REF: Defining Functions 4 PTS: 2 REF: Properties of Logarithms KEY: 3 PTS: 2 REF: fall0924a2 KEY: basic, group frequency distributions 77 ANS: 4 PTS: 2 TOP: Binomial Probability 78 ANS: 1 PTS: 2 TOP: Transformations with Functions 79 ANS: 2 1 K = (10)(18) sin 120 = 45 3 ≈ 78 2 PTS: 2 KEY: basic REF: fall0907a2 A2.A.75 081007a2 061303a2 TOP: STA: KEY: STA: Law of Sines - The Ambiguous Case A2.A.64 basic A2.A.43 061120a2 STA: A2.A.19 splitting logs STA: A2.S.4 TOP: Dispersion REF: 011605a2 KEY: modeling REF: 081022a2 STA: A2.S.15 STA: A2.A.46 STA: A2.A.74 TOP: Using Trigonometry to Find Area 9 ID: A 80 ANS: 2 PTS: 2 REF: 061011a2 STA: A2.A.10 TOP: Fractional Exponents as Radicals 81 ANS: 3 sin 2 x 1 cos 2 x 2 2 2 2 = sin 2 x − cos 2 x ≠ 1 = sin sin 2 x 1 + x + cos x = 1 cos x − 1 (cos x) = 1 2 2 cos 2 x sin x cos x 2 2 cos x 1 cos x 1 − 1 = − = csc 2 x − cot x = 1 2 2 sin 2 x cos 2 x sin x x sin PTS: 2 REF: 011515a2 82 ANS: 1 6 3 6 3 9 C 3 a (−4b) = −5376a b STA: A2.A.58 TOP: Reciprocal Trigonometric Relationships PTS: 2 83 ANS: 3 STA: A2.A.36 TOP: Binomial Expansions REF: 061126a2 (3 − 0) 2 + (−5 − (−2)) 2 = r= 9+9 = 18 PTS: 2 REF: 011624a2 84 ANS: 2 The roots are −1,2,3. STA: A2.A.48 PTS: 2 REF: 081023a2 85 ANS: 3 PTS: 2 TOP: Domain and Range 86 ANS: 1 2 3 2 2 5 C 3 (3x) (−2) = 10 ⋅ 9x ⋅ −8 = −720x STA: A2.A.50 TOP: Zeros of Polynomials REF: fall0923a2 STA: A2.A.39 KEY: real domain, radical PTS: 2 87 ANS: 4 STA: A2.A.36 x − 2 5 = 1 x PTS: 88 ANS: TOP: 89 ANS: REF: fall0919a2 2 5 = TOP: Binomial Expansions 1 5 x2 2 REF: 011118a2 3 PTS: 2 Defining Functions 3 PTS: 2 TOP: Equations of Circles REF: 011207a2 STA: A2.A.10 TOP: Fractional Exponents as Radicals REF: 011604a2 STA: A2.A.38 KEY: ordered pairs STA: A2.A.71 10 TOP: Graphing Trigonometric Functions ID: A 90 ANS: 2 Since the coefficient of t is greater than 0, r > 0. PTS: 2 91 ANS: 4 REF: 011303a2 STA: A2.S.8 TOP: Correlation Coefficient (−3) 2 − 4(1)(−9) 3 ± 45 3 ± 3 5 = = 2(1) 2 2 3± PTS: 2 92 ANS: 3 2!⋅ 2!⋅ 2! = 8 REF: 061009a2 STA: A2.A.25 TOP: Quadratics with Irrational Solutions PTS: 2 93 ANS: 3 27r 4 − 1 = 64 REF: 061425a2 STA: A2.S.10 TOP: Permutations r3 = 64 27 r= 4 3 PTS: 2 REF: 081025a2 STA: A2.A.31 TOP: Sequences 94 ANS: 3 6n −1 < 4n −1 . Flip sign when multiplying each side of the inequality by n, since a negative number. 6 4 < n n 6>4 PTS: 2 95 ANS: 4 r= REF: 061314a2 (6 − 3) 2 + (5 − (−4)) 2 = PTS: 2 96 ANS: 2 c −12 P= = = −4 a 3 9 + 81 = REF: 061415a2 PTS: 2 REF: 081506a2 97 ANS: 4 PTS: 2 TOP: Analysis of Data STA: A2.N.1 TOP: Negative and Fractional Exponents 90 STA: A2.A.48 TOP: Equations of Circles STA: A2.A.20 REF: 011601a2 TOP: Roots of Quadratics STA: A2.S.2 11 ID: A 98 ANS: 3 c −8 −b −(−3) 3 S= = = . P= = = −2 a 4 a 4 4 PTS: 2 KEY: basic 99 ANS: 3 2 2 + cos 2 A = 1 3 REF: fall0912a2 5 cos A = 9 2 cos A = + 5 , sin A is acute. 3 STA: A2.A.21 TOP: Roots of Quadratics sin 2A = 2 sinA cos A 2 5 = 2 3 3 = 4 5 9 PTS: 2 REF: 011107a2 KEY: evaluating 100 ANS: 3 5 10π 5π 2π ⋅ = = 12 12 6 STA: A2.A.77 TOP: Double Angle Identities PTS: 101 ANS: TOP: 102 ANS: 2 REF: 061125a2 3 PTS: 2 Defining Functions 2 STA: A2.M.1 TOP: Radian Measure REF: 011305a2 STA: A2.A.37 KEY: ordered pairs PTS: 103 ANS: TOP: 104 ANS: 2 REF: 061115a2 4 PTS: 2 Sigma Notation 3 x 2 = 12x − 7 STA: A2.A.66 REF: 011504a2 TOP: Determining Trigonometric Functions STA: A2.A.34 STA: A2.A.24 TOP: Solving Quadratics REF: 061127a2 STA: A2.S.6 x 2 − 12x = −7 x 2 − 12x + 36 = −7 + 36 (x − 6) 2 = 29 PTS: KEY: 105 ANS: TOP: 2 REF: 061505a2 completing the square 3 PTS: 2 Regression 12 ID: A 106 ANS: 1 PTS: 2 REF: 061223a2 TOP: Binomial Probability KEY: modeling 107 ANS: 3 1 f(4) = (4) − 3 = −1. g(−1) = 2(−1) + 5 = 3 2 STA: A2.S.15 PTS: KEY: 108 ANS: TOP: 109 ANS: STA: A2.A.42 TOP: Compositions of Functions REF: 011201a2 STA: A2.S.2 2 REF: fall0902a2 numbers 4 PTS: 2 Analysis of Data 1 2logx − (3log y + log z) = log x 2 − log y 3 − logz = log x2 y3z PTS: 2 REF: 061010a2 STA: A2.A.19 110 ANS: 4 6x − x 3 − x 2 = −x(x 2 + x − 6) = −x(x + 3)(x − 2) TOP: Properties of Logarithms PTS: 2 REF: fall0917a2 KEY: single variable 111 ANS: 3 PTS: 2 TOP: Graphing Logarithmic Functions 112 ANS: 2 f −1 (x) = log 4 x STA: A2.A.7 TOP: Factoring Polynomials REF: 011422a2 STA: A2.A.54 PTS: 2 REF: fall0916a2 113 ANS: 2 b 2 − 4ac = (−9) 2 − 4(2)(4) = 81 − 32 = 49 STA: A2.A.54 TOP: Graphing Logarithmic Functions PTS: 2 REF: 011411a2 STA: A2.A.2 KEY: determine nature of roots given equation 114 ANS: 1 | 1 | 1 4a + 6 = 4a − 10. 4a + 6 = −4a + 10. | 4 + 6 | − 4 = −10 || 2 || 2 6 ≠ −10 8a = 4 8 − 2 ≠ −10 4 1 a= = 8 2 TOP: Using the Discriminant PTS: 115 ANS: TOP: 116 ANS: TOP: TOP: Absolute Value Equations STA: A2.A.43 2 REF: 011106a2 STA: A2.A.1 3 PTS: 2 REF: 061501a2 Defining Functions 3 PTS: 2 REF: 061007a2 Differentiating Permutations and Combinations 13 STA: A2.S.9 ID: A 117 ANS: 3 period = 2π 2π 2 = = 3 b 3π PTS: 2 REF: 081026a2 KEY: recognize 118 ANS: 3 −b −6 c 4 = = −3. = =2 a a 2 2 STA: A2.A.70 TOP: Graphing Trigonometric Functions PTS: 2 KEY: basic 119 ANS: 4 9 3x + 1 = 27 x + 2 . REF: 011121a2 STA: A2.A.21 TOP: Roots of Quadratics PTS: 2 REF: 081008a2 KEY: common base not shown 120 ANS: 2 PTS: 2 TOP: Domain and Range 121 ANS: 2 8 2 = 64 STA: A2.A.27 TOP: Exponential Equations REF: 081003a2 KEY: graph STA: A2.A.51 (3 2 ) 3x + 1 = (3 3 ) x + 2 3 6x + 2 = 3 3x + 6 6x + 2 = 3x + 6 3x = 4 x= 4 3 PTS: 2 REF: fall0909a2 STA: A2.A.18 TOP: Evaluating Logarithmic Expressions 122 ANS: 1 PTS: 2 REF: 061019a2 STA: A2.N.7 TOP: Imaginary Numbers 123 ANS: 1 (4) shows the strongest linear relationship, but if r < 0, b < 0. The Regents announced that a correct solution was not provided for this question and all students should be awarded credit. PTS: 124 ANS: TOP: 125 ANS: TOP: 126 ANS: TOP: 2 REF: 011223a2 4 PTS: 2 Permutations 2 PTS: 2 Defining Functions 1 PTS: 2 Correlation Coefficient STA: A2.S.8 REF: 011409a2 TOP: Correlation Coefficient STA: A2.S.10 REF: 011507a2 KEY: graphs REF: 061316a2 STA: A2.A.38 14 STA: A2.S.8 ID: A 127 ANS: 1 Σ n 3 4 5 2 2 2 2 −r + r −3 + 3 = −6 −4 + 4 = −12−5 + 5 = −20 −38 PTS: 2 REF: 061118a2 STA: A2.N.10 KEY: basic 128 ANS: 1 cos 2 θ − cos 2θ = cos 2 θ − (cos 2 θ − sin 2 θ) = sin 2 θ TOP: Sigma Notation PTS: 2 REF: 061024a2 KEY: simplifying 129 ANS: 4 7 2 = 3 2 + 5 2 − 2(3)(5) cos A STA: A2.A.77 TOP: Double Angle Identities STA: A2.A.73 TOP: Law of Cosines REF: 061322a2 KEY: modeling STA: A2.A.73 49 = 34 − 30 cos A 15 = −30 cos A 1 − = cos A 2 120 = A PTS: 2 REF: 081017a2 KEY: angle, without calculator 130 ANS: 2 PTS: 2 TOP: Law of Sines 131 ANS: 3 sin 2 θ + cos 2 θ 1 = = sec 2 θ 2 2 1 − sin θ cos θ PTS: 132 ANS: TOP: 133 ANS: TOP: 134 ANS: TOP: 2 REF: 061123a2 STA: 2 PTS: 2 REF: Graphing Quadratic Functions 1 PTS: 2 REF: Graphing Logarithmic Functions 3 PTS: 2 REF: Using Inverse Trigonometric Functions A2.A.58 fall0926a2 TOP: Reciprocal Trigonometric Relationships STA: A2.A.46 061211a2 STA: A2.A.54 011104a2 STA: A2.A.64 KEY: unit circle 15 ID: A 135 ANS: 3 3x + 16 = (x + 2) 2 . −4 is an extraneous solution. 3x + 16 = x 2 + 4x + 4 0 = x 2 + x − 12 0 = (x + 4)(x − 3) x = −4 x = 3 PTS: KEY: 136 ANS: TOP: 137 ANS: 2 REF: 061121a2 extraneous solutions 2 PTS: 2 Inverse of Functions 1 cos K = STA: A2.A.22 TOP: Solving Radicals REF: 081523a2 STA: A2.A.44 KEY: ordered pairs 5 6 K = cos −1 5 6 K ≈ 33°33' PTS: 138 ANS: TOP: 139 ANS: TOP: 140 ANS: 2 REF: 061023a2 STA: A2.A.55 3 PTS: 2 REF: 061001a2 Sequences 4 PTS: 2 REF: 011124a2 Evaluating Logarithmic Expressions 1 3 +5 3 −5 PTS: 2 ⋅ 3 +5 3 +5 = TOP: Trigonometric Ratios STA: A2.A.30 STA: A2.A.18 3 + 5 3 + 5 3 + 25 28 + 10 3 14 + 5 3 = = − −22 11 3 − 25 REF: 061012a2 STA: A2.N.5 16 TOP: Rationalizing Denominators ID: A 141 ANS: 2 π 2π 3 3 3 1 = = 3 2π 2π + π PTS: 2 142 ANS: 1 π = − 7π −420 180 3 REF: 011108a2 STA: A2.S.13 TOP: Geometric Probability PTS: 2 KEY: radians 143 ANS: 1 REF: 081002a2 STA: A2.M.2 TOP: Radian Measure 4 2 5 1 4 2 4 81x y = 81 x y 5 4 1 2 = 3x y 5 4 PTS: 2 REF: 081504a2 STA: A2.A.11 144 ANS: 1 PTS: 2 REF: 011117a2 TOP: Differentiating Permutations and Combinations 145 ANS: 2 x 2 − x − 6 = 3x − 6 TOP: Radicals as Fractional Exponents STA: A2.S.9 x 2 − 4x = 0 x(x − 4) = 0 x = 0,4 PTS: 2 REF: 081015a2 KEY: algebraically STA: A2.A.3 17 TOP: Quadratic-Linear Systems ID: A 146 ANS: 1 tan θ − 3 =0 tan θ = . . 3 θ = tan−1 3 θ = 60, 240 PTS: KEY: 147 ANS: TOP: 148 ANS: 2 REF: fall0903a2 STA: A2.A.68 basic 4 PTS: 2 REF: 061124a2 Average Known with Missing Data 3 PTS: 2 149 ANS: 4 x x− REF: 061020a2 × x x+ x x+ x PTS: 2 KEY: index = 2 150 ANS: 2 = STA: A2.A.71 TOP: Trigonometric Equations STA: A2.S.3 TOP: Graphing Trigonometric Functions x(x + x ) x + x x2 + x x = = 2 x(x − 1) x−1 x −x REF: 061325a2 STA: A2.A.15 TOP: Rationalizing Denominators STA: REF: KEY: REF: TOP: Negative and Fractional Exponents STA: A2.N.3 1 1 −5 2 w −9 = (w 4 ) 2 = w 2 w PTS: 151 ANS: TOP: 152 ANS: TOP: 153 ANS: TOP: 154 ANS: TOP: 2 REF: 081011a2 2 PTS: 2 Operations with Polynomials 2 PTS: 2 Conjugates of Complex Numbers 2 PTS: 2 Reference Angles 1 PTS: 2 Sigma Notation A2.A.8 011114a2 subtraction 081024a2 STA: A2.N.8 REF: 081515a2 STA: A2.A.57 REF: 061420a2 STA: A2.A.34 18 ID: A 155 ANS: 1 8 × 8 × 7 × 1 = 448. The first digit cannot be 0 or 5. The second digit cannot be 5 or the same as the first digit. The third digit cannot be 5 or the same as the first or second digit. PTS: 2 156 ANS: 1 a n = − 5(− REF: 011125a2 STA: A2.S.10 TOP: Permutations 2) n − 1 a 15 = − 5(− 2) 15 − 1 = − 5(− 2 ) 14 = − 5 ⋅ 2 7 = −128 5 PTS: 2 REF: 061109a2 157 ANS: 4 PTS: 2 TOP: Zeros of Polynomials 158 ANS: 3 75000 = 25000e .0475t STA: A2.A.32 REF: 061005a2 TOP: Sequences STA: A2.A.50 TOP: Exponential Growth STA: A2.A.43 3 = e .0475t ln 3 = ln e .0475t ln 3 .0475t ⋅ ln e = .0475 .0475 23.1 ≈ t PTS: 159 ANS: TOP: 160 ANS: TOP: 161 ANS: TOP: 162 ANS: 2 REF: 061117a2 2 PTS: 2 Defining Functions 3 PTS: 2 Inverse of Functions 4 PTS: 2 Using the Discriminant 1 STA: A2.A.6 REF: 011407a2 PTS: 163 ANS: TOP: 164 ANS: x = 54 2 REF: 011203a2 1 PTS: 2 Solving Radicals 3 = 625 STA: A2.A.66 TOP: Determining Trigonometric Functions REF: 061018a2 STA: A2.A.22 KEY: extraneous solutions PTS: KEY: 165 ANS: TOP: 2 REF: 061106a2 basic 3 PTS: 2 Logarithmic Equations STA: A2.A.28 TOP: Logarithmic Equations REF: 011503a2 KEY: basic STA: A2.A.28 REF: KEY: REF: KEY: 081027a2 STA: A2.A.44 equations 011323a2 STA: A2.A.2 determine nature of roots given equation 19 ID: A 166 ANS: 3 3x 2 + x − 14 = 0 1 2 − 4(3)(−14) = 1 + 168 = 169 = 13 2 PTS: 2 REF: 061524a2 STA: KEY: determine nature of roots given equation 167 ANS: 2 PTS: 2 REF: TOP: Simplifying Trigonometric Expressions 168 ANS: 4 PTS: 2 REF: TOP: Domain and Range KEY: 169 ANS: 3 (−5) 2 − 4(2)(0) = 25 A2.A.2 TOP: Using the Discriminant 011208a2 STA: A2.A.67 061518a2 graph STA: A2.A.51 PTS: 2 REF: 061423a2 STA: A2.A.2 KEY: determine equation given nature of roots 170 ANS: 1 6x − 7 ≤ 5 6x − 7 ≥ −5 6x ≤ 12 x≤2 PTS: KEY: 171 ANS: TOP: TOP: Using the Discriminant 6x ≥ 2 x≥ 1 3 2 REF: fall0905a2 graph 1 PTS: 2 Defining Functions STA: A2.A.1 TOP: Absolute Value Inequalities REF: 061409a2 KEY: graphs STA: A2.A.38 20 ID: A Algebra 2/Trigonometry Multiple Choice Regents Exam Questions Answer Section 172 ANS: TOP: 173 ANS: TOP: 174 ANS: 4 PTS: 2 REF: 011513a2 Equations of Circles 1 PTS: 2 REF: 061025a2 Sigma Notation 2 −b 4 2 c −12 = = . product: = = −2 sum: 6 3 6 a a 2 REF: 011209a2 2 PTS: 2 Conjugates of Complex Numbers 2 25b 4 5 2 a −3 b 4 = 3 a STA: A2.A.49 STA: A2.A.34 PTS: 175 ANS: TOP: 176 ANS: STA: A2.A.20 REF: 011213a2 TOP: Roots of Quadratics STA: A2.N.8 PTS: 2 REF: 011514a2 177 ANS: 2 cos(−305° + 360°) = cos(55°) STA: A2.A.9 TOP: Negative Exponents PTS: 2 178 ANS: 4 STA: A2.A.57 TOP: Reference Angles REF: 061104a2 34 12 = sin 30 sinB B = sin −1 ≈ sin −1 PTS: 179 ANS: TOP: 180 ANS: 4x − 5 3 12 sin30 34 6 5.8 2 REF: 011523a2 2 PTS: 2 Law of Cosines 3 4x − 5 < −1 > 1 or 3 4x − 5 > 3 4x > 8 x>2 PTS: 2 KEY: graph STA: A2.A.75 TOP: Law of Sines - The Ambiguous Case REF: 011501a2 STA: A2.A.73 KEY: side, without calculator 4x − 5 < −3 4x < 2 x< 1 2 REF: 061209a2 STA: A2.A.1 1 TOP: Absolute Value Inequalities ID: A 181 ANS: TOP: 182 ANS: TOP: 183 ANS: TOP: 184 ANS: 4 PTS: 2 REF: Defining Functions KEY: 3 PTS: 2 REF: Finding the Terminal Side of an Angle 2 PTS: 2 REF: Correlation Coefficient 4 fall0908a2 graphs 061412a2 STA: A2.A.38 061021a2 STA: A2.S.8 STA: A2.A.60 −180x 16 = 6x 8 i 5 PTS: 2 185 ANS: 2 REF: 081524a2 STA: A2.N.6 TOP: Square Roots of Negative Numbers STA: A2.A.58 REF: 061411a2 TOP: Reciprocal Trigonometric Relationships STA: A2.A.30 cos x sinx cot x = = cos x csc x 1 sinx PTS: 186 ANS: TOP: 187 ANS: 2 4 Sequences 4 REF: 061410a2 PTS: 2 1 2 2 7 cos 2A = 1 − 2 sin A = 1 − 2 = 1 − = 3 9 9 2 PTS: KEY: 188 ANS: TOP: 189 ANS: TOP: 190 ANS: 2 REF: 011311a2 STA: A2.A.77 evaluating 2 PTS: 2 REF: 061216a2 Compositions of Functions KEY: variables 1 PTS: 2 REF: 011310a2 Differentiating Permutations and Combinations 4 3 5 cos θ = − sec θ = − 5 3 PTS: 2 REF: 011621a2 191 ANS: 1 log x = log a 2 + log b TOP: Double Angle Identities STA: A2.A.42 STA: A2.S.9 STA: A2.A.62 TOP: Determining Trigonometric Functions STA: A2.A.19 TOP: Properties of Logarithms log x = log a 2 b x = a2b PTS: 2 REF: 061517a2 KEY: antilogarithms 2 ID: A 192 ANS: 3 s=θr= 4π 24 ⋅ = 16π 3 2 PTS: 2 REF: 011611a2 KEY: arc length 193 ANS: 3 34.1% + 19.1% = 53.2% STA: A2.A.61 TOP: Arc Length PTS: 2 KEY: probability 194 ANS: 2 STA: A2.S.5 TOP: Normal Distributions 3 = 2 x = 2⋅ REF: 011212a2 3 y = 2⋅ 1 =1 2 PTS: 2 195 ANS: 1 3 4 3 = − 2 1 − 2 REF: 061525a2 STA: A2.A.62 TOP: Determining Trigonometric Functions PTS: 2 196 ANS: 4 REF: 011508a2 STA: A2.A.31 TOP: Sequences 3− 8 3 ⋅ 3 3 = 3 3− 3 24 = 3 3 −2 6 = 3 3− 2 3 6 PTS: 2 REF: 081518a2 STA: A2.N.5 197 ANS: 4 x = 2y . y 2 − (3y) 2 + 32 = 0 . x = 3(−2) = −6 TOP: Rationalizing Denominators y 2 − 9y 2 = −32 −8y 2 = −32 y2 = 4 y = ±2 PTS: KEY: 198 ANS: TOP: 199 ANS: TOP: 2 REF: 061312a2 STA: A2.A.3 equations 4 PTS: 2 REF: 061206a2 Unit Circle 4 PTS: 1 REF: 011312a2 Determining Trigonometric Functions 3 TOP: Quadratic-Linear Systems STA: A2.A.60 STA: A2.A.56 KEY: degrees, common angles ID: A 200 ANS: 4 b 2 − 4ac = 3 2 − 4(9)(−4) = 9 + 144 = 153 PTS: 2 REF: 081016a2 STA: A2.A.2 KEY: determine nature of roots given equation 201 ANS: 4 (a − 1) 2 + (a − 2) 2 + (a − 3) 2 + (a − 4) 2 TOP: Using the Discriminant (a 2 − 2a + 1) + (a 2 − 4a + 4) + (a 2 − 6a + 9) + (a 2 − 8a + 16) 4a 2 − 20a + 30 PTS: 2 REF: 011414a2 STA: A2.N.10 KEY: advanced 202 ANS: 2 4 ⋅ 12 .0325 A = 50 1 + = 50(1.008125) 48 ≈ 73.73 4 TOP: Sigma Notation PTS: 2 203 ANS: 4 TOP: Evaluating Functions REF: 081511a2 STA: A2.A.12 PTS: 2 REF: 061222a2 STA: A2.A.50 204 ANS: 1 PTS: 2 REF: 011112a2 TOP: Using Inverse Trigonometric Functions 205 ANS: 4 PTS: 2 REF: 011101a2 TOP: Defining Functions KEY: graphs 206 ANS: 4 (x + 11)(x − 2) −1 −1 x 2 + 9x − 22 ÷ (2 − x) = ⋅ = 2 (x + 11)(x − 11) x − 2 x − 11 x − 121 TOP: STA: KEY: STA: Solving Polynomial Equations A2.A.64 advanced A2.A.38 PTS: 2 REF: 011423a2 STA: A2.A.16 TOP: Multiplication and Division of Rationals KEY: division 207 ANS: 3 f(x + 3) = 2(x + 3) 2 − 3(x + 3) + 4 = 2x 2 + 12x + 18 − 3x − 9 + 4 = 2x 2 + 9x + 13 PTS: 2 REF: 011619a2 208 ANS: 3 PTS: 2 TOP: Domain and Range STA: A2.A.41 REF: 061418a2 KEY: graph 4 TOP: Functional Notation STA: A2.A.51 ID: A 209 ANS: 4 A = 5000e (.04)(18) ≈ 10272.17 PTS: 2 REF: 011607a2 STA: A2.A.12 210 ANS: 4 3 27x 2 3 16x 4 = 3 3 3 ⋅ 2 4 ⋅ x 6 = 3 ⋅ 2 ⋅ x 2 3 2 = 6x 2 3 2 TOP: Evaluating Exponential Expressions PTS: 2 211 ANS: 1 STA: A2.N.2 TOP: Operations with Radicals STA: A2.A.11 TOP: Radicals as Fractional Exponents 4 REF: 011421a2 1 4 2 4 16x y = 16 x y 2 7 7 4 1 2 = 2x y 7 4 PTS: 2 REF: 061107a2 212 ANS: 3 3(1 − (−4) 8 ) 196,605 S8 = = = −39,321 1 − (−4) 5 PTS: 2 REF: 061304a2 STA: A2.A.35 KEY: geometric 213 ANS: 2 PTS: 2 REF: 061521a2 TOP: Inverse of Functions KEY: equations 214 ANS: 4 15 C 5 = 3,003. 25 C 5 = 25 C 20 = 53,130. 25 C 15 = 3,268,760. TOP: Summations PTS: 2 215 ANS: 1 TOP: Combinations REF: 061227a2 1 If sin x = 0.8, then cos x = 0.6. tan x = 2 PTS: 2 REF: 061220a2 216 ANS: 2 2 2 ⋅ 3 = 12 . 6 2 d = 12 42 ⋅ STA: A2.S.11 1 − 0.6 = 1 + 0.6 STA: A2.A.44 0.4 = 0.5. 1.6 STA: A2.A.77 TOP: Half Angle Identities REF: 061310a2 STA: A2.A.5 TOP: Inverse Variation REF: 081507a2 STA: A2.A.5 TOP: Inverse Variation 36d = 12 3 = 12 4 1 d= 3 PTS: 2 217 ANS: 4 3 ⋅ 400 = 8x 150 = x PTS: 2 5 ID: A 218 ANS: 4 x 2 (x + 2) − (x + 2) (x 2 − 1)(x + 2) (x + 1)(x − 1)(x + 2) PTS: 2 REF: 011426a2 STA: A2.A.7 TOP: Factoring by Grouping 219 ANS: 2 PTS: 2 REF: 011222a2 STA: A2.A.39 TOP: Domain and Range KEY: real domain, absolute value 220 ANS: 1 5x + 29 = (x + 3) 2 . (−5) + 3 shows an extraneous solution. 5x + 29 = x 2 + 6x + 9 0 = x 2 + x − 20 0 = (x + 5)(x − 4) x = −5,4 PTS: 2 REF: 061213a2 KEY: extraneous solutions 221 ANS: 3 c −3 = a 4 STA: A2.A.22 TOP: Solving Radicals PTS: 2 REF: 011517a2 STA: A2.A.20 222 ANS: 2 Top 6.7% = 1.5 s.d. + σ = 1.5(104) + 576 = 732 TOP: Roots of Quadratics PTS: 2 KEY: predict 223 ANS: 2 3 − a3b4 32 6b = − 2 1 5 3 a a b 64 STA: A2.S.5 TOP: Normal Distributions STA: A2.A.31 TOP: Sequences REF: 011420a2 PTS: 2 REF: 061326a2 224 ANS: 2 4 |2x + 6| < 32 2x + 6 < 8 2x + 6 > −8 |2x + 6| < 8 PTS: KEY: 225 ANS: TOP: 2x < 2 2x > −14 x<1 x > −7 2 REF: 011612a2 STA: A2.A.1 graph 4 PTS: 2 REF: 061402a2 Negative and Fractional Exponents 6 TOP: Absolute Value Inequalities STA: A2.A.8 ID: A 226 ANS: 2 8π 180 ⋅ = 288 5 π PTS: 2 REF: 061302a2 KEY: degrees 227 ANS: 1 5−2 (−3) 2 = 720x 3 5 C 2 (2x) PTS: 228 ANS: TOP: 229 ANS: 3 2 2 Dispersion 3 STA: A2.M.2 TOP: Radian Measure REF: 011519a2 STA: A2.A.36 TOP: Binomial Expansions PTS: 2 REF: 081509a2 STA: A2.S.4 KEY: basic, group frequency distributions 6a 4 b 2 + 3 (27 ⋅ 6)a 4 b 2 a 3 6ab 2 + 3a 4a PTS: 2 230 ANS: 3 9 C 3 = 84 3 3 6ab 2 6ab 2 REF: 011319a2 PTS: 2 REF: 081513a2 231 ANS: 4 f a + 1 = 4(a + 1) 2 − (a + 1) + 1 STA: A2.N.2 TOP: Operations with Radicals STA: A2.S.11 TOP: Combinations STA: A2.A.41 TOP: Functional Notation = 4(a 2 + 2a + 1) − a = 4a 2 + 8a + 4 − a = 4a 2 + 7a + 4 PTS: 2 REF: 011527a2 7 ID: A 232 ANS: 2 320 = 10(2) 32 = (2) t 60 log 32 = log(2) log 32 = t 60 t 60 t log 2 60 60 log 32 =t log 2 300 = t PTS: 2 233 ANS: 4 8 3k + 4 = 4 2k − 1 REF: 011205a2 STA: A2.A.6 TOP: Exponential Growth . (2 3 ) 3k + 4 = (2 2 ) 2k − 1 2 9k + 12 = 2 4k − 2 9k + 12 = 4k − 2 5k = −14 k= − PTS: KEY: 234 ANS: TOP: 235 ANS: 3 14 5 2 REF: 011309a2 STA: A2.A.27 common base not shown 4 PTS: 2 REF: 011627a2 Properties of Graphs of Trigonometric Functions 1 27a 3 ⋅ 4 TOP: Exponential Equations STA: A2.A.69 KEY: period 16b 8 = 3a ⋅ 2b 2 = 6ab 2 PTS: 2 REF: 061504a2 KEY: with variables | index > 2 236 ANS: 1 PTS: 2 TOP: Zeros of Polynomials 237 ANS: 3 20 ⋅ 2 = −5t STA: A2.A.14 TOP: Operations with Radicals REF: 081501a2 STA: A2.A.50 STA: A2.A.5 TOP: Inverse Variation −8 = t PTS: 2 REF: 011412a2 8 ID: A 238 ANS: 1 y ≥ x2 − x − 6 y ≥ (x − 3)(x + 2) PTS: 2 REF: 061017a2 KEY: two variables 239 ANS: 2 (2 sinx − 1)(sinx + 1) = 0 sin x = STA: A2.A.4 TOP: Quadratic Inequalities STA: A2.A.68 TOP: Trigonometric Equations 1 ,−1 2 x = 30,150,270 PTS: 2 KEY: quadratics 240 ANS: 3 2π =π 2 REF: 081514a2 PTS: 2 REF: 081519a2 STA: A2.A.69 TOP: Properties of Graphs of Trigonometric Functions 241 ANS: 1 3 64a 5 b 6 = 3 4 3 a 3 a 2 b 6 = 4ab 2 3 KEY: period a2 PTS: 2 REF: 011516a2 242 ANS: 3 8−3 ⋅ (−2) 3 = 56x 5 ⋅ (−8) = −448x 5 8 C3 ⋅ x STA: A2.N.2 TOP: Operations with Radicals PTS: 2 243 ANS: 4 2x 2 − 7x − 5 = 0 REF: 011308a2 STA: A2.A.36 TOP: Binomial Expansions REF: 061414a2 STA: A2.A.20 TOP: Roots of Quadratics c −5 = a 2 PTS: 2 244 ANS: 2 60 = −16t + 5t + 105 t = 2 −5 ± 5 2 − 4(−16)(45) −5 ± 53.89 ≈ ≈ 1.84 2(−16) −32 0 = −16t 2 + 5t + 45 PTS: 2 REF: 061424a2 KEY: quadratic formula STA: A2.A.25 9 TOP: Solving Quadratics ID: A 245 ANS: 1 The binomials are conjugates, so use FL. 246 247 248 249 250 PTS: KEY: ANS: TOP: ANS: TOP: ANS: KEY: ANS: TOP: ANS: 2 REF: multiplication 3 PTS: Sequences 1 PTS: Sequences 3 PTS: graph 1 PTS: Negative Exponents 2 061201a2 STA: A2.N.3 TOP: Operations with Polynomials 2 REF: 011110a2 STA: A2.A.30 2 REF: 081520a2 STA: A2.A.33 2 REF: 061308a2 TOP: Domain and Range 2 REF: 061324a2 STA: A2.A.9 7 25 7 24 sin A 7 = = − If sin A = − , cos A = , and tanA = cos A 24 24 25 25 25 − PTS: KEY: 251 ANS: TOP: 252 ANS: 2 REF: 011413a2 STA: A2.A.64 advanced 4 PTS: 2 REF: 011127a2 Analysis of Data 3 3 2 32 9 23 cos 2A = 1 − 2 sin 2 A = 1 − 2 = − = 8 32 32 32 PTS: 2 REF: 011510a2 KEY: evaluating 253 ANS: 3 3x 5 − 48x = 0 TOP: Using Inverse Trigonometric Functions STA: A2.S.1 STA: A2.A.77 TOP: Double Angle Identities STA: A2.A.26 TOP: Solving Polynomial Equations 3x(x 4 − 16) = 0 3x(x 2 + 4)(x 2 − 4) = 0 3x(x 2 + 4)(x + 2)(x − 2) = 0 PTS: 2 REF: 011216a2 10 ID: A 254 ANS: 2 2x 2 − (x + 2) 2 = 8 2x 2 − (x 2 + 4x + 4) − 8 = 0 x 2 − 4x − 12 = 0 (x − 6)(x + 2) = 0 x = 6,−2 PTS: 2 REF: 011609a2 STA: A2.A.3 KEY: equations 255 ANS: 4 3 x − 1 3 x + 1 − 3 x − 1 = 3 x − 1 (2) = 3x − 2 2 2 2 2 TOP: Quadratic-Linear Systems PTS: 2 REF: 011524a2 STA: A2.N.3 KEY: multiplication 256 ANS: 3 3 x 3 (−2y) 3 = 20 ⋅ x ⋅ −8y 3 = −20x 3 y 3 6 C3 2 8 TOP: Operations with Polynomials PTS: 2 REF: 061215a2 257 ANS: 3 PTS: 2 TOP: Operations with Polynomials 258 ANS: 4 91 − 82 = 2.5 sd 3.6 STA: A2.A.36 REF: 061515a2 KEY: subtraction TOP: Binomial Expansions STA: A2.N.3 PTS: KEY: 259 ANS: TOP: 260 ANS: 9 P9 STA: A2.S.5 TOP: Normal Distributions REF: 061013a2 STA: A2.A.38 2 REF: 081521a2 interval 1 PTS: 2 Defining Functions 1 362,880 = = 3,780 96 4!⋅ 2!⋅ 2! PTS: 2 REF: 061511a2 STA: A2.S.10 TOP: Permutations 261 ANS: 3 PTS: 2 REF: 061306a2 STA: A2.A.72 TOP: Identifying the Equation of a Trigonometric Graph 262 ANS: 4 (4) fails the horizontal line test. Not every element of the range corresponds to only one element of the domain. PTS: 2 REF: fall0906a2 STA: A2.A.43 11 TOP: Defining Functions ID: A 263 ANS: 4 y − 2 sin θ = 3 y = 2 sin θ + 3 f(θ) = 2 sin θ + 3 PTS: 2 REF: fall0927a2 264 ANS: 3 4 1 2 4 2 3 C 2 (2x ) (−y) = 6x y STA: A2.A.40 TOP: Functional Notation PTS: 2 REF: 011215a2 265 ANS: 3 PTS: 2 TOP: Binomial Expansions 266 ANS: 1 1 a 2 = (−6) − 2 = −5 2 STA: A2.A.36 REF: 081525a2 TOP: Binomial Expansions STA: A2.A.36 STA: A2.A.33 TOP: Sequences a3 = 1 11 (−5) − 3 = − 2 2 PTS: 2 267 ANS: 1 c= x + REF: 011623a2 2 2 + x − 2 2 = x2 + 2 2x + 2 + x2 − 2 2x + 2 = 2x 2 + 4 PTS: 2 REF: 011626a2 KEY: with variables | index = 2 268 ANS: 3 2π 3π s=θr= ⋅6 = 8 2 STA: A2.A.14 TOP: Operations with Radicals PTS: 2 KEY: arc length 269 ANS: 3 STA: A2.A.61 TOP: Arc Length sum of the roots, REF: 061212a2 c 3 −b −(−9) 9 = = . product of the roots, = a 4 4 a 4 PTS: 2 REF: 061208a2 STA: A2.A.21 KEY: basic 270 ANS: 3 Cofunctions tangent and cotangent are complementary PTS: 2 REF: 061014a2 STA: A2.A.58 12 TOP: Roots of Quadratics TOP: Cofunction Trigonometric Relationships ID: A 271 ANS: 4 4 + 3(2 − x) + 3(3 − x) + 3(4 − x) + 3(5 − x) 4 + 6 − 3x + 9 − 3x + 12 − 3x + 15 − 3x 46 − 12x PTS: 2 REF: 061315a2 KEY: advanced 272 ANS: 4 1 1 g = = 2. f(2) = 4(2) − 2 2 = 4 1 2 2 STA: A2.N.10 TOP: Sigma Notation PTS: 2 REF: 011204a2 STA: A2.A.42 TOP: Compositions of Functions KEY: numbers 273 ANS: 2 60 − 50 = 2 standards above the mean or 2.3% 2.3% ⋅ 1000 = 23 5 PTS: 2 KEY: predict 274 ANS: 3 REF: 011614a2 x+y = 5 STA: A2.S.5 TOP: Normal Distributions . −5 + y = 5 y = −x + 5 y = 10 (x + 3) 2 + (−x + 5 − 3) 2 = 53 x 2 + 6x + 9 + x 2 − 4x + 4 = 53 2x 2 + 2x − 40 = 0 x 2 + x − 20 = 0 (x + 5)(x − 4) = 0 x = −5,4 PTS: 2 KEY: circle 275 ANS: 2 REF: 011302a2 K = 8 ⋅ 12 sin120 = 96 ⋅ STA: A2.A.3 TOP: Quadratic-Linear Systems STA: A2.A.74 TOP: Using Trigonometry to Find Area 3 = 48 3 2 PTS: 2 REF: 061508a2 KEY: parallelograms 13 ID: A 276 ANS: 2 9 − x2 < 0 or x + 3 < 0 and x − 3 < 0 x < −3 and x < 3 x2 − 9 > 0 x < −3 (x + 3)(x − 3) > 0 x + 3 > 0 and x − 3 > 0 x > −3 and x > 3 x>3 PTS: 2 REF: 061507a2 STA: A2.A.4 KEY: one variable 277 ANS: 2 x − 2 = 3x + 10 −6 is extraneous. x − 2 = −3x − 10 −12 = 2x 4x = −8 −6 = x x = −2 PTS: 2 278 ANS: 1 4+ 11 11 4 + 11 5 4− REF: 061513a2 ⋅ = STA: A2.A.1 5(4 + 11) 5(4 + 11) = = 4+ 16 − 11 5 PTS: 2 REF: 061509a2 279 ANS: 1 PTS: 2 TOP: Operations with Polynomials 280 ANS: 2 x 2 − 2x + y 2 + 6y = −3 TOP: Quadratic Inequalities TOP: Absolute Value Equations 11 STA: A2.N.5 REF: 011314a2 KEY: subtraction TOP: Rationalizing Denominators STA: A2.N.3 STA: A2.A.47 TOP: Equations of Circles x 2 − 2x + 1 + y 2 + 6y + 9 = −3 + 1 + 9 (x − 1) 2 + (y + 3) 2 = 7 PTS: 2 281 ANS: 1 REF: 061016a2 8 17 8 15 8 = If sin θ = , then cos θ = . tan θ = 15 15 17 17 17 PTS: 2 KEY: advanced REF: 081508a2 STA: A2.A.64 14 TOP: Using Inverse Trigonometric Functions ID: A 282 ANS: 1 20(−2) = x(−2x + 2) −40 = −2x 2 + 2x 2x 2 − 2x − 40 = 0 x 2 − x − 20 = 0 (x + 4)(x − 5) = 0 x = −4,5 PTS: 2 REF: 011321a2 STA: A2.A.5 283 ANS: 2 4 1− x(x − 4) x x2 x 2 − 4x x × 2 = 2 = = (x − 4)(x + 2) x +2 2 8 x x − 2x − 8 1− − 2 x x 284 285 286 287 PTS: ANS: TOP: ANS: TOP: ANS: TOP: ANS: 1 7− 2 REF: 061305a2 4 PTS: 2 Properties of Logarithms 4 PTS: 2 Analysis of Data 2 PTS: 2 Sequences 1 7+ 11 11 7 + 11 ⋅ = STA: REF: KEY: REF: TOP: Inverse Variation A2.A.17 TOP: Complex Fractions 061207a2 STA: A2.A.19 antilogarithms 061101a2 STA: A2.S.1 REF: 011610a2 STA: A2.A.30 7 + 11 7 + 11 = 49 − 11 38 PTS: 2 REF: 011404a2 STA: A2.N.5 288 ANS: 3 4 ⋅5 .03 5000 1 + = 5000(1.0075) 20 ≈ 5805.92 4 TOP: Rationalizing Denominators PTS: 289 ANS: TOP: 290 ANS: TOP: 291 ANS: TOP: TOP: Evaluating Functions STA: A2.A.38 2 REF: 3 PTS: Defining Functions 4 PTS: Unit Circle 2 PTS: Domain and Range 011410a2 2 2 2 STA: REF: KEY: REF: A2.A.12 061114a2 graphs 081005a2 STA: A2.A.60 REF: 011521a2 STA: A2.A.39 KEY: real domain, rational 15 ID: A 292 ANS: 2 (x + 2) 2 = −9 x + 2 =± −9 x = −2 ± 3i PTS: 2 REF: 011408a2 STA: A2.A.24 TOP: Solving Quadratics KEY: completing the square 293 ANS: 1 f(g(x)) = 2(x + 5) 2 − 3(x + 5) + 1 = 2(x 2 + 10x + 25) − 3x − 15 + 1 = 2x 2 + 17x + 36 PTS: 2 REF: 061419a2 STA: A2.A.42 KEY: variables 294 ANS: 3 b 2 − 4ac = (−10) 2 − 4(1)(25) = 100 − 100 = 0 TOP: Compositions of Functions PTS: 2 REF: 011102a2 STA: A2.A.2 KEY: determine nature of roots given equation 295 ANS: 3 TOP: Using the Discriminant p(5) − p(0) = 17(1.15) PTS: 2 296 ANS: 2 2(5) − 17(1.15) 2(0) ≈ 68.8 − 17 ≈ 51 STA: A2.A.12 TOP: Functional Notation PTS: 2 REF: 011617a2 KEY: advanced 297 ANS: 2 2π s=θr= ⋅ 18 ≈ 23 5 STA: A2.N.10 TOP: Sigma Notation PTS: 2 KEY: arc length 298 ANS: 3 20 C 4 = 4,845 REF: 011526a2 STA: A2.A.61 TOP: Arc Length PTS: 2 299 ANS: 2 5 8 = sin 32 sinE REF: 011509a2 STA: A2.S.11 TOP: Combinations cos π 2 REF: 061527a2 + cos π + cos E ≈ 57.98 3π = 0 + −1 + 0 = −1 2 57.98 + 32 < 180 (180 − 57.98) + 32 < 180 PTS: 2 REF: 011419a2 STA: A2.A.75 300 ANS: 3 PTS: 2 REF: 061523a2 TOP: Differentiating Permutations and Combinations 16 TOP: Law of Sines - The Ambiguous Case STA: A2.S.9 ID: A 301 ANS: 3 n 19 S n = [2a + (n − 1)d] = [2(3) + (19 − 1)7] = 1254 2 2 PTS: 2 KEY: arithmetic 302 ANS: 1 3 3 10 ⋅ = p 2 5 15 = REF: 011202a2 STA: A2.A.35 TOP: Summations REF: 011226a2 STA: A2.A.5 TOP: Inverse Variation STA: A2.A.9 TOP: Negative Exponents 3 p 5 25 = p PTS: 2 303 ANS: 2 1 1+x +1 x x 1 x −1 + 1 = = = x x+1 x+1 x+1 PTS: 2 REF: 011211a2 304 ANS: 4 4 ⋅ 0 + 6 ⋅ 1 + 10 ⋅ 2 + 0 ⋅ 3 + 4k + 2 ⋅ 5 =2 4 + 6 + 10 + 0 + k + 2 4k + 36 =2 k + 22 4k + 36 = 2k + 44 2k = 8 k =4 PTS: 2 REF: 061221a2 305 ANS: 3 2(x − 3) x(x − 3) 5x − = x(x − 3) x(x − 3) x(x − 3) STA: A2.S.3 TOP: Average Known with Missing Data 5x − 2x + 6 = x 2 − 3x 0 = x 2 − 6x − 6 PTS: KEY: 306 ANS: TOP: 307 ANS: TOP: 2 REF: 011522a2 STA: A2.A.23 irrational and complex solutions 3 PTS: 2 REF: 061416a2 Evaluating Exponential Expressions 1 PTS: 2 REF: 061210a2 Negative Exponents 17 TOP: Solving Rationals STA: A2.A.12 STA: A2.A.9 ID: A 308 ANS: 3 log4m2 = log 4 + log m2 = log4 + 2 logm PTS: 2 REF: 061321a2 STA: A2.A.19 TOP: Properties of Logarithms KEY: splitting logs 309 ANS: 4 (3 − 2a) 0 + (3 − 2a) 1 + (3 − 2a) 2 = 1 + 3 − 2a + 9 − 12a + 4a 2 = 4a 2 − 14a + 13 PTS: 2 KEY: advanced 310 ANS: 2 x 3 − 2x 2 − 9x + 18 REF: 061526a2 STA: A2.N.10 TOP: Sigma Notation REF: 011511a2 STA: A2.A.7 TOP: Factoring by Grouping STA: A2.A.24 TOP: Solving Quadratics x 2 (x − 2) − 9(x − 2) (x 2 − 9)(x − 2) (x + 3)(x − 3)(x − 2) PTS: 2 311 ANS: 1 2 1 1 − = 1 2 4 64 PTS: KEY: 312 ANS: TOP: 313 ANS: TOP: 314 ANS: 2 REF: 081527a2 completing the square 3 PTS: 2 Domain and Range 1 PTS: 2 Negative and Fractional Exponents 4 REF: 081517a2 STA: A2.A.39 KEY: real domain, exponential REF: 011402a2 STA: A2.A.8 2 cos θ = 1 cos θ = 1 2 θ = cos −1 PTS: 2 KEY: basic 1 = 60, 300 2 REF: 061203a2 STA: A2.A.68 18 TOP: Trigonometric Equations ID: A 315 ANS: 4 3x + y xy 3x + y xy 3x + y = ⋅ = 2 xy 2 2 xy PTS: 2 316 ANS: 3 3 REF: 011603a2 = 3a 2 b PTS: KEY: 317 ANS: 3y 2y − 6 3 ⋅ a 3b 3b 3b = STA: A2.A.17 3 3b 3b = 3ab ab 2 REF: 081019a2 STA: A2.A.15 index = 2 3 3y 3y − 9 3(y − 3) 3 9 9 + = − = = = 6 − 2y 2y − 6 2y − 6 2y − 6 2(y − 3) 2 PTS: 2 318 ANS: 3 − 2 sec x = 2 TOP: Complex Fractions TOP: Rationalizing Denominators REF: 011325a2 STA: A2.A.16 TOP: Addition and Subtraction of Rationals PTS: 2 REF: 011322a2 KEY: reciprocal functions 319 ANS: 3 K = (10)(18) sin46 ≈ 129 STA: A2.A.68 TOP: Trigonometric Equations PTS: 2 REF: 081021a2 KEY: parallelograms 320 ANS: 1 180 360 2⋅ = STA: A2.A.74 TOP: Using Trigonometry to Find Area PTS: KEY: 321 ANS: TOP: STA: A2.M.2 TOP: Radian Measure REF: 061219a2 STA: A2.N.8 sec x = − 2 2 cos x = − 2 2 x = 135,225 π π 2 REF: 011220a2 degrees 3 PTS: 2 Conjugates of Complex Numbers 19 ID: A 322 ANS: 4 2π = 30 b b= π 15 PTS: 2 REF: 011227a2 STA: A2.A.72 TOP: Identifying the Equation of a Trigonometric Graph 323 ANS: 2 (x + 3)(x − 3) 5(x + 3) 30 + = 3 is an extraneous root. (x + 3)(x − 3) (x + 3)(x − 3) (x − 3)(x + 3) 30 + x 2 − 9 = 5x + 15 x 2 − 5x + 6 = 0 (x − 3)(x − 2) = 0 x=2 PTS: 2 REF: 061417a2 KEY: rational solutions 324 ANS: 2 −b −6 = =2 −3 a STA: A2.A.23 TOP: Solving Rationals PTS: 325 ANS: TOP: 326 ANS: x2 STA: A2.A.20 REF: 061514a2 TOP: Roots of Quadratics STA: A2.A.55 2 REF: 011613a2 3 PTS: 2 Trigonometric Ratios 3 + y 2 − 16x + 6y + 53 = 0 x 2 − 16x + 64 + y 2 + 6y + 9 = −53 + 64 + 9 (x − 8) 2 + (y + 3) 2 = 20 PTS: 2 REF: 011415a2 STA: A2.A.47 TOP: Equations of Circles 327 ANS: 4 Students entering the library are more likely to spend more time studying, creating bias. PTS: 2 REF: fall0904a2 328 ANS: 3 40 − 10 30 = = 6 a n = 6n + 4 5 6−1 a 20 = 6(20) + 4 = 124 PTS: 2 REF: 081510a2 STA: A2.S.2 TOP: Analysis of Data STA: A2.A.32 TOP: Sequences 20 ID: A 329 ANS: 2 cos(x − y) = cos x cos y + sin x siny = b ⋅b +a ⋅a = b2 + a2 PTS: 2 REF: 061421a2 STA: A2.A.76 TOP: Angle Sum and Difference Identities KEY: simplifying 330 ANS: 4 sin(θ + 90) = sin θ ⋅ cos 90 + cos θ ⋅ sin90 = sin θ ⋅ (0) + cos θ ⋅ (1) = cos θ PTS: 2 REF: 061309a2 KEY: identities 331 ANS: 3 PTS: 2 TOP: Operations with Radicals 332 ANS: 2 x 2 + 2 = 6x STA: A2.A.76 TOP: Angle Sum and Difference Identities REF: 061407a2 STA: A2.A.14 KEY: with variables | index = 2 x 2 − 6x = −2 x 2 − 6x + 9 = −2 + 9 (x − 3) 2 = 7 PTS: KEY: 333 ANS: TOP: 334 ANS: 2 REF: 011116a2 STA: completing the square 1 PTS: 2 REF: Domain and Range KEY: 1 5 3 12 4 15 48 cos(A − B) = − + = − + 65 65 13 5 13 5 PTS: 2 KEY: evaluating 335 ANS: 2 2x − 4 = x − 2 REF: 011214a2 A2.A.24 TOP: Solving Quadratics 011313a2 STA: A2.A.39 real domain, radical = 33 65 STA: A2.A.76 TOP: Angle Sum and Difference Identities STA: A2.A.22 TOP: Solving Radicals 2x − 4 = x 2 − 4x + 4 0 = x 2 − 6x + 8 0 = (x − 4)(x − 2) x = 4,2 PTS: 2 REF: 061406a2 KEY: extraneous solutions 21 ID: A 336 ANS: 2 x 3 + 3x 2 − 4x − 12 x 2 (x + 3) − 4(x + 3) (x 2 − 4)(x + 3) (x + 2)(x − 2)(x + 3) PTS: 2 REF: 061214a2 337 ANS: 1 PTS: 2 TOP: Transformations with Functions 338 ANS: 3 3 C 1 ⋅5 C 2 = 3 ⋅ 10 = 30 STA: A2.A.7 REF: 061516a2 TOP: Factoring by Grouping STA: A2.A.46 PTS: 2 REF: 061422a2 339 ANS: 4 (−3 − 2i)(−3 + 2i) = 9 − 4i 2 = 9 + 4 = 13 STA: A2.S.12 TOP: Combinations PTS: 2 REF: 011512a2 STA: A2.N.9 TOP: Multiplication and Division of Complex Numbers 340 ANS: 3 PTS: 2 REF: 011119a2 TOP: Families of Functions 341 ANS: 1 180 5⋅ ≈ 286 STA: A2.A.52 π PTS: KEY: 342 ANS: TOP: 343 ANS: TOP: 344 ANS: 2 REF: 011427a2 STA: A2.M.2 degrees 2 PTS: 2 REF: 011417a2 Differentiating Permutations and Combinations 1 PTS: 2 REF: 061202a2 Domain and Range KEY: graph 1 10x 2 log T = log = log 10 + log x 2 − log y = 1 + 2 logx − log y y TOP: Radian Measure STA: A2.S.9 STA: A2.A.51 PTS: 2 REF: 011615a2 STA: A2.A.19 TOP: Properties of Logarithms KEY: splitting logs 345 ANS: 3 PTS: 2 REF: fall0913a2 STA: A2.A.65 TOP: Graphing Trigonometric Functions 346 ANS: 3 (1) and (4) fail the horizontal line test and are not one-to-one. Not every element of the range corresponds to only one element of the domain. (2) fails the vertical line test and is not a function. Not every element of the domain corresponds to only one element of the range. PTS: 2 REF: 081020a2 STA: A2.A.43 22 TOP: Defining Functions ID: A 347 ANS: 1 1 (7.4)(3.8) sin 126 ≈ 11.4 2 PTS: KEY: 348 ANS: TOP: 349 ANS: TOP: 350 ANS: 3 2 REF: 011218a2 basic 4 PTS: 2 Negative Exponents 2 PTS: 2 Correlation Coefficient 3 STA: A2.A.74 TOP: Using Trigonometry to Find Area REF: 061506a2 STA: A2.A.9 REF: 081502a2 STA: A2.S.8 4 3 a 15 a = 4a 5 3 a PTS: 2 REF: 061204a2 STA: A2.A.13 KEY: index > 2 351 ANS: 4 (x + i) 2 − (x − i) 2 = x 2 + 2xi + i 2 − (x 2 − 2xi + i 2 ) = 4xi PTS: 2 REF: 011327a2 STA: A2.N.9 TOP: Multiplication and Division of Complex Numbers 352 ANS: 3 PTS: 2 REF: 061119a2 TOP: Graphing Trigonometric Functions 353 ANS: 1 (4a + 4) − (2a + 1) = 2a + 3 PTS: 2 354 ANS: 3 (3i)(2i) 2 (m + i) REF: 011401a2 STA: A2.A.30 (3i)(4i 2 )(m + i) (3i)(−4)(m + i) (−12i)(m + i) −12mi − 12i 2 −12mi + 12 PTS: 2 REF: 061319a2 STA: A2.N.9 TOP: Multiplication and Division of Complex Numbers 23 TOP: Simplifying Radicals STA: A2.A.65 TOP: Sequences ID: A 355 ANS: 4 1 2 f(16) = 4(16) + 16 + 16 0 = 4(4) + 1 + = 17 − 1 4 1 2 1 2 PTS: 2 REF: 081503a2 356 ANS: 1 2x − 1 > 5. 2x − 1 < −5 2x > 6 2x > −4 x>3 x < −2 PTS: 2 KEY: graph 357 ANS: 1 REF: 061307a2 STA: A2.N.1 TOP: Negative and Fractional Exponents STA: A2.A.1 TOP: Absolute Value Inequalities . PTS: 2 REF: 061225a2 STA: A2.S.8 358 ANS: 2 PTS: 2 REF: 011502a2 TOP: Identifying the Equation of a Graph 359 ANS: 2 PTS: 2 REF: 011315a2 TOP: Trigonometric Ratios 360 ANS: 2 12 − 7 = 5 TOP: Correlation Coefficient STA: A2.A.52 PTS: 2 KEY: frequency 361 ANS: 2 STA: A2.S.4 TOP: Central Tendency and Dispersion STA: A2.A.64 TOP: Using Inverse Trigonometric Functions tan30 = REF: 011525a2 STA: A2.A.55 3 3 = 30 . Arc cos k 3 3 k = cos 30 k =2 PTS: 2 KEY: advanced REF: 061323a2 24 ID: A 362 ANS: 1 11 P 11 3!2!2!2! = 39,916,800 = 831,600 48 PTS: 2 REF: 081512a2 363 ANS: 1 PTS: 2 TOP: Domain and Range 364 ANS: 2 1 (22)(13) sin 55 ≈ 117 2 STA: A2.S.10 TOP: Permutations REF: 011416a2 STA: A2.A.39 KEY: real domain, rational PTS: KEY: 365 ANS: 9 STA: A2.A.74 2 basic 3 −1 2 − PTS: 2 366 ANS: 1 11 P 11 REF: 061403a2 −1 16 TOP: Using Trigonometry to Find Area 2 = 3i 2 − 4i 2 = −i 2 STA: A2.N.6 TOP: Square Roots of Negative Numbers PTS: 2 REF: 011518a2 367 ANS: 4 5 2 3 1 225 = 3 C2 8 8 512 STA: A2.S.10 TOP: Permutations PTS: 2 REF: 011221a2 KEY: spinner 368 ANS: 3 3x 3 − 5x 2 − 48x + 80 STA: A2.S.15 TOP: Binomial Probability 2!2!2!2! REF: 061404a2 = 39,916,800 = 2,494,800 16 x 2 (3x − 5) − 16(3x − 5) (x 2 − 16)(3x − 5) (x + 4)(x − 4)(3x − 5) PTS: 2 REF: 011317a2 STA: A2.A.7 369 ANS: 2 PTS: 2 REF: 011301a2 TOP: Families of Functions 370 ANS: 3 x 1 2x 1 2x + 1 + = + = x − 1 2x − 2 2(x − 1) 2(x − 1) 2(x − 1) PTS: 2 REF: 011608a2 STA: A2.A.16 25 TOP: Factoring by Grouping STA: A2.A.52 TOP: Addition and Subtraction of Rationals ID: A 371 ANS: 1 sin(180 + x) = (sin 180)(cos x) + (cos 180)(sin x) = 0 + (−sinx) = −sinx PTS: 2 REF: 011318a2 STA: A2.A.76 KEY: identities 372 ANS: 1 1 + cos 2A 1 + 2 cos 2 A − 1 cos A = = = cot A sin 2A 2 sinA cos A sinA TOP: Angle Sum and Difference Identities PTS: KEY: 373 ANS: 2π = 6 TOP: Double Angle Identities 2 simplifying 2 REF: 061522a2 STA: A2.A.77 π 3 PTS: 2 REF: 061413a2 STA: A2.A.69 TOP: Properties of Graphs of Trigonometric Functions 374 ANS: 3 8x 3 2x 3 5 a 4 = 3xy = 3xy 5 3 = 24x 4 y 2 y y PTS: 2 375 ANS: 4 TOP: Sequences 376 ANS: 3 1000 = 500e .05t KEY: period REF: 061512a2 PTS: 2 STA: A2.A.33 REF: 061520a2 TOP: Sequences STA: A2.A.29 REF: 061313a2 STA: A2.A.6 TOP: Exponential Growth REF: 011316a2 STA: A2.A.74 TOP: Using Trigonometry to Find Area 2 = e .05t ln 2 = ln e .05t ln 2 .05t ⋅ ln e = .05 .05 13.9 ≈ t PTS: 2 377 ANS: 3 1 42 = (a)(8) sin 61 2 42 ≈ 3.5a 12 ≈ a PTS: 2 KEY: basic 26 ID: A 378 ANS: 4 PTS: 2 REF: 061217a2 379 ANS: 2 PTS: 2 TOP: Inverse Variation 380 ANS: 3 x(27i 6 ) + x(2i 12 ) = −27x + 2x = −25x STA: A2.A.66 REF: 061510a2 TOP: Determining Trigonometric Functions STA: A2.A.5 PTS: 381 ANS: TOP: 382 ANS: log x 2 STA: A2.N.7 REF: 061318a2 TOP: Imaginary Numbers STA: A2.A.49 STA: A2.A.19 TOP: Properties of Logarithms 2 REF: 011620a2 4 PTS: 2 Equations of Circles 2 = log 3a + log 2a 2 logx = log 6a 2 log 6 log a 2 log x = + 2 2 log x = 2 loga 1 log 6 + 2 2 log x = 1 log 6 + log a 2 PTS: 2 REF: 011224a2 KEY: splitting logs 383 ANS: 2 x ±σ 153 ± 22 131 − 175 PTS: KEY: 384 ANS: TOP: 385 ANS: TOP: 2 REF: 011307a2 STA: A2.S.5 interval 2 PTS: 2 REF: 061502a2 Radian Measure 1 PTS: 2 REF: 011306a2 Negative and Fractional Exponents 27 TOP: Normal Distributions STA: A2.M.1 STA: A2.A.8 ID: A 386 ANS: 1 2π =π 2 π =1 π PTS: 2 REF: 061519a2 STA: A2.A.69 TOP: Properties of Graphs of Trigonometric Functions 387 ANS: 4 log2x 3 = log 2 + log x 3 = log2 + 3logx KEY: period PTS: 2 REF: 061426a2 KEY: splitting logs 388 ANS: 2 The binomials are conjugates, so use FL. STA: A2.A.19 TOP: Properties of Logarithms PTS: 2 REF: 011206a2 KEY: multiplication 389 ANS: 2 STA: A2.N.3 TOP: Operations with Polynomials sin S = 8 17 S = sin −1 8 17 S ≈ 28°4' PTS: 2 REF: 061311a2 STA: A2.A.55 TOP: Trigonometric Ratios 390 ANS: 3 −b −(−4) = = 4. If the sum is 4, the roots must be 7 and −3. a 1 PTS: 2 REF: 011418a2 STA: A2.A.21 KEY: advanced 391 ANS: 4 g(−2) = 3(−2) − 2 = −8 f(−8) = 2(−8) 2 + 1 = 128 + 1 = 129 PTS: 2 KEY: numbers REF: 061503a2 STA: A2.A.42 28 TOP: Roots of Quadratics TOP: Compositions of Functions ID: A 392 ANS: 3 b ac + b a+ c c ac + b c ac + b = = ⋅ = c cd − b cd − b b cd − b d− c c PTS: 393 ANS: TOP: 394 ANS: x + 16 x−2 2 REF: 011405a2 STA: A2.A.17 TOP: Complex Fractions 1 PTS: 2 REF: 011320a2 STA: A2.A.72 Identifying the Equation of a Trigonometric Graph 3 7(x − 2) − ≤ 0 −6x + 30 = 0 x − 2 = 0 . Check points such that x < 2, 2 < x < 5, and x > 5. If x = 1 , x−2 x=2 −6x = −30 −6x + 30 ≤0 x−2 x=5 −6(1) + 30 24 −6(3) + 30 12 = = −24, which is less than 0. If x = 3, = = 12, which is greater than 0. If x = 6 , 1−2 3−2 −1 1 −6(6) + 30 −6 3 = = − , which is less than 0. 6−2 4 2 PTS: 2 395 ANS: 2 sec θ = REF: 011424a2 x2 + y2 = x STA: A2.A.23 TOP: Rational Inequalities (−4) 2 + 0 2 4 = = −1 −4 −4 PTS: 2 396 ANS: 1 720 6 P6 = = 60 12 3!2! REF: 011520a2 STA: A2.A.62 TOP: Determining Trigonometric Functions PTS: 2 397 ANS: 1 REF: 011324a2 STA: A2.S.10 TOP: Permutations 2 3 9 9 8 1 cos 2θ = 2 − 1 = 2 − 1 = − = 8 8 8 4 16 PTS: 2 KEY: evaluating 398 ANS: 3 4 = −2 −2 PTS: 2 REF: 081522a2 STA: A2.A.77 TOP: Double Angle Identities REF: 011304a2 STA: A2.A.31 TOP: Sequences 29 ID: A 399 ANS: 1 sin 120 = 3 2 csc 120 = ⋅ 2 3 3 3 = PTS: 2 REF: 081505a2 400 ANS: 2 PTS: 2 TOP: Trigonometric Ratios 401 ANS: 3 PTS: 2 TOP: Domain and Range 402 ANS: 2 log 9 − log 20 2 3 3 STA: A2.A.59 REF: 081010a2 TOP: Reciprocal Trigonometric Relationships STA: A2.A.55 REF: 061022a2 STA: A2.A.63 STA: A2.A.19 TOP: Properties of Logarithms log 3 2 − log(10 ⋅ 2) 2 log 3 − (log 10 + log 2) 2b − (1 + a) 2b − a − 1 PTS: 2 REF: 011326a2 KEY: expressing logs algebraically 403 ANS: 4 2x + 4 ⋅ x+2 x+2 x+2 = 2(x + 2) x + 2 = 2 x+2 x+2 PTS: 2 REF: 011122a2 STA: A2.A.15 TOP: Rationalizing Denominators KEY: index = 2 404 ANS: 3 1 1 h(−8) = (−8) − 2 = −4 − 2 = −6. g(−6) = (−6) + 8 = −3 + 8 = 5 2 2 PTS: 2 KEY: numbers 405 ANS: 4 10 = 2.5 4 PTS: 2 REF: 011403a2 STA: A2.A.42 TOP: Compositions of Functions REF: 011217a2 STA: A2.A.29 TOP: Sequences 30 ID: A Algebra 2/Trigonometry 2 Point Regents Exam Questions Answer Section 406 ANS: K = absinC = 6 ⋅ 6 sin50 ≈ 27.6 PTS: 2 REF: 011429a2 KEY: parallelograms 407 ANS: STA: A2.A.74 TOP: Using Trigonometry to Find Area PTS: 2 REF: 011230a2 KEY: basic 408 ANS: 2 5 3 = 6 32 3 = 576 C 6 5 5 5 3125 5 15,625 STA: A2.N.10 TOP: Sigma Notation PTS: 2 KEY: exactly 409 ANS: x < −1 or x > 5 . STA: A2.S.15 TOP: Binomial Probability −104. REF: 011532a2 x 2 − 4x − 5 > 0. x − 5 > 0 and x + 1 > 0 or x − 5 < 0 and x + 1 < 0 (x − 5)(x + 1) > 0 x > 5 and x > −1 x < 5 and x < −1 x>5 x < −1 PTS: 2 REF: 011228a2 STA: A2.A.4 KEY: one variable 410 ANS: 479,001,600 12 P 12 = = 39,916,800 39,916,800. 3!⋅ 2! 12 TOP: Quadratic Inequalities PTS: 2 411 ANS: REF: 081035a2 STA: A2.S.10 TOP: Permutations REF: fall0935a2 STA: A2.S.12 TOP: Sample Space 41,040. PTS: 2 1 ID: A 412 ANS: xi 8 − yi 6 = x(1) − y(−1) = x + y PTS: 2 REF: 061533a2 STA: A2.N.7 413 ANS: 2xi(i − 4i 2 ) = 2xi 2 − 8xi 3 = 2xi 2 − 8xi 3 = −2x + 8xi TOP: Imaginary Numbers PTS: 2 REF: 011533a2 STA: A2.N.9 TOP: Multiplication and Division of Complex Numbers 414 ANS: D: −5 ≤ x ≤ 8. R: −3 ≤ y ≤ 2 PTS: 2 KEY: graph 415 ANS: REF: 011132a2 STA: A2.A.51 TOP: Domain and Range PTS: 2 REF: 081029a2 416 ANS: cos θ 1 ⋅ sin2 θ ⋅ = cos θ sin θ sin θ STA: A2.A.34 TOP: Sigma Notation REF: 011634a2 STA: A2.A.67 TOP: Proving Trigonometric Identities PTS: 2 REF: 061528a2 KEY: common base shown 418 ANS: (x + 3) 2 + (y − 4) 2 = 25 STA: A2.A.27 TOP: Exponential Equations 15 ∑ 7n n=1 cos θ = cos θ PTS: 2 417 ANS: x−1 5 4x = 5 3 4x = 3x − 3 x = −3 PTS: 2 REF: fall0929a2 STA: A2.A.49 419 ANS: a 1 = 3. a 2 = 2(3) − 1 = 5. a 3 = 2(5) − 1 = 9. PTS: 2 REF: 061233a2 STA: A2.A.33 2 TOP: Writing Equations of Circles TOP: Sequences ID: A 420 ANS: b 2 − 4ac = 0 k 2 − 4(1)(4) = 0 k 2 − 16 = 0 (k + 4)(k − 4) = 0 k = ±4 PTS: 2 REF: 061028a2 STA: A2.A.2 KEY: determine equation given nature of roots 421 ANS: y = x 2 − 6 . f −1 (x) is not a function. TOP: Using the Discriminant x = y2 − 6 x + 6 = y2 ± x+6 = y PTS: 2 REF: 061132a2 KEY: equations 422 ANS: 45, 225 2 tan C − 3 = 3 tan C − 4 STA: A2.A.44 TOP: Inverse of Functions 1 = tanC tan−1 1 = C C = 45,225 PTS: 2 REF: 081032a2 STA: A2.A.68 TOP: Trigonometric Equations KEY: basic 423 ANS: Controlled experiment because Howard is comparing the results obtained from an experimental sample against a control sample. PTS: 2 424 ANS: a2b3 − 4 REF: 081030a2 PTS: 2 REF: 011231a2 KEY: index > 2 425 ANS: 3,628,800 10 P 10 = = 50,400 72 3!⋅ 3!⋅ 2! PTS: 2 REF: 061330a2 STA: A2.S.1 TOP: Analysis of Data STA: A2.A.13 TOP: Simplifying Radicals STA: A2.S.10 TOP: Permutations 3 ID: A 426 ANS: Q 1 = 3.5 and Q 3 = 10.5. 10.5 − 3.5 = 7. PTS: 2 KEY: compute 427 ANS: 2x + 1 = 4 REF: 011430a2 STA: A2.S.4 TOP: Central Tendency and Dispersion 2x + 1 = 16 2x = 15 x= 15 2 PTS: 2 REF: 011628a2 STA: A2.A.22 TOP: Solving Radicals KEY: basic 428 ANS: 37 2 1 1 2 1 3 3 2 1 37 2 1 6y 3 − y − y. y − y 12y + = 6y 3 + y − 4y 2 − y = 6y 3 − y − y 3 5 10 5 10 5 10 5 2 PTS: 2 REF: 061128a2 KEY: multiplication 429 ANS: 5 180 = 81°49' π 11 π STA: A2.N.3 TOP: Operations with Polynomials PTS: 2 KEY: degrees 430 ANS: STA: A2.M.2 TOP: Radian Measure STA: A2.A.67 TOP: Proving Trigonometric Identities REF: 011432a2 STA: A2.A.1 TOP: Absolute Value Inequalities REF: 011129a2 STA: A2.M.2 TOP: Radian Measure REF: 011531a2 sec θ sin θ cot θ = 1 cos θ ⋅ sin θ ⋅ =1 sin θ cos θ PTS: 2 REF: 011428a2 431 ANS: −4x + 5 < 13 −4x + 5 > −13 −2 < x < 4.5 −4x < 8 −4x > −18 x > −2 PTS: 2 432 ANS: 180 2.5 ⋅ ≈ 143.2° x < 4.5 π PTS: 2 KEY: degrees 4 ID: A 433 ANS: y = 180.377(0.954) x PTS: 2 KEY: exponential 434 ANS: sec x = 2 cos x = 1 2 cos x = 2 2 REF: 061231a2 STA: A2.S.7 TOP: Regression x = 45°,315° PTS: 2 REF: 061434a2 STA: A2.A.68 TOP: Trigonometric Equations KEY: reciprocal functions 435 ANS: 230. 10 + (1 3 − 1) + (2 3 − 1) + (3 3 − 1) + (4 3 − 1) + (5 3 − 1) = 10 + 0 + 7 + 26 + 63 + 124 = 230 PTS: 2 KEY: basic 436 ANS: y = 0.488(1.116) x REF: 011131a2 STA: A2.N.10 TOP: Sigma Notation PTS: 2 KEY: exponential 437 ANS: 594 = 32 ⋅ 46 sinC REF: 061429a2 STA: A2.S.7 TOP: Regression STA: A2.A.74 TOP: Using Trigonometry to Find Area STA: A2.A.58 TOP: Reciprocal Trigonometric Relationships 594 = sinC 1472 23.8 ≈ C PTS: 2 REF: 011535a2 KEY: parallelograms 438 ANS: cos x sinx sin x cot x sinx = = cos 2 x 1 sec x cos x PTS: 2 REF: 061334a2 5 ID: A 439 ANS: 83°50'⋅ π 180 ≈ 1.463 radians s = θ r = 1.463 ⋅ 12 ≈ 17.6 PTS: 2 KEY: arc length 440 ANS: REF: 011435a2 − STA: A2.A.61 TOP: Arc Length 3 2 PTS: 2 441 ANS: 6.6 r= = 9.9 2 3 REF: 061033a2 STA: A2.A.60 TOP: Unit Circle PTS: 2 KEY: radius 442 ANS: REF: 081532a2 STA: A2.A.61 TOP: Arc Length PTS: 2 REF: 061331a2 KEY: degrees, common angles STA: A2.A.56 TOP: Determining Trigonometric Functions 2 6 3 × = 2 2 4 6 ID: A 443 ANS: PTS: 2 444 ANS: A = 750e (0.03)(8) 3(x + 1) STA: A2.A.53 TOP: Graphing Exponential Functions REF: 061229a2 STA: A2.A.12 TOP: Evaluating Exponential Expressions REF: 011630a2 STA: A2.A.28 TOP: Logarithmic Equations STA: A2.M.2 TOP: Radian Measure STA: A2.S.15 TOP: Binomial Probability ≈ 953 PTS: 2 445 ANS: 8 x + 1 = 16 2 REF: 011234a2 = 24 3x + 3 = 4 3x = 1 x= 1 3 PTS: 2 KEY: basic 446 ANS: π ≈ 3.8 216 180 PTS: 2 REF: 061232a2 KEY: radians 447 ANS: 2 4 1 3 = 35 16 1 = 560 C 81 27 2187 7 4 3 3 PTS: 2 KEY: exactly REF: 081531a2 7 ID: A 448 ANS: 5 csc θ = 8 csc θ = 8 5 sin θ = 5 8 θ ≈ 141 PTS: 2 REF: 061332a2 STA: A2.A.68 KEY: reciprocal functions 449 ANS: 20(5 + 176) = 1810 a n = 9n − 4 . Sn = 2 a 1 = 9(1) − 4 = 5 TOP: Trigonometric Equations a 20 = 9(20) − 4 = 176 PTS: 2 REF: 011328a2 STA: A2.A.35 TOP: Summations KEY: arithmetic 450 ANS: no. over 20 is more than 1 standard deviation above the mean. 0.159 ⋅ 82 ≈ 13.038 PTS: 2 REF: 061129a2 KEY: predict 451 ANS: 81 − 57 sd = =8 3 STA: A2.S.5 TOP: Normal Distributions PTS: 2 REF: 011534a2 KEY: mean and standard deviation 452 ANS: −b −2 c k = . Product = Sum a a 3 3 STA: A2.S.5 TOP: Normal Distributions PTS: 2 453 ANS: STA: A2.A.20 TOP: Roots of Quadratics 57 + 8 = 65 81 − 2(8) = 65 REF: 061534a2 5(3 + 2) 3+ 5 × . 7 3− 2 3+ PTS: 2 2 2 = 5(3 + 2) 5(3 + 2) = 9−2 7 REF: fall0928a2 STA: A2.N.5 8 TOP: Rationalizing Denominators ID: A 454 ANS: (x + yi)(x − yi) = x 2 − y 2 i 2 = x 2 + y 2 PTS: 2 REF: 061432a2 STA: A2.N.9 TOP: Multiplication and Division of Complex Numbers 455 ANS: 108x 5 y 8 6xy = 18x 4 y 3 = 3x 2 y 2y 5 PTS: 2 REF: 011133a2 KEY: with variables | index = 2 456 ANS: a + 15 + 2a = 90 STA: A2.A.14 TOP: Operations with Radicals REF: 011330a2 STA: A2.A.58 TOP: Cofunction Trigonometric Relationships REF: 011229a2 STA: A2.A.22 TOP: Solving Radicals REF: 011333a2 STA: A2.A.6 TOP: Exponential Growth 3a + 15 = 90 3a = 75 a = 25 PTS: 2 457 ANS: 7. 4 − 2x − 5 = 1 − 2x − 5 = −3 2x − 5 = 9 2x = 14 x=7 PTS: 2 KEY: basic 458 ANS: 30700 = 50e 3t 614 = e 3t ln 614 = ln e 3t ln 614 = 3t ln e ln 614 = 3t 2.14 ≈ t PTS: 2 9 ID: A 459 ANS: 7.4 PTS: 2 REF: 061029a2 STA: A2.S.4 KEY: basic, group frequency distributions 460 ANS: TOP: Dispersion 2,298.65. PTS: 2 REF: fall0932a2 461 ANS: 1 1 −b c = − . Product = − Sum 12 2 a a STA: A2.A.12 TOP: Evaluating Exponential Expressions PTS: 2 462 ANS: STA: A2.A.20 TOP: Roots of Quadratics REF: 061328a2 3 2 3 2 ⋅ . If sin 60 = , then csc 60 = 3 2 3 PTS: 2 REF: 011235a2 463 ANS: 2x − 3 > 5 or 2x − 3 < −5 2x > 8 2x < −2 x>4 x < −1 3 3 = 2 3 3 STA: A2.A.59 PTS: 2 REF: 061430a2 STA: A2.A.1 464 ANS: (x + 1) 2 − (x + 1) = x 2 + 2x + 1 − x − 1 = x 2 + x TOP: Reciprocal Trigonometric Relationships TOP: Absolute Value Inequalities PTS: 2 REF: 081530a2 STA: A2.A.42 TOP: Compositions of Functions KEY: variables 465 ANS: 2 2 2 4 2 4 2 4 2 2 4 4 x − x + 1. x − 1 = x − 1 x − 1 = x 2 − x − x + 1 = x 2 − x + 1 3 9 3 3 3 3 9 3 3 9 PTS: 2 REF: 081034a2 KEY: multiplication STA: A2.N.3 10 TOP: Operations with Polynomials ID: A 466 ANS: PTS: 2 467 ANS: REF: 061435a2 197º40’. 3.45 × PTS: KEY: 468 ANS: 10x = 4 2 degrees 180 π STA: A2.A.46 TOP: Graphing Quadratic Functions STA: A2.M.2 TOP: Radian Measure ≈ 197°40 ′. REF: fall0931a2 1 x + x 4 9x 1 = 4 x 9x 2 = 4 x2 = 4 9 x= ± 2 3 PTS: 2 REF: 081534a2 STA: A2.A.23 KEY: rational solutions 469 ANS: 12t 8 − 75t 4 = 3t 4 (4t 4 − 25) = 3t 4 (2t 2 + 5)(2t 2 − 5) TOP: Solving Rationals PTS: 2 REF: 061133a2 STA: A2.A.7 TOP: Factoring the Difference of Perfect Squares 470 ANS: r A ≈ 0.976 r B ≈ 0.994 Set B has the stronger linear relationship since r is higher. PTS: 2 REF: 061535a2 STA: A2.S.8 11 TOP: Correlation Coefficient ID: A 471 ANS: r= 13 . (x + 5) 2 + (y − 2) 2 = 13 22 + 32 = PTS: 2 REF: 011234a2 STA: A2.A.49 TOP: Writing Equations of Circles 472 ANS: 68% of the students are within one standard deviation of the mean. 16% of the students are more than one standard deviation above the mean. PTS: 2 KEY: percent 473 ANS: (x + 1) 3 = 64 REF: 011134a2 STA: A2.S.5 TOP: Normal Distributions PTS: 2 KEY: basic 474 ANS: 180 2.5 ⋅ ≈ 143°14' REF: 061531a2 STA: A2.A.28 TOP: Logarithmic Equations PTS: 2 KEY: degrees 475 ANS: g(10) = a(10) REF: 061431a2 STA: A2.M.2 TOP: Radian Measure x+1 = 4 x=3 π PTS: 2 476 ANS: 2 1 − 10 = 100a 2 (−9) = −900a 2 REF: 061333a2 K = absinC = 18 ⋅ 22sin60 = 396 STA: A2.A.41 TOP: Functional Notation 3 = 198 3 2 PTS: 2 REF: 061234a2 STA: A2.A.74 KEY: parallelograms 477 ANS: 4xi + 5yi 8 + 6xi 3 + 2yi 4 = 4xi + 5y − 6xi + 2y = 7y − 2xi TOP: Using Trigonometry to Find Area PTS: 2 REF: 011433a2 STA: A2.N.7 478 ANS: 7. f(−3) = (−3) 2 − 6 = 3. g(x) = 2 3 − 1 = 7. TOP: Imaginary Numbers PTS: 2 KEY: numbers REF: 061135a2 STA: A2.A.42 12 TOP: Compositions of Functions ID: A 479 ANS: 1 ⋅ 15 ⋅ 31.6sin 125 ≈ 194 2 PTS: 2 KEY: advanced 480 ANS: STA: A2.A.74 TOP: Using Trigonometry to Find Area PTS: 2 REF: 011335a2 KEY: degrees 481 ANS: 2 2 3 11 2 7 x + x − x− 8 9 9 3 STA: A2.M.2 TOP: Radian Measure PTS: 2 REF: 011635a2 KEY: subtraction 482 ANS: 1 −1 cos 2 x cos 2 x 1 − cos 2 x ⋅ = = sin 2 x 1 1 cos 2 x cos 2 x STA: A2.N.3 TOP: Operations with Polynomials PTS: 2 483 ANS: STA: A2.A.58 TOP: Reciprocal Trigonometric Relationships 3× 2± 180 π REF: 011633a2 ≈ 171.89° ≈ 171°53′. REF: 081533a2 (−2) 2 − 4(6)(−3) 2 ± 76 2 ± 4 19 2 ± 2 19 1 ± 19 = = = = 2(6) 12 12 12 6 PTS: 2 REF: 011332a2 KEY: quadratic formula 484 ANS: (6 − x)(6 + x) (x + 6)(x − 3) ⋅ = 6−x (x + 6)(x + 6) x−3 PTS: 2 REF: 011529a2 STA: A2.A.25 TOP: Solving Quadratics STA: A2.A.17 TOP: Complex Fractions 13 ID: A 485 ANS: 11! = 1,663,200 3!⋅ 2!⋅ 2! PTS: 2 REF: 011631a2 486 ANS: 1 1 3 2 = 3 ⋅ 1 ⋅ 9 = 27 C 3 1 4 4 4 16 64 STA: A2.S.10 TOP: Permutations PTS: 2 REF: 061530a2 KEY: exactly 487 ANS: 1 sin 2 A cos 2 A + = 2 2 cos A cos A cos 2 A STA: A2.S.15 TOP: Binomial Probability STA: A2.A.67 TOP: Proving Trigonometric Identities tan2 A + 1 = sec 2 A PTS: 2 488 ANS: (5x − 1) 1 3 REF: 011135a2 =4 5x − 1 = 64 5x = 65 x = 13 PTS: 2 REF: 061433a2 STA: A2.A.28 TOP: Logarithmic Equations KEY: advanced 489 ANS: y = −3sin 2x . The period of the function is π , the amplitude is 3 and it is reflected over the x-axis. PTS: 2 REF: 061235a2 STA: A2.A.72 TOP: Identifying the Equation of a Trigonometric Graph 490 ANS: −b 11 c 6 = . Product = = 2 3x 2 − 11x + 6 = 0. Sum 3 a a 3 PTS: 2 491 ANS: 12 ⋅ 6 = 9w REF: 011329a2 STA: A2.A.20 TOP: Roots of Quadratics REF: 011130a2 STA: A2.A.5 TOP: Inverse Variation 8=w PTS: 2 14 ID: A 492 ANS: x 2 (x + 3) + 2(x + 3) = (x 2 + 2)(x + 3) PTS: 2 REF: 011629a2 493 ANS: 180 = 143°14' 2.5 π STA: A2.A.7 TOP: Factoring by Grouping PTS: 2 KEY: degrees 494 ANS: STA: A2.M.2 TOP: Radian Measure REF: 081528a2 y=0 PTS: 2 495 ANS: REF: 061031a2 5 3x 3 − 2 27x 3 = 5 x 2 3x − 2 9x 2 STA: A2.A.53 3x = 5x 3x − 6x TOP: Graphing Exponential Functions 3x = −x 3x PTS: 2 496 ANS: 25 C 20 = 53,130 REF: 061032a2 STA: A2.N.2 TOP: Operations with Radicals PTS: 2 497 ANS: REF: 011232a2 STA: A2.S.11 TOP: Combinations STA: A2.A.58 TOP: Reciprocal Trigonometric Relationships cos θ ⋅ 1 − cos 2 θ = 1 − cos 2 θ = sin 2 θ cos θ PTS: 2 REF: 061230a2 15 ID: A 498 ANS: 2x − 1 = 27 4 3 2x − 1 = 81 2x = 82 x = 41 PTS: 2 REF: 061329a2 STA: A2.A.28 TOP: Logarithmic Equations KEY: advanced 499 ANS: 3x −4 y 5 3y 5 (2x 3 y −7 ) 2 3y 5 (4x 6 y −14 ) 12x 6 y −9 12x 2 12x 2 = = = = 9 . x4 (2x 3 y −7 ) −2 x4 x4 y y9 PTS: 2 REF: 061134a2 500 ANS: K = absinC = 24 ⋅ 30 sin57 ≈ 604 STA: A2.A.9 TOP: Negative Exponents PTS: 2 REF: 061034a2 STA: A2.A.74 KEY: parallelograms 501 ANS: 10ax 2 − 23ax − 5a = a(10x 2 − 23x − 5) = a(5x + 1)(2x − 5) TOP: Using Trigonometry to Find Area PTS: 2 REF: 081028a2 KEY: multiple variables 502 ANS: x(x + 3) = 10 TOP: Factoring Polynomials STA: A2.A.7 x 2 + 3x − 10 = 0 (x + 5)(x − 2) = 0 x = −5, 2 PTS: 2 REF: 011431a2 STA: A2.A.3 KEY: equations 503 ANS: 31 − 19 12 = = 4 x + (4 − 1)4 = 19 a n = 7 + (n − 1)4 7−4 3 x + 12 = 19 TOP: Quadratic-Linear Systems x=7 PTS: 2 REF: 011434a2 STA: A2.A.29 16 TOP: Sequences ID: A 504 ANS: 2 −4 = 2 3x − 1 −4 = 3x − 1 −3 = 3x −1 = x PTS: 2 REF: 081529a2 STA: A2.A.27 TOP: Exponential Equations KEY: common base shown 505 ANS: Less than 60 inches is below 1.5 standard deviations from the mean. 0.067 ⋅ 450 ≈ 30 PTS: 2 REF: 061428a2 KEY: predict 506 ANS: i 13 + i 18 + i 31 + n = 0 STA: A2.S.5 TOP: Normal Distributions STA: A2.N.7 TOP: Imaginary Numbers PTS: 2 REF: fall0930a2 KEY: rational solutions 508 ANS: (x + 5) 2 + (y − 3) 2 = 32 STA: A2.A.23 TOP: Solving Rationals PTS: 2 REF: 081033a2 509 ANS: x 2 (x − 6) − 25(x − 6) STA: A2.A.49 TOP: Writing Equations of Circles STA: A2.A.7 TOP: Factoring by Grouping i + (−1) − i + n = 0 −1 + n = 0 n=1 PTS: 2 507 ANS: no solution. REF: 061228a2 4x 12 = 2+ x−3 x−3 4x − 12 =2 x−3 4(x − 3) =2 x−3 4≠ 2 (x 2 − 25)(x − 6) (x + 5)(x − 5)(x − 6) PTS: 2 REF: 061532a2 17 ID: A 510 ANS: 25 ⋅ 6 = 30q 5=q PTS: 2 511 ANS: −130 ⋅ π 180 REF: 011528a2 STA: A2.A.5 TOP: Inverse Variation REF: 011632a2 STA: A2.M.2 TOP: Radian Measure ≈ −2.27 PTS: 2 KEY: radians 512 ANS: 16 2x + 3 = 64 x + 2 (4 2 ) 2x + 3 = (4 3 ) x + 2 4x + 6 = 3x + 6 x=0 PTS: 2 REF: 011128a2 STA: A2.A.27 KEY: common base not shown 513 ANS: 1 3 3 4 = 35 1 81 = 2835 ≈ 0.173 7 C3 4 4 64 256 16384 TOP: Exponential Equations PTS: 2 KEY: exactly 514 ANS: ln e 4x = ln 12 REF: 061335a2 STA: A2.S.15 TOP: Binomial Probability PTS: 2 REF: 011530a2 KEY: without common base 515 ANS: −3,− 5,− 8,− 12 STA: A2.A.27 TOP: Exponential Equations STA: A2.A.33 TOP: Sequences 4x = ln 12 x= ln 12 4 ≈ 0.62 PTS: 2 REF: fall0934a2 18 ID: A 516 ANS: d−8 1 4 − 2d 2 d d − 8 2d 2 d − 8 = = × = 2d 5 1 2d + 3d 5d 3 + d 2d 2d 2 PTS: 2 517 ANS: y = 10.596(1.586) x REF: 061035a2 STA: A2.A.17 PTS: 2 REF: 081031a2 STA: A2.S.7 KEY: exponential 518 ANS: 2 8 = 85 + 14.4 < 180 1 triangle sin 85 sinC 2 sin 85 85 + 165.6 ≥ 180 −1 C = sin 8 TOP: Complex Fractions TOP: Regression C ≈ 14.4 PTS: 2 519 ANS: REF: 061529a2 x 2 − 6x − 27 = 0, STA: A2.A.75 TOP: Law of Sines - The Ambiguous Case −b c = 6. = −27. If a = 1 then b = −6 and c = −27 a a PTS: 4 KEY: basic 520 ANS: REF: 061130a2 STA: A2.A.21 TOP: Roots of Quadratics PTS: 2 REF: 061131a2 521 ANS: x − 1 + x − 4 + x − 9 + x − 16 = 4x − 30 STA: A2.A.12 TOP: Evaluating Exponential Expressions PTS: 2 KEY: advanced 522 ANS: STA: A2.N.10 TOP: Sigma Notation 3 e 3 ln 2 = e ln 2 = e ln 8 = 8 13 . sin θ = 2 PTS: 2 REF: 081535a2 y x2 + y2 = 2 (−3) 2 + 2 2 REF: fall0933a2 = 2 . csc θ = 13 STA: A2.A.62 19 13 . 2 TOP: Determining Trigonometric Functions ID: A 523 ANS: 11 3 −b c = − . Product = − Sum 5 5 a a PTS: 2 REF: 061030a2 STA: A2.A.20 TOP: Roots of Quadratics 524 ANS: Ordered, the heights are 71, 71, 72, 74, 74, 75, 78, 79, 79, 83. Q 1 = 72 and Q 3 = 79. 79 − 72 = 7. PTS: 2 REF: 011331a2 KEY: compute 525 ANS: 3 − 2x ≥ 7 or 3 − 2x ≤ −7 −2x ≥ 4 x ≤ −2 PTS: 2 KEY: graph STA: A2.S.4 TOP: Central Tendency and Dispersion STA: A2.A.1 TOP: Absolute Value Inequalities −2x ≤ −10 x≥5 REF: 011334a2 20 ID: A Algebra 2/Trigonometry 4 Point Regents Exam Questions Answer Section 526 ANS: x 3 + 5x 2 − 4x − 20 = 0 x 2 (x + 5) − 4(x + 5) = 0 (x 2 − 4)(x + 5) = 0 (x + 2)(x − 2)(x + 5) = 0 x = ±2,−5 PTS: 4 REF: 061437a2 527 ANS: sin(45 + 30) = sin 45 cos 30 + cos 45 sin 30 = STA: A2.A.26 6+ 4 2 3 2 1 6 2 ⋅ + ⋅ = + = 2 2 2 2 4 4 PTS: 4 REF: 061136a2 KEY: evaluating 528 ANS: 2 sin 2 x + 5 sin x − 3 = 0 STA: A2.A.76 TOP: Solving Polynomial Equations 2 TOP: Angle Sum and Difference Identities (2 sinx − 1)(sinx + 3) = 0 sinx = x= 1 2 π 5π 6 , 6 PTS: 4 REF: 011436a2 STA: A2.A.68 KEY: quadratics 529 ANS: y = 215.983(1.652) x . 215.983(1.652) 7 ≈ 7250 PTS: 4 KEY: exponential REF: 011337a2 STA: A2.S.7 1 TOP: Trigonometric Equations TOP: Regression ID: A 530 ANS: 3 1 ± ,− . 2 2 8x 3 + 4x 2 − 18x − 9 = 0 4x 2 (2x + 1) − 9(2x + 1) = 0 (4x 2 − 9)(2x + 1) = 0 4x 2 − 9 = 0 or 2x + 1 = 0 (2x + 3)(2x − 3) = 0 x= ± x= − 1 2 3 2 PTS: 4 REF: fall0937a2 531 ANS: (x + 4) 2 = 17x − 4 STA: A2.A.26 TOP: Solving Polynomial Equations STA: A2.A.28 TOP: Logarithmic Equations x 2 + 8x + 16 = 17x − 4 x 2 − 9x + 20 = 0 (x − 4)(x − 5) = 0 x = 4,5 PTS: 4 KEY: basic 532 ANS: 800. x = 4 2.5 REF: 011336a2 = 32. y − 3 2 = 125 y = 125 − 2 3 . = 1 25 x 32 = = 800 y 1 25 PTS: 4 REF: 011237a2 STA: A2.A.28 TOP: Logarithmic Equations KEY: advanced 533 ANS: 2 6 1 2 2 7 1 1 2 8 1 0 0.468. 8 C 6 ≈ 0.27313. 8 C 7 ≈ 0.15607. 8 C 8 ≈ 0.03902. 3 3 3 3 3 3 PTS: 4 REF: 011138a2 KEY: at least or at most 534 ANS: a = 3, b = 2, c = 1 y = 3cos 2x + 1. STA: A2.S.15 PTS: 2 REF: 011538a2 STA: A2.A.72 TOP: Identifying the Equation of a Trigonometric Graph 2 TOP: Binomial Probability ID: A 535 ANS: 2 cos 2 x − 1 = cos x 2 cos 2 x − cos x − 1 = 0 (2 cos x + 1)(cos x − 1) = 0 1 cos x = − ,1 2 x = 0,120,240 PTS: 4 REF: 011638a2 KEY: double angle identities 536 ANS: 15 1 a = . (15)(10.3) sin35 ≈ 44 sin 103 sin 42 2 STA: A2.A.68 TOP: Trigonometric Equations STA: A2.A.74 TOP: Using Trigonometry to Find Area a ≈ 10.3 PTS: 4 REF: 061337a2 KEY: advanced 537 ANS: x 2 + 10x + 25 = 8 + 25 (x + 5) 2 = 33 x + 5 = ± 33 x = −5 ± 33 PTS: 4 REF: 011636a2 STA: A2.A.24 538 ANS: y = 27.2025(1.1509) x . y = 27.2025(1.1509) 18 ≈ 341 TOP: Completing the Square PTS: 4 KEY: exponential 539 ANS: 3 x 2 + = − x x+2 x+2 STA: A2.S.7 TOP: Regression STA: A2.A.23 TOP: Solving Rationals REF: 011238a2 x+2 3 = − x+2 x 1= − 3 x x = −3 PTS: 4 REF: 061537a2 KEY: rational solutions 3 ID: A 540 ANS: 13 = 10 − x x . x= 10 ± 100 − 4(1)(13) 10 ± 48 10 ± 4 3 = = = 5±2 3 2(1) 2 2 13 = 10x − x 2 x 2 − 10x + 13 = 0 PTS: 4 REF: 061336a2 STA: A2.A.23 TOP: Solving Rationals KEY: irrational and complex solutions 541 ANS: 362,880 9 P9 = = 3,780. VERMONT: 7 P 7 = 5,040 No. TENNESSEE: 96 4!⋅ 2!⋅ 2! PTS: 4 542 ANS: 10 12 = sin 32 sinB B = sin −1 REF: 061038a2 STA: A2.S.10 . C ≈ 180 − (32 + 26.2) ≈ 121.8. 10 sin32 ≈ 26.2 12 TOP: Permutations c 12 = sin32 sin 121.8 c= 12 sin121.8 ≈ 19.2 sin 32 PTS: 4 REF: 011137a2 STA: A2.A.73 KEY: basic 543 ANS: y = 2.001x 2.298 , 1,009. y = 2.001(15) 2.298 ≈ 1009 TOP: Law of Sines PTS: 4 REF: fall0938a2 544 ANS: 3 ± 7 . 2x 2 − 12x + 4 = 0 STA: A2.S.7 TOP: Power Regression STA: A2.A.24 TOP: Solving Quadratics x 2 − 6x + 2 = 0 x 2 − 6x = −2 x 2 − 6x + 9 = −2 + 9 (x − 3) 2 = 7 x−3= ± 7 x = 3± 7 PTS: 4 REF: fall0936a2 KEY: completing the square 4 ID: A 545 ANS: 1+ 1− 3 x 5 24 − x x2 ⋅ x(x + 3) x2 x 2 + 3x x = = = 2 2 x − 5x − 24 (x − 8)(x + 3) x − 8 x PTS: 4 REF: 061436a2 546 ANS: 2 4 1 1 − = 2 x +3 3−x x −9 3 STA: A2.A.17 TOP: Complex Fractions STA: A2.A.23 TOP: Solving Rationals 1 2 4 + = x + 3 x − 3 x2 − 9 x − 3 + 2(x + 3) 4 = (x + 3)(x − 3) (x + 3)(x − 3) x − 3 + 2x + 6 = 4 3x = 1 x= 1 3 PTS: 4 REF: 081036a2 KEY: rational solutions 547 ANS: 100 100 b a = = . sin 32 sin 105 sin 32 sin 43 b ≈ 182.3 a ≈ 128.7 PTS: 4 REF: 011338a2 STA: A2.A.73 TOP: Law of Sines KEY: basic 548 ANS: 0 5 1 4 2 3 5 C 0 ⋅ 0.57 ⋅ 0.43 + 5 C 1 ⋅ 0.57 ⋅ 0.43 + 5 C 2 ⋅ 0.57 ⋅ 0.43 ≈ 0.37 PTS: 4 REF: 061438a2 STA: A2.S.15 KEY: at least or at most 549 ANS: σ x = 14.9. x = 40. There are 8 scores between 25.1 and 54.9. TOP: Binomial Probability PTS: 4 KEY: advanced 550 ANS: TOP: Dispersion a 2 = 3 2 PTS: 4 −2 REF: 061237a2 STA: A2.S.4 3 −2 16 16 −2 27 3 a 3 = 3 = a 4 = 3 = = 3 256 4 4 3 REF: 011537a2 STA: A2.A.33 5 TOP: Sequences ID: A 551 ANS: 100 x T = . sin66 ≈ 88. sin 33 sin 32 97.3 x ≈ 97.3 t ≈ 88 PTS: 4 REF: 011236a2 STA: A2.A.73 TOP: Law of Sines KEY: advanced 552 ANS: |3x − 5| < x + 17 3x − 5 < x + 17 and 3x − 5 > −x − 17 −3 < x < 11 PTS: 4 553 ANS: 83°50'⋅ 2x < 22 4x > −12 x < 11 x > −3 REF: 081538a2 π 180 STA: A2.A.1 TOP: Absolute Value Inequalities ≈ 1.463 radians s = θ r = 1.463 ⋅ 12 ≈ 17.6 PTS: 2 KEY: arc length 554 ANS: −3 |6 − x| < −15 REF: 011435a2 STA: A2.A.61 TOP: Arc Length . |6 − x | > 5 6 − x > 5 or 6 − x < −5 1 > x or 11 < x PTS: 2 REF: 061137a2 STA: A2.A.1 KEY: graph 555 ANS: 4 1 5 0 5 C 4 ⋅ 0.28 ⋅ 0.72 + 5 C 5 ⋅ 0.28 ⋅ 0.72 ≈ 0.024 TOP: Absolute Value Inequalities PTS: 4 REF: 011437a2 KEY: at least or at most 556 ANS: TOP: Binomial Probability a= STA: A2.S.15 8 2 + 11 2 − 2(8)(11) cos 82 ≈ 12.67. The angle opposite the shortest side: 12.67 8 = sinx sin82 x ≈ 38.7 PTS: 4 KEY: advanced REF: 081536a2 STA: A2.A.73 6 TOP: Law of Cosines ID: A 557 ANS: 28 2 = 47 2 + 34 2 − 2(47)(34) cos A 784 = 3365 − 3196 cos A −2581 = −3196 cos A 2581 = cos A 3196 36 ≈ A PTS: 4 KEY: find angle 558 ANS: 23 2 REF: 061536a2 cos 2 B + sin 2 B = 1 cos B + 2 tanB = 5 = 1 41 2 cos 2 B + STA: A2.A.73 sinB = cos B TOP: Law of Cosines 5 2 5 8 + 15 23 + 41 3 4 12 12 23 5 tan(A + B) = = = = = 2 4 12 10 2 4 2 5 − 1 − 12 12 12 41 3 4 25 41 = 41 41 cos 2 B = cos B = 16 41 4 41 PTS: 4 REF: 081037a2 STA: A2.A.76 TOP: Angle Sum and Difference Identities KEY: evaluating 559 ANS: 32x 5 − 80x 4 + 80x 3 − 40x 2 + 10x − 1. 5 C 0 (2x) 5 (−1) 0 = 32x 5 . 5 C 1 (2x) 4 (−1) 1 = −80x 4 . 5 C 2 (2x) 3 (−1) 2 = 80x 3 . 5 C 3 (2x) 2 (−1) 3 = −40x 2 . 5 C 4 (2x) 1 (−1) 4 = 10x. 5 C 5 (2x) 0 (−1) 5 = −1 PTS: 4 REF: 011136a2 STA: A2.A.36 TOP: Binomial Expansions 560 ANS: 0.167. 10 C 8 ⋅ 0.6 8 ⋅ 0.4 2 + 10 C 9 ⋅ 0.6 9 ⋅ 0.4 1 + 10 C 10 ⋅ 0.6 10 ⋅ 0.4 0 ≈ 0.167 PTS: 4 REF: 061036a2 KEY: at least or at most STA: A2.S.15 7 TOP: Binomial Probability ID: A 561 ANS: y = 2.19(3.23) x 426.21 = 2.19(3.23) x 426.21 = (3.23) x 2.19 426.21 = x log(3.23) 2.19 log 426.21 2.19 =x log(3.23) log x ≈ 4.5 PTS: 4 REF: 011637a2 STA: A2.S.7 TOP: Exponential Regression 562 ANS: σ x ≈ 6.2. 6 scores are within a population standard deviation of the mean. Q 3 − Q 1 = 41 − 37 = 4 x ≈ 38.2 PTS: 4 REF: 061338a2 STA: A2.S.4 TOP: Dispersion KEY: advanced 563 ANS: 26.2%. 10 C 8 ⋅ 0.65 8 ⋅ 0.35 2 + 10 C 9 ⋅ 0.65 9 ⋅ 0.35 1 + 10 C 10 ⋅ 0.65 10 ⋅ 0.35 0 ≈ 0.262 PTS: 4 REF: 081038a2 STA: A2.S.15 KEY: at least or at most 564 ANS: y = 733.646(0.786) x 733.646(0.786) 12 ≈ 41 TOP: Binomial Probability PTS: 4 REF: 011536a2 KEY: exponential 565 ANS: x 2 (2x − 1) − 4(2x − 1) = 0 STA: A2.S.7 TOP: Regression STA: A2.A.26 TOP: Solving Polynomial Equations (x 2 − 4)(2x − 1) = 0 (x + 2)(x − 2)(2x − 1) = 0 x = ± 2, PTS: 4 1 2 REF: 081537a2 8 ID: A 566 ANS: 3 2 1 2 40 51 . 5 C 3 = 243 3 3 243 4 1 1 2 10 C 5 4 3 3 = 243 1 5 2 0 = 1 C 5 3 3 3 243 PTS: 4 REF: 061138a2 KEY: at least or at most 567 ANS: STA: A2.S.15 TOP: Binomial Probability STA: A2.A.73 TOP: Vectors F1 F2 27 27 = = . . sin 75 sin 60 sin 75 sin 45 F 1 ≈ 24 PTS: 4 568 ANS: 5.17 84.46 ± 5.17 F 2 ≈ 20 REF: 061238a2 79.29 − 89.63 5 + 7 + 5 = 17 PTS: 4 REF: 061538a2 STA: A2.S.4 KEY: advanced, group frequency distributions 569 ANS: −(x 2 − 4) −(x + 2)(x − 2) −(x + 2) x+3 1 × = × = (x + 4)(x + 3) 2(x − 2) x+4 2(x − 2) 2(x + 4) PTS: 4 REF: 061236a2 STA: A2.A.17 9 TOP: Dispersion TOP: Complex Fractions ID: A 570 ANS: 0, 60, 180, 300. sin 2θ = sin θ sin 2θ − sin θ = 0 2 sin θ cos θ − sin θ = 0 sin θ(2 cos θ − 1) = 0 sin θ = 0 2 cos θ − 1 = 0 θ = 0,180 cos θ = 1 2 θ = 60,300 PTS: 4 REF: 061037a2 KEY: double angle identities STA: A2.A.68 10 TOP: Trigonometric Equations ID: A Algebra 2/Trigonometry 6 Point Regents Exam Questions Answer Section 571 ANS: 3 81 x + 2x 4 x 3 3 4x 2 = 27 5x 3 3 + 2x 2 = 3 3 3 + 8x 2 = 3 5x 5x 3 4x 3 + 8x 2 − 5x = 0 x(4x 2 + 8x − 5) = 0 x(2x − 1)(2x + 5) = 0 x = 0, 1 5 ,− 2 2 PTS: 6 REF: 061239a2 KEY: common base not shown 572 ANS: R= STA: A2.A.27 28 2 + 40 2 − 2(28)(40) cos 115 ≈ 58 TOP: Exponential Equations 40 58 = sin 115 sinx x ≈ 39 PTS: 6 573 ANS: 33. a = REF: 061439a2 STA: A2.A.73 TOP: Vectors 10 2 + 6 2 − 2(10)(6) cos 80 ≈ 10.7. ∠C is opposite the shortest side. 10.7 6 = sinC sin80 C ≈ 33 PTS: 6 KEY: advanced 574 ANS: REF: 061039a2 (x + 14)(x + 22) = 800 x = −36 ± STA: A2.A.73 TOP: Law of Cosines (−36) 2 − 4(1)(−492) −36 + 3264 = ≈ 10.6 10 feet increase. 2(1) 2 x 2 + 36x + 308 = 800 x 2 + 36x − 492 = 0 PTS: 6 REF: 011539a2 KEY: quadratic formula STA: A2.A.25 1 TOP: Solving Quadratics ID: A 575 ANS: 2 x − 7x + 12 = 3 log 2 2x − 10 x= 23 ± (−23) 2 − 4(1)(92) ≈ 17.84, 5.16 2(1) x 2 − 7x + 12 =8 2x − 10 x 2 − 7x + 12 = 16x − 80 x 2 − 23x + 92 = 0 PTS: 6 REF: 081539a2 STA: A2.A.28 KEY: applying properties of logarithms 576 ANS: log (x + 3) (2x + 3)(x + 5) = 2 −6 is extraneous TOP: Logarithmic Equations (x + 3) 2 = (2x + 3)(x + 5) x 2 + 6x + 9 = 2x 2 + 13x + 15 x 2 + 7x + 6 = 0 (x + 6)(x + 1) = 0 x = −1 PTS: 6 REF: 011439a2 STA: A2.A.28 KEY: applying properties of logarithms 577 ANS: ln(T − T 0 ) = −kt + 4.718 . ln(T − 68) = −0.104(10) + 4.718. TOP: Logarithmic Equations ln(150 − 68) = −k(3) + 4.718 ln(T − 68) = 3.678 4.407 ≈ −3k + 4.718 k ≈ 0.104 PTS: 6 KEY: advanced T − 68 ≈ 39.6 T ≈ 108 REF: 011139a2 STA: A2.A.28 2 TOP: Logarithmic Equations ID: A 578 ANS: x 2 + x − 1 = −4x + 3 x 2 + x − 1 = 16x 2 − 24x + 9 2 −4 + 3 ≥ 0 3 1 ≥0 3 0 = 15x 2 − 25x + 10 0 = 3x 2 − 5x + 2 −4(1) + 3 < 0 0 = (3x − 2)(x − 1) x= 1 is extraneous 2 ,x≠1 3 PTS: 6 REF: 011339a2 KEY: extraneous solutions 579 ANS: x 4 + 4x 3 + 4x 2 + 16x = 0 STA: A2.A.22 TOP: Solving Radicals STA: A2.A.26 TOP: Solving Polynomial Equations x(x 3 + 4x 2 + 4x + 16) = 0 x(x 2 (x + 4) + 4(x + 4)) = 0 x(x 2 + 4)(x + 4) = 0 x = 0,±2i,−4 PTS: 6 580 ANS: REF: 061339a2 r 2 = 25 2 + 85 2 − 2(25)(85) cos 125. 101.43, 12. r 2 ≈ 10287.7 r ≈ 101.43 101.43 2.5 = sinx sin 125 x ≈ 12 PTS: 6 REF: fall0939a2 STA: A2.A.73 3 TOP: Vectors ID: A 581 ANS: 16 15 = sinA sin 40 sin A = 10 12 = sin 50 sinC 16 sin40 15 A ≈ 43.3 sin C = d 12 = sin 63.2 sin66.8 12 sin50 10 C ≈ 66.8 d= 12 sin 63.2 sin 66.8 d ≈ 11.7 PTS: 6 REF: 011639a2 STA: A2.A.73 TOP: Law of Sines KEY: advanced 582 ANS: 9 1 − , and 1 , 11 . y = x + 5 . 4x 2 + 17x − 4 = x + 5 2 2 2 2 y = 4x 2 + 17x − 4 4x 2 + 16x − 9 = 0 (2x + 9)(2x − 1) = 0 x= − 1 9 and x = 2 2 9 1 1 11 y = − + 5 = and y = + 5 = 2 2 2 2 PTS: 6 REF: 061139a2 STA: A2.A.3 KEY: algebraically 583 ANS: −2(x 2 + 6) x 2 (x − 3) + 6(x − 3) 2x − 4 x 2 + 2x − 8 ⋅ ÷ . 16 − x 2 x 4 − 3x 3 x4 x 2 − 4x TOP: Quadratic-Linear Systems (x 2 + 6)(x − 3) 2(x − 2) (4 + x)(4 − x) ⋅ 3 ⋅ x(x − 4) x (x − 3) (x + 4)(x − 2) −2(x 2 + 6) x4 PTS: 6 KEY: division REF: 011239a2 STA: A2.A.16 4 TOP: Multiplication and Division of Rationals ID: A 584 ANS: 5 cos θ − 2 sec θ + 3 = 0 5 cos θ − 2 +3= 0 cos θ 5 cos 2 θ + 3 cos θ − 2 = 0 (5 cos θ − 2)(cos θ + 1) = 0 cos θ = 2 ,−1 5 θ ≈ 66.4,293.6,180 PTS: 6 REF: 061539a2 KEY: reciprocal functions 585 ANS: 1 x3 + x − 2 =2 x = − ,−1 log x + 3 x 3 STA: A2.A.68 TOP: Trigonometric Equations x3 + x − 2 = (x + 3) 2 x x3 + x − 2 = x 2 + 6x + 9 x x 3 + x − 2 = x 3 + 6x 2 + 9x 0 = 6x 2 + 8x + 2 0 = 3x 2 + 4x + 1 0 = (3x + 1)(x + 1) 1 x = − ,−1 3 PTS: 6 KEY: basic REF: 081039a2 STA: A2.A.28 5 TOP: Logarithmic Equations

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