Class: Date: Final Exam Review Sheet June 2011 Write an equation of the line with the given slope and y-intercept 1. slope: 2, y-intercept: 3 7 Beach Bike Rentals charges $5.00 plus $0.20 per mile to rent a bicycle. 2. Write an equation for the total cost C of renting a bicycle and riding for m miles. Write a linear equation in slope-intercept form to model the situation. 3. A television repair shop charges $35 plus $20 per hour. Write an equation of the line that passes through each point with the given slope. 4. 3, 4 ˆ, m = 3 Write an equation of the line that passes through the pair of points. 5. Ë Á 5, 2 ˆ, 3, 1 ˆ Write each equation in standard form. 6. y + 6 = (x + 4) 1
Write the equation in slope-intercept form. 7. y + 3 = 3 ( x 1) Write the slope-intercept form of an equation of the line that passes through the given point and is parallel to the graph of the equation. 8. (5, 1), y = 3 4 x + 1 Determine whether the graph shows a positive correlation, a negative correlation, or no correlation. If there is a positive or negative correlation, describe its meaning in the situation. 9. People Entering Amusement Park Time (minutes) a. positive; as time passes, the number of people entering decreases. b. negative; as time passes, the number of people entering decreases. c. no correlation d. positive; as time passes, the number of people entering increases. 10. Cindy started her bank account with $400, and she deposited $50 per week. Write a linear equation in slope-intercept form to find the total amount in her account after w weeks. Then graph the equation. 2
Solve the inequality. Graph the solution on a number line. 11. k 3 < 2 Solve the inequality. 12. b 4 12 13. 3h + 9 > 15 14. 2x 10 + 3x 4 < 5 15. 5(2g 3) 6g 2(g 6) + 3 16. 0.3(2j + 2) > 2.4 ( 0.4j 3) Solve the compound inequality and graph the solution set. 17. g 6 > 1 or g + 2 > 8 18. Solve d + 1 > 8. 3
Solve the system of inequalities by graphing. 19. y x + 4 y > 2x 4 20. y x 4 y < 4 21. Solve 2d 1 3 = 2 and graph the solution set. 22. Solve 3t 2 > 1 and graph the solution set. 4
Use the graph below to determine the number of solutions the system has. 23. x = 4 y = x + 3 24. 2x = 2y 6 y = x + 3 Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it. 25. y = x + 5 y = 6x 2 5
Use substitution to solve the system of equations. 26. y = x + 1 8x 4y = 0 27. The length of a rectangular poster is 10 inches longer than the width. If the perimeter of the poster is 124 inches, what is the width? 28. At a local electronics store, CDs were on sale. Some were priced at $14.00 and some at $12.00. Sabrina bought 9 CDs and spent a total of $114.00. How many $12.00 CDs did she purchase? 29. Dakota s math test grade was 7 points less than his science test grade. The sum of the grades was 183%. What did Dakota get on his math test? Use elimination to solve the system of equations. 30. 2x 10y = 10 3x + 10y = 10 31. 8x + 8y = 8 8x + 4y = 8 32. 3x 2y = 5 7x + 6y = 1 6
33. The cost of 3 large candles and 5 small candles is $6.40. The cost of 4 large candles and 6 small candles is $7.50. Which pair of equations can be used to determine, t, the cost of a large candle, and s, the cost of a small candle? 34. A hotel has 150 rooms. The charges for a double room and a single room are $270 per night and $150 per night respectively. On a night when the hotel was completely occupied, revenues were $33,300. Which pair of equations can be used to determine the number of double room, d, and the number of single room, s, in the hotel? Determine the best method to solve the system of equations. Then solve the system. 35. x = 2y 1 3x 3y = 9 36. 3x 2y = 4 2x 2y = 8 37. 4x + 5y = 9 4x 5y = 7 38. Dylan has 15 marbles. Some are red and some are white. The number of red marbles is three more than six times the number of the white marbles. Write a system of equations that can be used to find the number of white marbles, x, and the number of red marbles, y. 7
39. The table below shows the number of users of broadband and dial-up Internet and the average annual increase of users for each. Connection type Number of users (millions) Average increase per year (millions) Broadband 8.2 2.5 Dial-Up 11.6 1.4 Graph the equations representing the number of broadband and dial-up users for any year. Estimate the solution and interpret what it means. 40. Two trains A and B are 240 miles apart. Both start at the same time and travel toward each other. They meet 3 hours later. The speed of train A is 20 miles faster than train B. Find the speed of each train. 41. Scott bought a pen and received change of $4.75 in 25 coins, all dimes and quarters. How many of each kind did he receive? 42. To fill two new aquariums, Laura bought some saltwater fish for $2 each and some freshwater fish for $1 each. If she bought a total of 15 fish and spent a total of $23, how many fish of each kind did she buy? Simplify. Assume that no denominator is equal to zero. 43. a 5 b 5 ˆ a 5 b 3 ˆ 44. 4g 3 h 4 ˆ 3 8
45. 3 10 3 7 46. 2a a 2 ˆ 2 Express the number in scientific notation. 47. 0.0003054 Evaluate. Express the result in scientific notation. 48. 7.5 10 3 ˆ 5 10 5 ˆ Find the degree of the polynomial. 49. 10a 5 b 4 9
50. Write a P (polynomial), T (trinomial), B (binomial), M (monomial) or N (none of these) next to the following to indicate its description. Put down more than one of these if appropriate. Also indicate the degree. Description Degree 1. 2. 3. 4. Arrange the terms of the polynomial so that the powers of x are in descending order. 51. 2xy 2 + x 2 y 4 2x 3 + y 3 Find the sum or difference. 52. 5a 3a 2 ˆ + ( 8 + 7a) 53. 5a 3a 2 ˆ ( 6a 6) Solve the equation. 54. 4x( x 3) = 2 2x 2 ˆ 2 2 10
55. m ( m 3) 2m ( m 4) = m 2 4m ˆ + 6 56. 4g Ë Á g 3 ˆ 2g g 2 ˆ = 2 g 2 ˆ + 3 6g 2 57. 7p + 14 ˆ 8 2p ˆ = 0 58. 24c 2 = 36c Find the product. 59. ( r 8) ( r + 5) 60. ( 6k + 4) 7k 2 ˆ + 2k 7 61. ( 4r 9) 2 Find the product of each sum and difference. 62. ( 3l + 9) ( 3l 9) 11
Express the area of the figure as a monomial. 63. Write a polynomial to represent the area of the shaded region. 64. Find the area of the shaded region in the simplest form. 65. 12
Find the area of the shaded region. 66. 67. 13
Factor the monomial completely. 68. 63a 3 b 3 Find the GCF of the set of monomials. 69. 36s 5 t 2, 120s 2 t Factor the polynomial. 70. 12g + 20h Factor the trinomial. 71. x 2 + 15x + 14 Solve the trinomial equation. 72. r 2 18r + 56 = 0 Factor the trinomial, if possible. If the trinomial cannot be factored using integers, write prime. 73. 3t 2 + 10t + 8 Solve the equation. 74. 8y 2 12y + 4 = y + 10 14
Factor the polynomial, if possible. If the polynomial cannot be factored, write prime. 75. 9n 3 + 18n 2 121n 242 Solve the equation by factoring. 76. 25m 3 75m 2 9m + 27 = 0 Factor the polynomial. 77. 45m 4 + 18m 3 20m 2 n 2 8mn 2 Solve the equation by factoring. 78. ( w 13) 2 = 16 79. A rectangle has an area of 90 square millimeters and its length and width are both whole numbers. What is the minimum value for the perimeter of the rectangle? 80. The length of a rectangle is 4 more than its width. The area of the rectangle is 45 square centimeters. What is the length and width of the rectangle? Graph the function. 81. y = x 2 1 15
Write the equation of the axis of symmetry. 82. y = 2x 2 + 4x 6 Find the coordinates of the vertex of the graph of the function. 83. y = 5x 2 4 Solve the equation by graphing. 84. m 2 + 4m = 5 Describe how the graph of the function is related to the graph of f(x) = x 2. 85. g(x) = x 2 + 3 Solve the quadratic equation by completing the square. 86. g 2 10g + 7 = 0 Solve the equation by using the Quadratic Formula. Round to the nearest tenth if necessary. 87. h 2 + 28h 3 = 0 State the value of the discriminant. Then determine the number of real roots of the equation. 88. n ( 8n + 10) = 15 16