( ) = 80cos 2π. ( ) = 40cos 2π. ( ) = 45cos 2π. ( ) = 5cos 65

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Brendan Wade
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1 Part I Answer all 24 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each question, write on the separate answer sheet the numeral preceding the word or expression that best completes the statement or answers the question. [48] 1 A survey of 150 randomly selected members of a fitness club were asked if they use the fitness club as much as they would like to. The staff then conducted a simulation of 50 more polls of 150 members, assuming that 40% of members are using the club as much as they would like to. The output of the simulation is shown in the diagram below. Given this output, and assuming 95% confidence level, the margin of error for the poll is closest to (1) 0.05 (3) 0.08 (2) 0.06 (4) A Ferris wheel has a diameter of 80 feet. Andy enters the Ferris wheel at its lowest point, 5 feet above the ground, at t = 0 seconds. One complete rotation takes 65 seconds. Which function models Andy s vertical height, h( t ), at t seconds? (1) h t (2) h t ( ) = 80cos 2π ( ) = 45cos 2π 65 t t + 40 (3) h t (4) h t ( ) = 40cos 2π ( ) = 5cos t π t +80

2 3 When factored completely, x 4 13x is equivalent to (1) ( x 2 6) ( x 2 6) (3) ( x 2) ( x 2) ( x 3) ( x 3) (2) ( x 2 4) ( x 2 9) (4) ( x 2) ( x +2) ( x 3) ( x +3) 4 Which ordered pair is a solution to the system below? x 2 4 y 2 = 16 y = x 4 (1) (0, -4) (3) (6, 2) (2) (4, 0) (4) (2, -2) 5 Suppose that A and B are events in a sample space with ( ) = 0.8, P( B) = 0.7, and P( B A) = 0.5. Then P( A B) = P A (1) 0.35 (3) (2) 0.4 (4) Julianne scored an 88 on her physics test. The class average was 79.3, and the standard deviation was 7.5. What is the z- score for Julianne s test score? (1) 1.16 (3) 1.30 (2) 1.45 (4) 1.60

3 7 Which summation will not produce ? 12 (1) b (3) 2d 2 b=2 6 7 d=2 ( ) (2) 2a (4) 2 c +1 a=1 5 c=0 ( ) 8 Last year, the total revenue for Coyle s Ice Cream increased 3.45% over the previous year. If this trend were to continue, which expression, using x as the number of months, could the owner of Coyle s use to approximate their monthly percent increase in revenue? (1) ( ) x (3) ( ) x (2) ( ) 12 x (4) ( ) x 12 When you plug in 12 for x, you should get Identify the vertex, focus, and directrix of y = 1 ( 8 x 2 ) 2 +5 (1) Vertex (2, 5), Focus (2, 7), Directrix y = 3 (2) Vertex (2, -5), Focus (0, -1), Directrix at y = -9 (3) Vertex (2, -5), Focus (0,-9), Directrix at y = -1 (4) Vertex (2, 5), Focus (2, 3), Directrix at y = 7 10 The expression 3i ( 2i 2 5i) is equivalent to (1) 15 6i (3) 15 5i (2) 15 5i (4) 1+0i USE THE CALCULATOR!!!!

11 Given the functions f ( x), g( x), and h( x) shown below: x 1 g(x) 5 0 3 1 1 2 1 3 3 4 5 5 7 6 9 Which describes the average rate of change for each function over the interval [3, 6]?

4 11 Given the functions f ( x), g( x), and h( x) shown below: x 1 g(x) Which describes the average rate of change for each function over the interval [3, 6]? (1) f x (2) g x (3) h x ( ) has the greatest average rate of change ( ) has the greatest average rate of change ( ) has the greatest average rate of change (4) All three have the same rate of change 12 If $1,200 is invested at a nominal interest rate of 3.2% compounded quarterly, then what is it worth after 10 years if no additional money is deposited or withdrawn from the investment? (1) $ (3) $ (2) $ (4) $ Which expression below represents the y-intercept of the function 3 ( ) = 24log b x + b f x ( ) +5? (1) 5 (3) 72 (2) 13 (4) 77

14 The first two terms of a geometric sequence

Which of the following would be closest to the

(1) 2,664 (3) 2,668 (2) 2,666 (4) 2,670 15 What

5 14 The first two terms of a geometric sequence are 2000 and 500. Which of the following would be closest to the sum of the first six terms? (1) 2,664 (3) 2,668 (2) 2,666 (4) 2, What is the solution set of the equation 30 x = 5 x 3? (1) {2, 3} (3) {3} (2) {2} (4) { } 16 The graph below represents f ( x) Which of the following is the graph of f ( x)? (1) (3) (2) (4)

6 17 A cliff diver on a Carribean 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 t seconds is h t ( ) = 16t 2 +5t How many seconds, to the nearest hundredth, does it take the diver to fall 45 feet below his starting point? (1) 1.45 (3) 2.10 (2) 1.84 (4) The formula for the nth term of the sequence 3, -6, 12, -24, 48 is (1) a n = 2( 3) n (3) a n = 2( 3) n 1 (2) a n = 3( 2) n (4) a n = 3( 2) n 1 19 Mrs. Harding bowls regularly and her average score is 182. Her bowling scores approximate a normal distribution with a standard deviation of 8.5. Mrs. Harding can expect to bowl between 182 and 199: (1) About 47.7% of the time (3) About 34% of the time (2) More than 50% of the time (4) Less than 16% of the time

7 ( ) 20 Which statement is incorrect for the graph of y = 3cos π 3 x 4 +7? (1) The period is 6 (2) The amplitude is 3 (3) The range is [4, 10] (4) The midline is y = 4 21 Functions f, g, and h are given below ( ) = sin( 2x) ( ) = f ( x)+1 f x g x Which statement is true about functions f, g, and h? (1) f x (2) f x (3) f x (4) f x ( ) and g( x) are odd, h( x) is even ( ) and g( x) are even, h( x) is odd ( ) is odd, g( x) is neither, h( x) is even ( ) is even, g( x) is neither, h( x) is odd

8 22 Chadley was trying to solve the following system of equations: 2x + y 3z = 11 2y + 4z = x 3 x 5 y +2z = 18 Which ordered triple represents the solution to the system? (1) (-1, 1, -4) (3) (3, 8, 1) (2) (1, 3, -2) (4) (2, -3, 0) 23 The total area of a parallelogram is 4x 4 +3x 3 14x 2 +33x 35. Which of the following expressions best represents the length of the base of the parallelogram if the height is 4x 5? (1) x 3 +2x 2 x +7 (2) x 3 2x 2 + x 7 (3) 4x 4 +3x 3 14x 2 +33x 7 (4) x 3 +5x 2 x Which expression is the simplified version of log x + log y klogr? (1) log xy r k (3) log(x + y) r k (2) log( x + y r ) k (4) log( x + y) klogr

9 Part II Answer all 8 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 25 Use the properties of rational exponents to determine the value of y for the equation: 3 x 8 ( x 4 ) 1 3 = x y,x >1

10 26 Use an appropriate procedure to show that x 4 is a factor of the function ( ) = 2x 3 5x 2 11x 4 f x x - 4 is a factor. When 4 is substituted into the equation, the result is zero. When I divided f(x) by x - 4, the remainder is zero. This means that x - 4 must be a factor.

11 27 For the function!! = (! 3)! + 1, find!!! (!)

12 28 A survey of 850 alumni from St. Joseph s College was conducted to determine their gender and the highest degree they had achieved. Associate s Bachelor s Master s Doctorate Total Female Male Total Are the events student is a male and student has a doctorate degree independent? Justify your answer

13 29 Eastman Kodak Company stopped making Kodachrome film in 2003 due to the drop in use of the film. The table below shows the sales for film cameras, in thousands, and graph shows sales of digital cameras, in thousands, from 2004 to Determine which sales, film or digital, had the greatest average rate of change from 2005 to 2008.

14 30 The function f ( x) is graphed on the set of axes below. On the same set of axes, graph f ( x +2)+1

15 31 Show algebraically that 2 x ( ) x = 2+ 2 x

16 32 The table below shows the concentration of ozone in Earth s atmosphere at different altitudes. Write a regression equation that models these data, rounding all value to the nearest thousandth. 16

17 Part III Answer all 4 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [16] 33 The Bay Shore Bean is considering whether to sell a new coffee flavor, Java Junkie, in its store. The owners will launch a new flavor if at least 35% of its users will enjoy the particular flavor. Fifty customers are randomly selected to take a survey. Thirteen out of fifty customers said they would be willing to buy the flavor. Ms. Mauri, who loves everything coffee related, creates a simulation for them based on the requirement that 35% of their customers like the new flavor. Each dot in the graph shown below represents the proportion of users who would be in enjoy of the new flavor of coffee, each of sample size 50, simulated 100 times. Mean = Std. Dev = Assume the set of data is approximately normal and the owners want to be 95% confident of the results. Identify the 95% confidence interval Bay Shore Bean decides to move forward with the new blend, even though only 13 out of 50 customers said they would purchase it. Describe how the simulation data could be used to support this decision. 17

18 34 In negotiations between a local union and a company, it is estimated that there is a 70% chance that there will be an agreement on insurance benefits. It is also estimated that there is a 50% chance that there will be an agreement over salaries for the workers at that company. There is a 20% chance that no agreement will be reached on either issue. Find the probability that an agreement will be reached on both issues. Based on your answer, determine whether the agreement on salaries and the agreement on insurance are independent events. Justify your answer. 18

19 35 Titanium-44 is a radioactive isotope such that every 63 years, its mass decreases by half. For a sample of titanium-44 with an initial mass of 100 grams, write a function that will give the mass of the sample remaining, A t ( ), after t years. Algebraically, determine how long it will take, to the nearest tenth of a year, for the mass of the sample to weigh 70 grams. 19

20 36 Solve the following system of equations algebraically for all values of x, y, and z x +3y +5z = 45 6x 3y +2z = 10 2x +3y +8z = 72 20

21 Part IV Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen, except for graphs and drawings, which should be done in pencil. [6] 37 The ocean tides near Carr Beach follow a repeating pattern over time, with the amount of time between each low and high tide remaining relatively constant. On a certain day, low tide occurred at 8:30 AM, and high tide occurred at 3:00 PM. At high tide, the water was 12 inches above the average local sea level; at low tide, it was 12 inches below the average local sea level. Write a cosine function of the form f t ( ) = Acos( bt ) that models the water level, f ( t ), in inches above or below average Carr Beach sea level, as a function of the time t, measured in hours since 8:30 AM. 21

22 Question 37 continued Graph one cycle of this function on the grid provided People who fish in Carr Beach know that a certain species of fish is most plentiful when the water level is increasing. Explain whether you would recommend fishing for this species at 7:30 pm or 10:30 pm, based upon your model.

2015 Algebra II Common Core State Standards Sample Items

Algebra II Sample Items 2015 www.jmap.org 2015 Algebra II Common Core State Standards Sample Items 1 If a, b, and c are all positive real numbers, which graph could represent the sketch of the graph of