SY14-15 Algebra Exit Exam - PRACTICE Version

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1 Student Name: Directions: Solve each problem. You have a total of 90 minutes. Choose the best answer and fill in your answer document accordingly. For questions requiring a written response, write your answers neatly in the space provided in the test booklet. Do not use too much time on any one question. Solve as many as you can; then return to the others in the time you have left for this assessment. 1. Which of the following relations represent a function? You may use a calculator for any problems you choose, but some of the problems may best be done without using a calculator. Note: Unless otherwise stated, all of the following should be assumed. 1. Illustrative figures are NOT necessarily drawn to scale. 2. Geometric figures lie in a plane. 3. The word line indicates a straight line. 4. The word average indicates arithmetic mean. a. {( 14,7), (1,8), (1,7)} b. {( 19,10), (0,5), (16,17)} c. {(3,8), ( 19,15), (3,5)} d. {(1,10), (1, 1), (2,2)} 2. If A = 3x 3 and B = 2x 2 + 3x 5, what is B A? a. 2x 2 8 b. 2x 2 2 c. 2x 2 + 6x 8 d. 2x 2 6x 2 3. Which of the following is NOT a factor of x 3 9x x? a. x b. x 3 c. x + 6 d. x 6 4. Solve for x: (x 11) 5 < (2x 11) + 1 a. x > 6 b. x < 6 c. x < 2 d. x > 2 1 Continue on Next Page >

2 5. Solve for x in terms of p: x p x + p = 2 7 a. x = 9p 5 b. x = 5p 9 c. x = 2p 9 d. x = 5p How many solutions does the following system of equations have? 2x + 3y = 9 x + y = 3 a. 0 b. 1 c. 2 d. infinitely many 7. The graphs of y = f(x) and y = g(x) are shown below: For what values of x on the interval shown will f ( x) g( x)? a. 5 and 6 b. 4 and 7 c. 3, 1, and 4 d. 3, 1, 3 and 5 2 Continue on Next Page >

3 8. Which of the following statements is NOT true of the graph of the linear equation 2x + 6y = 26? a. The slope of a line perpendicular to this is 1/3. b. The x-intercept is 13. c. The line intersects the y axis at a positive value. d. As the values of x increase, the values of y decrease. 9. Solve for x in terms of b. Show your work in the space provided below. Write your final answer in the shaded box below. bx = Suppose the area of a rectangle (in square centimeters) is a rational number. Which of the following statements is true about the perimeter of the rectangle? a. The perimeter (in centimeters) must be rational. b. The perimeter (in centimeters) must be irrational. c. The perimeter (in centimeters) could be rational or irrational. d. The perimeter (in centimeters) is neither rational nor irrational. 3 Continue on Next Page >

4 11. The table below represents a linear model of the depth d (in meters) a submarine is located from the ocean s surface as a function of time t (in minutes). t (minutes) d (meters) Which of the following statements represents a correct interpretation of the slope? a. The total meters traveled for any number of minutes b. The number of meters traveled each minute c. The depth at 0 minutes d. The difference between the depth in meters at 0 minutes and 13 minutes 12. If A = 3x 4 and B = x 2 + 4x + 5, what is A B, the product of A and B? a. x 2 + 7x + 1 b. 3x 3 4x x 20 c. 3x 3 + 8x 2 x 20 d. 3x 3 + 8x x Solve for x. Show your work. Write your final answer in the shaded box below. 3x 2 27x 30 = 0 4 Continue on Next Page >

5 14. During the 2011 season, baseball player Smith s earnings, s, were $500,000 more than those of his teammate Jones s earnings, j. The two players earned a total of $6.75 million dollars. Which system of equations could be used to determine the amount each player earned in millions of dollars? a. { s + j = 6.75 s = j s 6.75 = j b. { j = s j 6.75 = s c. { s = j s + j = 6.75 d. { j = s 15. Jose is creating a map in the shape of a rectangle whose length is 4 inches longer than its width. Let w stand for the width of the map in inches. Which equation gives the perimeter P of the map in terms of w? a. P = 4w + 4 b. P = 4w + 8 c. P = 2w + 4 d. P = 2w The dimensions in inches of a rectangle are consecutive odd integers. Its area is 323 in 2. Which equation could be used to find the length of one of its sides? a. x(x + 2) = 323 b. 2x + 2(x + 2) = 323 c. x(x + 1) = 323 d. 2x + 2(x + 1) = Continue on Next Page >

6 17. The table shows x and y values for a given quadratic function. x y Based on the table, which of the following statements is true? a. The minimum y-value of the function is 4. b. The equation of the axis of symmetry is x = 2. c. The parabola opens downward. d. The related equation has no real solutions. 18. If 4 is one of the zeros of function f(x) = 2(x + 4)(7x 35), what is the other zero of this function? a. 5 b. 2 c. 5 d Suppose the graph of linear function f(x) = 1 x 3 is 4 shown below and that g(x) = 8. For what value of x does f(x) = g(x)? a. 20 b. 5 c. 1 d Continue on Next Page >

7 20. On one day, a business sold 21 sweatshirts. Gray sweatshirts each cost $19.95, while sweatshirts in other colors each cost $ In all, $ worth of sweatshirts were sold. How many gray sweatshirts and how many sweatshirts in other colors were sold? Define any variables you use, and show all your work. Provide your final answer in the shaded box below. 7 Continue on Next Page >

8 21. For homework, Terry has to create an equation of a parabola that has a vertex ( 6, 12) and includes point ( 10, 0). She proceeds with the following steps: y = a(x h) 2 + k step 0 y k = a(x h) 2 step 1 y 12 = a(x + 6) 2 step = a( ) 2 step 3 12 = a( 4) 2 step 4 12 = 16a step y 12 = = a step (x + 6)2 step 7 Where does Terry make her first mathematical error? a. Going from step 3 to step 4. b. Going from step 4 to step 5. c. Going from step 5 to step 6. d. Going from step 6 to step 7. 8 Continue on Next Page >

9 22. The function h(t) = 16t represents the height, h(t), in feet, of an object from the ground at t seconds after it is dropped. Which of the following is a realistic domain for this function? a. 4 t 4 b. 0 t 4 c. 0 h(t) 256 d. All real numbers 23. The following scatterplot shows the cost of a used Honda as a function of the miles driven. If the equation of the line of best fit for the data shown is y = x, which of the following statements best describes the slope of the equation? a. The advertised price for a used Honda increases on average $86.16 for every 1,000 miles the car is driven. b. The advertised price for a used Honda decreases on average $86.16 for every 1,000 miles the car is driven. c. The advertised price for a used Honda decreases on average $18,773 for every miles the car is driven. d. The advertised price for a used Honda increases on average $18,773 for every miles the car is driven. 9 Continue on Next Page >

10 24. The temperature, T, in degrees Fahrenheit in Chicago on January 10, 2015 h hours after 2 am is modeled by the function: T(h) = h 2 8h + 12, 0 h 10. For each of the below, use the space provided for your calculations. Write your final answer in the shaded boxes. a. According to the function, at what time(s) on January 10, 2015 was the temperature 5 degrees? a. b. According to the function, how long did it take for the temperature to reach its lowest point? b. c. According to the function, what was the lowest temperature that was reached? c. 25. There is a maximum of 800 tickets available for a basketball game. Ticket costs are $6 before the day of the game and $9 on the day of the game. The goal is to raise $5,000. Before the day of the game, 440 tickets were sold. Which inequality represents y, the number of tickets that need to be sold on the day of the game to meet the goal? a. y 262 b. y 263 c. 262 y 360 d. 263 y Continue on Next Page >

11 26. For a school play, Lisa is charging $6 for adult tickets and $4 for student tickets. There are enough seats in the school s auditorium for at most 80 people and Lisa s goal is to raise over $400. The following inequalities can be used to represent this situation where a is the number of adult tickets sold and s is the number of student tickets sold. 6a + 4s > 400 a + s 80 Which of the following does not represent a possible combination of tickets sold for Lisa to meet her goal? a. a = 43, s = 36 b. a = 46, s = 33 c. a = 52, s = 26 d. a = 58, s = The above graph represents Orlando s walk to school one morning. Which of the following provides a description of Orlando s walk? a. Orlando starts by walking, sprints as fast as he can and stops to catch his breath. b. Orlando starts by walking, stops to talk to his friend and runs to get to school on time. c. Orlando starts by running, stops to catch his breath and then walks slowly the rest of the way. d. Orlando starts by running, sprints as fast as he can and stops to catch his breath. 11 Continue on Next Page >

12 28. A box has a height h and a square base with side b. Its surface area, S, is given by the formula S = 2b 2 + 4bh. Which of the following equations expresses h in terms of S and b? a. h = S b2 2b b. h = S b 2 c. h = S 2b2 4b d. h = S 2b 2 +4b 29. What are all of the solutions of 4(x 1) 2 = 28? a. 1 ± 2 6 b. 1 ± 7 c. 1 ± 14 d. 1 ± Given the quadratic equation y = 2(x 1) 2 + 8, which point does NOT lie on the graph of the equation? a. (0, 8) b. (1, 8) c. ( 1, 16) d. (2, 10) 12 Continue on Next Page >

13 31. The graph of a linear equation in the form y = mx + b passes through the points (0,6) and (3,162). The graph of an exponential equation in the form y = a(r) x also passes through the same two points. Part I: What must be the value of m in y = mx + b in order for this to be true? Part II: What must be the value of a in y = a(r) x in order for this to be true? Write and bubble in your answers in the appropriate space on your answer sheet. Make sure to start in the first, farthest left box for each part on the answer sheet, for your response. Make sure to fill in the appropriate bubble below each box you write in. 32. Jane dives off a diving board that is 8 feet above the water. Her height in feet above the water h(t) is given by the equation h(t) = 16t t + 8 where t is time in seconds. Which of the following is the best interpretation of h(t) = 0 within this context? a. t is the time when she begins her dive. b. t is time when she hits the water. c. t is time when she is the highest above the water. d. t is the time when she passes the diving board. 33. Given f(n + 1) = 3f(n) and f(0) = 4, what is f(3)? a. 3 b. 9 c. 81 d Continue on Next Page >

14 34. Sam gets an afternoon job selling ice cream bars from a food cart. He must pay $0.85 for each ice cream bar that he is going to sell and a fixed cost of $25.00 to rent the cart each day. If he purchases x ice cream bars each day, which equation expresses his total daily costs, c? a. c = 0.85x b. c = 25x c. c = x d. c = 25x Jamal saves the same amount every week. After 4 weeks of working, he saved a total of $32. By the end of week 15, Jamal had saved a total of $120. Which function represents Jamal s total savings, f(w)? a. f(w) = 8w, where w is the number of weeks Jamal worked b. f(w) = 8w, where w is the amount Jamal saved per week c. f(w) = 8w + 32, where w is the number of weeks and 32 is the amount Jamal saved each week d. f(w) = 8w + 32, where w is the amount Jamal saved per week and 32 is his initial deposit 14 Continue on Next Page >

15 36. The graph below shows Marianna s distance from home (in yards) as she walks to school in the morning as a function of time in minutes. The graph has been divided into five intervals labeled with letters A-E. How much faster (in yards per minute) does Marianna walk during interval D than interval B? Write and bubble in your answer in the appropriate space on your answer sheet. Make sure to start in the first, farthest left box on the answer sheet for your response. Make sure to fill in the appropriate bubble below each box you write in. 37. A ball is dropped from a height of 500 inches. The following table gives the height of each bounce. bounce number n bounce height h Which equation below fits this data shown? a. h = n b. h = n c. h = n d. h = n 15 Continue on Next Page >

16 38. The function f(x) = (x + 3) 2 4 is a transformation of function h(x) = x 2. Which of the following best describes the transformations that were applied? a. Translated 3 units to the left and 4 units down. b. Translated 3 units to the right and 4 units down. c. Translated 4 units to the left and 3 units up. d. Translated 4 units to the right and 3 units up. 39. A portion of the graph of a quadratic function f(x) is shown in the xy plane. Selected values of a linear function g(x) are shown in the table. x g(x) Given the graph and table which statement below about f(x) and g (x) is true? a. f( 1) < g( 3) b. f( 1) > g( 3) c. f( 2) < g(6) d. f( 2) > g(6) 16 Continue on Next Page >

17 W (gallons) High School Algebra I for Middle Grades Students 40. Ms. Porter needs to empty her pool for the winter. She creates a mathematical model to determine the number of gallons of water, w, remaining in the pool after t hours. If Ms. Porter s model is graphed below, what does the number 1400 represent in this context? DO YOUR FIGURING HERE t (hours) a. The amount of time it takes to empty the pool b. The amount of water being emptied each hour c. The amount of water in the pool when the Ms. Porter started emptying the pool d. The amount of water in the pool after 4 hours 17 END