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MMA Spring 2012 FINAL REVIEW Name___________________period______ 1. Identify the slope and y-intercept y = 4x 5 2. Identify the rate of change and beginning value 3. Identify the x and y intercepts y= 1 x7 2 x + 3y = -15 -5x + y = -10 2x + 3y = -12 -2x + 5y = -10 4. Laura’s cell phone plan costs $32 plus $.08 for every minute. Identify the slope and the y –intercept._________________________ _________________________ Identify the independent and dependent variable.________________________ ______________________ What is the equation that represents this scenario._________________________________________ 5. Sean’s gym membership costs $270 for the year plus $ 3.00 for every towel he uses. Identify the Rate of Change and the Base. _________________________ Identify the input and output. ___________________________ _________________________ ________________________________ What is the equation that represents this scenario. _________________________________________ 6. Sam gets $50 for Mowing the lawn. He wants to buy some (x) t-shirts for the summer. The shirts are $4.50 each he will spend no more than y dollars. What is the Base_________ What is the rate_________ ( is it negative or positive) What symbol means no more than_______________ What is the equation/inequality that represents this scenario. _________________________________________ 7. SOLVE FOR Y: Identify m =______ and b=______ and sketch the graph 5x + 3y = -6 What is the slope and the base in this scenario: 8. Julie earns $14.75 an hour pulling weeds._______________________ ____________________ Write the equation_____________________________ 9. Find the function values of the following: 10. Find the function values of the following: 4 g(s) = s2 f(x) = -2x - 5 f(½ ) ___ f(-2) f(4) g(0) ______ g(-3) g(6) Find the x and y intercepts and sketch the graph. 11.( , ) ( , ) 2x + 8y = 16 Write and solve the following linear functions. 12. John is paid $350 a month plus a 15% commission on the equipment he sells. If he sells $1200 worth of equipment in a month, how much will he make? What is the slope________what is the y-intercept____________ What is the independent variable________________________________________ What is the dependent variable_________________________________________ Equation: Solution: 13. Jack earns $7.50 an hour at his job. How much will Jack make in a 8-hour work day? What is the slope________what is the y-intercept____________ What is the independent variable________________________________________ What is the dependent variable_________________________________________ Equation: Solution: Write and graph the following linear functions. 14. Sara has 15 apps on her phone. Each week she buys 2 more. What is the slope________what is the y-intercept____________ What is the independent variable________________________________________ What is the dependent variable_________________________________________ Equation Graph Write the equation of the lines parallel and perpendicular to the given information. 15. m=½ (3,1) Parallel equation: Perpendicular equation: ________________________ 16. y = -3x + 5 Parallel equation: (3,4) Perpendicular equation: ________________________ Find the slope of a line given two points. 17. (0, 2) and (3, 4) 18. (-3, 4) and (5, 1) Write the equation of the line given the table or graph. 19. 20. Time (seconds) 0 4.50 9.00 13.50 ______________________________ 21. __ 2004 Summer Exit The graph is the solution for which inequality? 23. spend. Distance (meters) 25 75 125 175 _________________________________ 22. ___ Which inequality best describes the graph shown below? Your parents say must save at least 85% of your graduation money and the rest you can 24. You want to be in the top of your MMA class you must get no less than an 87% on this test to achieve this goal. 25. y ≥ 2x – 4 26. y ≤ -½x + 5 27. -4x + 2y > 8 Write the system of equations: 28. The length of a rectangle is equal to 5 less than triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 85 centimeters? 29. Karen bought some 2 neon fish and 6 angel fish at $6.75 for her new aquarium. Then Karen bought 5 neon fish and 1 angel fish and spent $5.25. Write the system of equations to determine how much she spent on each type of fish. Solve by graphing: 30. x 2y 8 3x y 7 The solution is where the two lines cross. Solve for y. 31. y 2x 1 2x 4 y 4 ( , ) The solution is where the two lines cross. ( , Graph the following linear inequalities Hint: dashed or solid Hint: shade above or below 34. 32. The solution is the commonly shaded region. Solve by substitution: HINT: get one variable alone. 35. y 6x x y 28 x coordinate =________ y coordinate =________ The solution is the commonly shaded region. 36. 3 x y 1 2 x 3 y 24 ( , ) ) Solve by the elimination method with addition and subtraction. 37. 38. 3x 2 y 7 3 x 5 y 45 3 x 13 y 9 5x 2 y 1 ( x coordinate =________ , ) y coordinate =________ List the rules of transformation for each of the following parts of a quadratic equation y = a(x – h) + k 39. a:________________________ _________________________ ___________________ h: ____________________________________ k:_____________________________________ 40. What is the Quadratic parent function:__________________ List ALL of the ways the given function is different from the quadratic parent function. 41. f(x) = 1 x2 – 5 42. f(x) = 2(x - 4)2 - 8 3 1. 2. 3. 1. 2. Write the new equations given the following changes. 43. If “a” in this quadratic function is f(x) = -2x2 – 4 is increased by 3 what will new equation look like? 44. If “c” in this quadratic function is f(x) = ½ x2 – 4 is changed to 0 what will the new equation look like? 1 2 1 x – 2 to g(x) = x2 + 5 create a wider parabola or narrower parabola or same size? 4 4 1 2 1 46. Does going from f(x) = x – 2 to g(x) = x2 + 5 create a wider parabola or narrower parabola or same size? 4 6 47. Which function has the widest graph? (A) y 2 x 2 (B) y x 2 (C) y 0.5 x 2 (D) y x 2 45. Does going from f(x) = 48. Which function has the narrowest graph? (A) y 2 x 2 (B) y x 2 (C) y 0.5 x 2 (D) y x 2 1 49. (2005 October Exit) How does the graph of y = 5x differ from the graph of y = x2__________________ 5 2 2 50. (2004 10 Grade) How does the graph of y = x differ from the graph of y = x − 8___________________ 2 th 51. What are the zeros of the following equation: y x 2 4 x 12 ? 52. What are the roots of the following equation: y x2 4 ? 53. Find the solutions of f(x) = x2 – 8x + 15 by using a graph or table in your calculator. 54. Find the root(s), zeros, x-intercepts, solutions from the graph and table below. Then find the y- intercept, if posssible. 55. 56. 57. x- intercepts ___________ __________ y-intercept__________ x- intercept ___________ x y -2 0 -1 0 1 2 3 -5 -8 -9 -8 -5 4 0 58. x- intercepts __________ ______________ y-intercept__________ x 0 1 2 3 4 6 y 4 0 -2 -2 0 10 x- intercepts _________ ______________ y-intercept___________ 59. Write the GCF. ___________ ( x3 4 x5 ) ____________ 8a 3b3 18a 2b __________ 3x5 - 12x4 + 6x3 _________13x 5 y 2 Write the GCF and in Parentheses write what is left. To check: multiply your answer and see if you get the original problem. 60.___________( ) 6x5y2 - 61.___________( ) 4r 2 28x3y 3 yz 2 18r 3 z 5 6ryz Factor. 62. x2 + 8x +16 63. x2 – 13x + 40 64. x2 – x – 12 65. x2 + 2x – 48 66. x2 – 25 67. 6x2 + 5x +1 68. If the landing strip at the airport has an area of 9x2 – 121, what is the length and width? 69. The AHS parking lot has an area of x2 + 9x + 20. What is the length and width of the parking lot? Simplify each radical expression. 70. 54 71. 24 72. 48