James J. Kaput Center for Research and Innovation in Mathematics Education 200 Mill Rd., Suite 150B Fairhaven, MA 02719, USA Full Name: Date: 20 (month/day/year) Teacher Name: Amount of Time to Complete (to be filled in by your teacher): mins. Instructions The test is comprised of 19 questions. Please fill in the bubble for your chosen answer, A, B, etc. on the answer sheet or write clearly in the space provided in the test booklet where indicated. Be sure to use blue or black ball-point pens or a pencil (no felt tips or gel pens) and if you fill in an incorrect bubble, simply cross it out and fill in the correct bubble. For each question there is a confidence scale from 1 to 7. Please fill in the bubble on the answer sheet that relates to the number to indicate how confident you were in answering each question. You are not allowed a calculator and you have 45 minutes to complete the test. Please try your best. This test is designed by the University of Massachusetts Dartmouth to help us assess your mathematical knowledge. Thank you. Place ID label below: Please do not write below this line. 3001
Item #1a Which of the following best represents the graph of a line with an undefined slope? A B C D Item #1b
Item #2a Amy is choosing between two local Internet service providers, Simple.com and Call.com. The graph shows the relationship between the total cost per month of each Internet provider and the hours spent on-line. According to the graph, which of these statements is true? A B C D Simple.com would cost less than Call.com if Amy used the Internet more than 5 hours a month. Call.com would cost less than Simple.com if Amy used the Internet less than 5 hours a month. Simple.com would cost less than Call.com if Amy used the Internet for exactly 5 hours a month. Call.com would cost less than Simple.com if Amy used the Internet more than 5 hours a month. Item #2b
Item #3a Which type of parent function is represented by the function graphed below? A B C D Exponential Absolute Value Linear Quadratic Item #3b
Item #4a What is the factored form of the expression below? x 2! 16 A (x! 4)(x + 4) B (x! 8)(x + 8) C (x! 4)(x! 4) D (x! 8)(x! 8) Item #4b
Item #5a The graph represents the relationship between the height of a ball and the distance it traveled after the ball was thrown. What conclusion can be drawn from the graph about this relationship? A The ball reached a maximum height of about 16 feet after traveling a horizontal distance of approximately 33 yards. B The ball reached a maximum height of about 13 feet after traveling a horizontal distance of approximately 14 yards. C The ball was thrown from a height of approximately 6 feet above the ground and traveled a horizontal distance of approximately 20 yards before it reached its maximum height. D The ball was thrown from a height of approximately 7 feet above the ground and traveled a horizontal distance of approximately 10 yards before it reached its maximum height. Item #5b
Item #6a If the graph of the equation y = x 2 + 1 is translated 3 units down, what will be the equation of the new graph? A y = (x! 3) 2 + 1 B y = x 2! 2 C y = x 2 + 4 D y =!3x 2 + 1 Item #6b
Item #7a In a laboratory experiment, the number of bacteria in a petri dish doubled every hour. The table below shows the total number of bacteria, in thousands, for the first 3 hours growth. Bacteria Growth Numbers of Total Number Hours Growth of Bacteria (in thousands) 0 1 1 2 2 4 3 8 If the pattern established in the table continues, which of the following expressions best represents the total number of bacteria, in thousands, in the Petri dish after t hours growth? A 2t B 2t 2 C 2 t D t 2 Item #7b
Item #8a The graphs below represent functions of the form y = ax 2. In which of the following graphs does a have the smallest value? A B C D Item #8b
Item #9a A function is described by the equation y = 2x 2! 5x! 3, in which y is dependent on x. If a value for the independent variable is selected from the set!4,!1,0,2,5 { }, which of the following is a corresponding dependent value? A 9 B!6 C!5 D 0 Item #9b
Item #10a Nancy threw a ball upward from the roof of a 50-foot-high building at an initial velocity of 40 feet per second. The table shows the relationship between the time elapsed and the ball s height above the ground. Time After Nancy Threw the Ball (seconds) Height of the Ball Above the Ground (feet) 0 50 0.5 66 1.0 74 1.5 74 2.0 66 2.5 50 If the height of the ball is a quadratic function of time, between what times did the ball reach a height of 70 feet? A Between 0 seconds and 0.5 second B Between 1 second and 1.5 seconds C D Between 0.5 second and 1 second and between 1.5 seconds and 2 seconds Between 1 second and 1.5 seconds and between 1.5 seconds and 2 seconds Item #10b
Item #11a The path of a rocket fired during a fireworks display is given by the equation s(t) = 64t! 16t 2, where t is the time, in seconds, and s is the height, in feet. Show all work. What is the maximum height, in feet, the rocket will reach? In how many seconds will the rocket hit the ground? Item #11b
Item #12a The graph of a function of the form y = ax 2 + c is shown below. If the graph is translated only up or down to include the ordered pair (6, 7), which of the following equations best represents the resulting graph? A y =! 1 3 x2 + 3 B y = 1 3 x2 + 1 C y =! 1 3 x2! 10 D y = 1 3 x2! 5 Item #12b
Item #13a A biologist noticed that the population of ladybugs in a sample doubled every 3 days. If the initial population sample was 30 ladybugs, what was the population of ladybugs at the end of 9 days? A 90 B 270 C 120 D 240 Item #13b
Item #14a Look at the equations shown below. y = 4 5 x2 + 3, y = 4 5 x2, y = 4 5 x2! 5, y = 4 5 x2 + 3 5 Which of the following statements is true for the graphs of all the equations given? A B C D The graphs are congruent and open downward. The graphs open upward and are symmetrical about the y- axis. The graphs are congruent and are listed from narrowest to widest. The graphs open downward and are symmetrical about the y- axis. Item #14b
Item #15a Mike was driving his car at a constant speed of 50 miles per hour. Then he accelerated at a constant rate for 7 seconds. What additional information is needed to determine the speed of the car after 7 seconds? A The speed of the car prior to acceleration B The length of time Mike accelerated C The speed limit D The rate of acceleration Item #15b
Item #16a Which of the following polynomial equations best represents this graph? A B C D (x + 6)(x! 2) = y (x! 2)(x! 16) = y (x! 6)(x + 2) = y (x + 2)(x + 16) = y Item #16b
Item #17a How does the graph of y =! 3 4 x2 differ from the graph of y = 4 3 x2? A The graph of y =! 3 4 x2 opens downward and is wider than the graph of y = 4 3 x2 B The graph of y =! 3 4 x2 opens upward and is wider than the graph of y = 4 3 x2 C The graph of y =! 3 4 x2 opens upward and is narrower than the graph of y = 4 3 x2 D The graph of y =! 3 4 x2 opens downward and is narrower than the graph of y = 4 3 x2 Item #17b
Item #18a What are the x-intercepts of the graph of the equation y = x 2 + x! 12? A x = 4, x = 3 B x =!4, x = 3 C x =!4, x =!3 D x = 4, x =!3 Item #18b
Item #19a The formula for the volume of a cylinder with a height of 5 units can be represented as y = 5! x 2, where x represents the radius. If the cylinder s height is tripled, what is the effect on the graph of y as a function of x? A B C D The graph is translated up The graph remains the same The graph becomes narrower The graph becomes wider Item #19b