ECM Final Exam Review

Transcription

1 Name: Date: 1. Which of the following is the graph of the solution set of the system? y 2 y x 3 2. Three times a number n is greater than 8 more than the number. Which of the following inequalities best represents this information? 3n > n + 8 3n > 8 3n + 8 > n 3(n + 8) > n 3. Find the value of the discriminant of the quadratic equation 2x 2 3x + 3 = Write the number and the nature of the roots of the quadratic equation whose discriminant is Given the graph, determine the number of real solutions. 6. Factor: x 2 4x Which equation represents a line that will be perpendicular to the graph of 2x 4y = 12? y = 2x + 6 y = 2x 6 y = 1 2 x + 3 y = 1 2 x 3 page 1

2 8. What are the solutions of the equation (y 3)(y 6) = 0? 13. What is the solution to this system of equations? y = 3x 2 6x + 2y = 4 9. Express the product in standard form. (2 + 36)(3 4) 14. Express the product in standard form. 3i(6 2i) 10. Find the point of intersection of the lines: y = 4x + 1 and y = 2x What is the solution to the equation 6(x 5) 4x = 3(4x 5)? 15. What value of x makes the equation below true? 3x + 2(x 5) = Given the graphs of y = 3x 1 and y = 2x + 1, determine which ordered pair is a solution to: y < 3x 1 y > 2x + 1 (0, 4) (4, 2) (0, 4) 16. State the operations used to solve the following equation. 2x + 8 = 9 (2, 4) page 2

3 17. Which graph below represents a function? 18. How many real solutions are shown by the graph of the quadratic function? 19. Is the vertex of the parabola shown in the graph a maximum or a minimum? What are the coordinates of the vertex? 20. When 4x 2 9y 2 is factored completely, one of the factors will be. page 3

4 21. Cody and Oren are each saving money to buy a new video game. The amount of money Cody has saved at the end of each week is shown in the graph below. 23. Find the roots of the equation 3x 2 + 5x + 4 = 0 Cody s Savings Account 24. Keith uses this formula to calculate the monthly profit of his bicycle store. P = 400n 7, 200 In the formula, P is the monthly profit and n is the number of bicycles sold in a month. How many bicycles must he sell to make a profit of exactly $2,000 in a month? The amount of money, y, Oren has saved at the end of each week, x, can be determined by the equation below. y = 3.50x The equation of the axis of symmetry of the graph of y = 2x 2 4x 1 is: Which description correctly compares the amount of money Cody has been saving to the amount of money Oren has been saving? Cody started saving with more money than Oren, but Oren has been saving more money each week. Cody started saving with more money than Oren, and he has been saving more money than Oren each week. 26. Add: (8 + 4i) + (10 2i) oth Cody and Oren had the same amount of money saved when they started, but Oren has been saving more money each week than Cody. oth Cody and Oren started saving with the same amount of money, but Cody has been saving more money each week than Oren. 27. Solve 3x 2 5x 1 = 0 using the quadratic formula. 22. Solve: 4(6x 10) = 8x + 40 page 4

5 28. Which of the following graphs is a function? 31. Solve: a 2 5a 14 = Which graph represents the inequality y 3x 2? 29. Solve: 2x + y = 1 2x + 5y = Which of these linear equations is parallel to y = 3x + 5? y = 3 1 x + 5 y = 3x Solve: 3x 2 = 48 y = 3x + 5 y = 1 3 x + 10 page 5

6 34. A total of 120 adults and students attended a school volleyball game. Each adult paid $2.50, and each student paid $1.00. The total paid by the adults and students attending the game was $189. Which of the following systems of equations can be used to find a, the number of adults attending, and s, the number of students attending the game? a + s = a + 2.5s = a + s = 120 a + s = a + s = a + 3.5s = 189 a + s = a + s = Solve the following equation: 4x 3 = 12 + x 40. Which one of the following expressions is a step in solving the given quadratic equation by the process of completing the square? x 2 14x 12 = 0 x 7 = ± 37 x 7 = ± 61 x + 7 = ± 37 x + 7 = ± Solve for x given x = 6x 41. Solve: x = 0 over the set of complex numbers. 36. Solve: 5x 2 = 4 2x 42. Tim plotted the points (2, 4) and (6, 10). 37. Factor: 2p 2 + p 6 What is the equation of a line that passes through both of Tim s points? 38. Follow the steps in solving this linear equation: 3(x 7) = 42 3x 7 = 42 3x = 49 x = What is the greatest monomial factor in 2xy 2 + 4x 2 y? Which statement best describes the error in this work? Improper use of the Distributive Property. Improper use of the Associative Property of Addition. Improper use of the Additive Inverse Property. Improper use of the Multiplicative Inverse Property. 44. Which set or sets represent functions? M = (1, 4), (2, 3), (4, 1), (5, 2)} N = (4, 6), (2, 6), ( 1, 6), (3, 6)} R = (3, 7), (4, 9), (3, 3), (5, 1)} page 6

7 45. Kelly solved the equation below using the steps shown. Given: 3(x 4) 4 = 1 Step 1: 3x 12 4 = 1 Step 2: 3x 16 = 1 Step 3: Step 4: 3x = 15 x = Which of the following is the graph of y = 2(x + 3) 2 1? Which step contains Kelly s first mistake? 46. Consider solving x x + 5 = 0 by completing the square. x x + = 5 + What is the number that goes in the blanks? 47. Solve: 3x 4y = 6 3x 2y = 2 page 7

8 49. Which statement is not supported by the graph shown? 52. Consider solving x x + 3 = 0 by completing the square. At which of the following equations will you arrive? (x + 7) 2 = 46 (x 7) 2 = 52 (x 7) 2 = 46 (x + 14) 2 = When using elimination to solve 3x + 4y = 6 4x 2y = 3 The vertex of the graph is (2, 1). what is a possible first step? The roots of the quadratic function are 0 and 3. The coefficient of x 2 in the equation of this quadratic function is positive. The quadratic function graphed has no real solution. 54. For a few months, Dexter recorded the amounts, in fluid ounces, of laundry detergent remaining, y, after he and his family washed x loads of laundry. The equation of the line of best fit for his data is shown below. y = 1.6x Which of the following is a quadratic function? f (x) = 3x 4 2x f (x) = 3x 5 f (x) = 2x 2 3x + 6 f (x) = What are the roots of the graphed function? Which statement correctly describes the slope of Dexter s equation of the line of best fit in the context of the situation? The bottle Dexter s family buys holds about 50 fluid ounces of detergent. For each load of laundry, Dexter s family uses about 1.6 fluid ounces of detergent. With 50 fluid ounces of detergent, Dexter s family can wash about 1.6 loads of laundry. With 1.6 bottles of laundry detergent, Dexter s family can wash about 50 loads of laundry. 55. Write the number and the nature of the roots of the quadratic equation whose discriminant is What is the equation of the line that has a slope of 4 and passes through the point (3, 10)? page 8

9 57. Which model is not a function? 60. The only coins that Alexis has are dimes and quarters. Her coins have a total value of $5.80. She has a total of 40 coins. Which of the following systems of equations can be used to find the number of dimes, d, and the number of quarters, q, Alexis has? d + q = d + 40q = 5.80 d + q = d q = 5.80 d + q = d q = 40 d + q = d q = Karen and Henry each sold food at the fair. The table below shows the total number of corn dogs Karen sold at different times of the day. Karen s Corn Dog Sales Time Total Corn Dogs Sold 12:00 P.M. 42 2:00 P.M. 56 4:00 P.M. 70 6:00 P.M. 84 Henry uses the equation below to show the number of hot dogs, h, he has sold after t hours. h = 14t Which statement about Karen and Henry is true? 58. Simplify: The rate that Henry sells hot dogs is half the rate that Karen sells corn dogs. The rate that Henry sells hot dogs is double the rate that Karen sells corn dogs. The rate that Karen sells corn dogs is 7 times the rate that Henry sells hot dogs. 59. Find the roots of x 2 4x + 6 = 0 The rate that Karen sells corn dogs is the same as the rate that Henry sells hot dogs. page 9

10 Problem-Attic format version c EducAide Software Licensed for use by Cathy Smith Terms of Use at 6/1/ C REI.12 A CE1 15 REI.4 2 real rational roots REI.4 two solutions F.IF.4 6. (x + 2)(x 6) SSE.3A y = 3 and y = 6 REI i N.CN.2 ( 12, 3 ) REI.6 REI.12 Infinitely many solutions i N.CN Subtract 8 from both sides, divide by 2 on both sides A zero 19. maximum; ( 2, 4) F.IF x 3y SSE.2 C ± i 23 6 N.CN.7 23 bicycles 25. x = 1 F.IF.8A i N.CN.2 5 ± 37 6 REI.4 D F.IF (1, 1) 30.

11 Teacher s Key Page , 7} REI ( 2 3, 2) REI REI C F.IF.7A 33. 4, 4} REI F.IF D 3 ± i N.CN REI (2p 3)(p + 2) SSE.3A 38. A REI x = REI.4A, 1 } C F.IF , 5} F.IF A REI.4A 3x + 4y = 6 8x 4y = 6 REI y = 4x 22 2 imaginary roots (complex conjugates) REI ±3i N.CN y = 3 2 x C 7i N.CN xy SSE.1A 45. Step 3 Sets M and N only ± i 2 N.CN D REI.4A