Final Exam 2016 Practice Exam Short Answer 1. Multiply. 2. Multiply. 3. Find the product.. 4. Use the Quadratic Formula to solve. 5. Faye is 20 feet horizontally from the center of a basketball hoop that is at a height of 10 feet. She shoots a basketball straight toward the hoop with a horizontal velocity of 18 feet per second. The quadratic equation that models the height, in feet, of the ball after t seconds is. Does Faye make the basket? Explain your reasoning. 6. Find the value of c that makes the expression a perfect square trinomial. 7. Solve by completing the square. 8. Solve by completing the square. 9. Solve the equation by completing the square. 10. A rectangle is 5 cm longer than it is wide, and its area is 176 m 2. Find its dimensions. 11. Marcus makes an investment of $2000. Write an expression that shows its value after it increases in value by 8% for 9 years. 12. The population of Westport was 43,000 at the beginning of 1980 and has steadily decreased by 1% per year since. Write an expression that shows the population of Westport at the beginning of 1994. 13. An oil painting from the early twentieth century, originally purchased for $8500, has been increasing in value by 7.5% for the 24 years since its purchase. Write an expression that gives its current value. 14. The population of Greenfield was 52,500 at the beginning of 1980 and has steadily decreased by 2.1% per year since. Write an equation to find the year, t, when Greenfield s population will drop to 30,000. 15. What are all the roots of?
16. Factor the trinomial. 17. Tell whether the function has a minimum value or a maximum value. Then find the minimum or maximum value. 18. Suppose a table-tennis ball is hit in such a way that its path can be modeled by, where h is the height in meters above the table and t is the time in seconds. Estimate the maximum height reached by the table-tennis ball. Round to the nearest tenth. 19. The revenue from selling x units of a product is given by. How many units must be sold in order to have the greatest revenue? (Find the x-coordinate of the vertex of the parabola.) 20. Suppose a table-tennis ball is hit in such a way that its path can be modeled by, where h is the height in meters above the table and t is the time in seconds. About how many seconds did it take for the table-tennis ball to reach its maximum height after its initial bounce? Round to the nearest tenth. 21. Simplify 22. Rewrite the expression using positive exponents. 23. Solve the equation using the graph. 24. Tell whether the graph represents a linear function, an exponential function, or a quadratic function.
25. A city had a declining population from 1992 to 1998. The population in 1992 was 200,000. Each year for 6 years, the population declined by 3%. Write an exponential decay model to represent this situation. 26. A triangle with vertices,, and is reflected across the y-axis. Identify the coordinates of the image of point Q. 27. Given:. State the congruence that is needed to prove using the Hypotenuse-Leg Congruence Theorem. 28. Given:,. State the congruence that is needed to prove using ASA. 29. If, write a statement about point E that would allow you to prove by SSS.
30. Find the volume of the cylinder in terms of. 31. To the nearest cubic centimeter, determine the volume of packing peanuts needed to fill the box if the radius of the enclosed cylinder is 4 centimeters and the cylinder is centered in the box. 32. Segment is the result of a dilation of segment. The dilation was centered at the origin and has a scale factor of. Graph segment and explain how you obtained your answer. y 8 6 4 2 10 8 6 4 2 2 4 6 8 10 x 2 R' 4 6 8 10 12 S' 33. Determine whether the triangles are similar. If they are, write a similarity statement. 34. Determine whether the triangles are similar. If they are, write a similarity statement.
35. True or false: triangle ABC is similar to triangle DEF. 36. Given:,,,, and Prove: 37. Can you use the SAS Congruence Postulate to prove that the two triangles are congruent? Explain your reasoning. 38. Find the indicated probability. 39. Find the probability that a point, selected randomly on, is on the given segment. Express your answer as a fraction, decimal, and percent. 40. Tell whether the events are independent or dependent. Explain your reasoning. A jar contains 6 red marbles and 4 blue marbles. You randomly choose a marble from the jar. Without replacing the marble you took out, you randomly choose a second marble from the jar. Event A: The first marble is blue. Event B: The second marble is blue.
41. Tell whether the situation describes independent events or dependent events. Then answer the question. A drawer contains 7 black socks, 5 gray socks, and 3 blue socks. Without looking, you draw out a sock and then draw out a second sock without returning the first sock. What is the probability that the two socks you draw are the same color? 42. A drawer contains 10 red socks, 6 white socks, and 4 blue socks. Without looking, you draw out a sock, return it, and draw out a second sock. What is the probability that the first sock is red and the second sock is white? Round your answer to the nearest hundredth. 43. Suppose A and B are independent events. The probability that event A will not occur is 0.1 and the probability that event B will occur is 0.7. Find P(A), P(not B) and P(A and B). 44. You randomly draw letter tiles from a bag containing the letters from the word PENNSYLVANIA. Find the probability that you draw an A from the bag, replace it, and then draw an N. Then tell whether the events are independent or dependent. 45. You randomly draw letter tiles from a bag containing the letters from the word INDEPENDENT. What is the probability that a randomly chosen letter will be a D? 46. Of 100 students, 37 are taking Calculus, 40 are taking French, and 14 are taking both Calculus and French. If a student is picked at random, what is the probability that the student is taking Calculus or French? 47. Draw a scatter plot of the data. If possible, draw a best-fitting line for the scatter plot and write an equation of the line. State whether x and y have a positive correlation, a negative correlation, or no correlation. 48. Make a scatter plot of the data in the table below, identify the correlation, and then sketch a line of best fit and find its equation.
y 24 22 20 18 16 14 12 10 8 6 4 2 2 4 6 8 10 12 14 16 18 20 22 24 26 x 49. The table shows the lengths (in inches) of winning zucchinis at a state fair during the period 1986-1995. Year 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 Length 32.4 32.6 29.9 33.2 34.0 34.3 35.2 36.9 34.4 35.3 (in.) Part A: Make a scatter plot of the data. Let x represent the number of years after 1985 and y represent the winning length that year. Part B: Use technology to perform a linear regression. What is the equation of the linear regression model? Graph the equation on the scatter plot for Part A. Part C: Predict the winning length for the year 2000. 50. Find the approximate correlation coefficient for a linear model for the data.
Final Exam 2016 Practice Exam Answer Section SHORT ANSWER 1. ANS: 2. ANS: 3. ANS: 4. ANS: 5. ANS: No; solving the equation gives the solutions t = 0.25 and t = 1. These are the times at which the ball is at a height of 10 feet--the first when the ball is going up and the second when it is coming down. When t = 1 second, however, the ball has traveled only 18 feet horizontally from Faye. Because it is falling, however, it will be below the hoop when it is 20 feet from Faye, so she misses the basket. 6. ANS: 7. ANS: and 8. ANS: 3, 1 9. ANS:, 10. ANS: 16 cm by 11 cm 11. ANS: 12. ANS:
13. ANS: 14. ANS: 15. ANS:, 0, 1.5 16. ANS: 17. ANS: The minimum value of the function is. 18. ANS: About 0.22 m 19. ANS: 100,000 units 20. ANS: About 0.2 sec 21. ANS: 22. ANS: 23. ANS: no solution 24. ANS: exponential function 25. ANS: 26. ANS: 27. ANS:
28. ANS: 29. ANS: E bisects both and, or E is the midpoint of both and. 30. ANS: 31. ANS: 32. ANS: y 8 6 4 2 10 8 6 4 2 2 4 6 8 10 x 2 R' R 4 6 8 10 12 S' S Sample answer: Divide the x- and y-coordinates of point R and S by the scale factor,. Point R is located at. Point S is located at. 33. ANS: Similar; 34. ANS: Similar; 35. ANS: true 36. ANS: Sample answer:,
So Therefore, by SSS. 37. ANS: No. In order to use the SAS Congruence Postulate, the sides that form the congruent angles must be congruent. In the diagram, the right angles are congruent, but only 1 pair of sides that forms the right angle are congruent. 38. ANS: 0.45 39. ANS: 40. ANS: Because the occurrence of event A affects the likelihood of event B, the two events are dependent. 41. ANS: dependent: 42. ANS: 0.15 43. ANS: 0.9; 0.3; 0.63 44. ANS: 45. ANS: 46. ANS: 47. ANS: ; positive
48. ANS: positive correlation; line of best fit may vary; sample answer: 49. ANS: Part A: Part B: Part C: 38.4 in. 50. ANS: Answers may vary, near