Name Per. _ Date Algebra B Chapter 9 Unit Test Version 1 of 3 Instructions: 1. Reduce all radicals to simplest terms. Do not approximate square roots as decimals. 2. Place your name, period and the date on this page. 3. Use of books, notes and/or calculators is not permitted. Only your test, a pencil and an eraser are allowed on your desk. 4. This is a test. No talking is permitted. If you need to ask a question, please raise your hand. 5. When you are finished, place your test in the orange box. You may then work on your class project. 1
Multiple Choice (1 points each). For each question, circle the letter of the correct response. Show your work. 1. Which number is a perfect square? A. 155 B. 12 C. 29 D. 64 2. Which radical expression is in simplest form? _ A. ± 9 B. ½ C. 3 6 D. None of these 3. The area of a rectangle is given by the formula, Area = length width. Find the area of a rectangle with length = 20 and width = 12 A. 60 B. 240 C. 12 5 D. 4 15 4. What is the value of the discriminant of the equation 4x 2 3x + 2 = 0? A. -23 B. 5 C. 25 D. 0 2
Multiple Choice (continued). 5. Which statement best explains why there is no real solution to the quadratic equation 2x 2 + x + 3 = 0? A. The value of 1 2 4 2 3 is positive B. The value of 1 2 4 2 3 is equal to 0 C. The value of 1 2 4 2 3 is negative D. The value of 1 2 4 2 3 is not a perfect square 6. Which function has a y-intercept of 3? A. y = x 2 + 3x + 4 B. y = -x 2 + 4x 3 C. y = x 2 2x + 3 D. y = 3x 2 + 2x + 6 7. What are the x-intercepts of the graph of y = -x 2 + 3x + 4? A. -4 and 3 B. -1 and 4 C. 0 and -3 D. -1 and 3 8. What is the x-coordinate of the vertex of the parabola represented by y = x 2 + 2x 1? A. ½ B. 1 C. -1 D. -2 3
Multiple Choice (continued). 9. Circle the letter of the graph that matches the function y = -x 2 + 2x +3. A. B. C. 10. You throw your keys with an initial velocity of -10 feet per second out of a window to a friend 20 feet below. Your friend does not catch them. Which equation correctly uses the vertical motion model to set up the problem? A. 0 = -16t 2-10t + 20 B. 0 = -16t 2 10 C. 0 = -16t 2 +10t 20 D. 20 = -16t 2 10 4
Problems. Show all your work. Draw a Evaluate the expression (2 points each). 11. 49 around your answers. 12. - 36 Simplify the Expression (2 points each) 27 13. 16 14. 16 5 5
Problems (cont). Show all your work. Solve the equation or write no real solution (2 points each). 15. 3x 2 = 12 16. 5x 2 7 = 38 Find the value of the discriminant. Then determine whether the equation has two solutions, one solution, or no real solution (2 points each). 17. -3x 2 + x 2 18. x 2 4x + 4 6
Problems (continued). Show all your work. Use the quadratic formula to solve each equation (4 points each). 19. x 2 4x 5 = 0 20. x 2 + 2x = 8 7
Problems (continued). Show all your work. Finding the roots of a function (2 points each). 21. How many times does the graph of y = 2x 2 2x + 3 intersect the x-axis? 22. The graph of the function y = x 2 4x + 3 is shown below. For what values of x is y = 0? 8
Graphing (4 points). Solve by graphing. Justify each step of the solution. Show all your work. 23. Graph the function y = x 2 + 4x + 3. Use your graph to estimate the roots of the function. 9
Application (4 points each). Show all your work. Assume a batter hits a pitched baseball when it is 3 feet off the ground with an initial velocity of 80 feet per second. Assume no one catches the ball. Use the vertical motion model, h = -16t 2 + vt + 3 to answer the next 2 questions. 24. When will the ball described above hit the ground? 25. What is the maximum height the ball will reach? 10
Multiple Choice (xx points). For each question, choose the letter of the correct response. 1. Which number is a perfect square? A. 155 B. 12 C. 29 D. 64 2. What are the x-intercepts of the graph of y = -x 2 + 3x + 4? A. -4 and 3 B. 1 and 4 C. 0 and -3 D. -1 and 3 3. Which function has a y-intercept of 3? A. y = x 2 + 3x + 4 B. y = -x 2 + 4x 3 C. y = x 2 2x + 3 D. y = 3x 2 + 2x + 6 4. What is the value of the discriminant of the equation 4x 2 3x + 2 = 0? A. -23 B. 5 C. 25 D. 0 5. Which radical expression is in simplest form? _ A. 3 6 B. ½ C. ± 9 D. None of these 6. The area of a rectangle is given by the formula, Area = length x width. Find the area of a rectangle with length = 20 and width = 12 A. 60 B. 240 C. 12 5 D. 4 15 11
7. Give the letter of the graph that matches the function y = -x 2 + 2x +3. A. B. C. 8. Which statement best explains why there is no real solution to the quadratic equation 2x 2 + x + 7 = 0? A. The value of 1 2 4 2 7 is positive B. The value of 1 2 4 2 7 is equal to 0 C. The value of 1 2 4 2 7 is negative D. The value of 1 2 4 2 7 is not a perfect square 9. The graph of the equation y = x 2 4x + 3 is shown below. For what values of x is y = 0? 10. How many times does the graph of y = 2x 2 2x + 3 intersect the x-axis? 12
Evaluate the expression. 11. 49 11. 12. - 36 Solve the equation or write no real solution. 13. 3x 2 = 12 14. 5x 2 7 = 38 Simplify the Expression. _ 15. 147 4 16. 16 16 17. 5 Use the quadratic formula to solve the equation. 18. x 2 4x 5 = 0 19. x 2 + 2x = 8 Find the value of the discriminant. Then determine whether the equation has two solutions, one solution, or no real solution. 20. -3x 2 + x 2 21. x 2 4x + 4 The vertical motion model for objects is: h = -16t 2 +vt + s, where s is the initial height of the object, v is the object s initial velocity in feet per second, h is the object s ending height and t is time in seconds. Assume a batter hits a pitched baseball when it is 3 feet off the ground with an initial velocity of 80 feet per second. 22. Assuming no one catches the ball, when will it hit the ground? 23. What is the maximum height the ball will reach? 13
10. The height of a triangle is 4 inches greater than twice its base. The area of the triangle is 168 square inches. What is the base of the triangle? 14