SEMESTER 1 EXAM REVIEW PACKET

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Mervin Warren
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1 SEMESTER 1 EXAM REVIEW PACKET Expressions, Equations, and Inequalities: - Translating and evaluating - Solving equations, proportions and inequalities - Literal equations (rearranging for a given variable) - Justifying the steps in solving an equation (Proofs) - Solving and graphing compound inequalities - Equation, proportion and inequality word problems Graphing and Functions: - Domain and range - Functions (be able to determine if a table and a graph are functions) - Graphing using x- and y- intercepts and slope-intercept form (m and b) - Finding slope given two points, a graph, and an equation - Getting an equation into slope-intercept form (y = form) - Finding the zeros (roots) - Evaluating equations written in function notation - Graphing inequalities - Graphing systems of equations/ inequalities Writing Equations of Lines: - Writing the equation of a line given: a) slope and y intercept b) slope and one point c) two points d) a graph - Writing an equation in standard form - Parallel and perpendicular lines Variation - Direct variation - Inverse variation Name:

2 Exam Topics Self Assessment Look over the topics that will be on the semester 1 exam. Categorizing each topic in the chart below will help you to decide where to start studying and where to focus most of your time! GOT IT! I can do these problems accurately WITHOUTassistance immediately upon seeing them ALMOST THERE! I can do these problems, but I am still making careless mistakes or I require a jump start from the teacher or a friend. I DON T KNOW I do not know how to start these problems and still have trouble even with a hint from the teacher. Study Tips 1. Get immediate help on the topics in the I DON T KNOW column attend a review session or ask for help during resource or homeroom. 2. Do the ENTIRE exam review packet AND check your answers, paying close attention to the topics you have listed in the ALMOST THERE column. Do not wait until the last minute to start the packet!!! 3. To get extra practice on topics you are still struggling with, use old tests, formatives, homework assignments and notes as a source of practice problems. Cover up the answer with a sticky note and redo the problem on a separate sheet of paper. Then, check the original assignment to make sure you got the correct answer. 4. Pay attention during class reviews and seek help if you need it!!!

3 Equations and Inequalities Write an algebraic expression, equation or inequality for each statement. 1. The sum of the square of a number and Fourteen less than a number is at least twenty. 3. Three times the quantity of eight and a number is sixty. Evaluate the expressions (2 + 1) w + n(x y) if w= 4 n = xy y² if x = 6 and y = -5 x = 5 y = ² 9. [10 + (5² 2)] Simplify completely (x² + 4x 5) (2x + 9) + 5(x 6) 13. 7(2x + 6) 2(3x + 4)

4 Solve each equation or inequality. Leave answers as fractions unless decimals are given in the problem! If you need to round your answer, round to the place value given in the problem. 14. x (-3) = (y 2) = 3y x > x + 7 2x = (2x + 3) > ¾(4x 8) 19. 2x 9 < ( x) = 17.2x (2 x) + 7x = -3(x + 5) Solve each proportion. 22. x = = 4 x z + 4 z

5 Solve and graph each compound inequality < 2x + 4 < x + 1 < x + 1 > 9 or 3x 5 < x or 5x 4 > 6 Solve for the indicated variable. 30. A = ½h(b 1 + b 2 ) Solve for b I = Prt Solve for t 32. F = 9 C + 32 Solve for C 33. V = lwh Solve for h 5

6 Match each statement to the corresponding property. 34. If 3 = y, then y = = a = a 37. 5(4 + 7x) = 5(7x + 4) 38. If x = y and y = z + 2, then x = z x(9 + 4) = 9x + 4x 40. (3x + 7y) + 2y = 3x + (7y + 2y) A. Associative Property B. Commutative Property C. Distributive Property D. Identity Property E. Reflexive Property F. Symmetric Property G. Transitive Property 41. Use the box to the right to fill in the property that justifies each step. Steps Justification 11( x +2) = y if y = 9 Given 11(x + 2) = 9 11x +22 = 9 11x = - 13 x = Distributive Property Division Property of Equality Associative Property Substitution Property Subtraction Property of Equality Multiplicative Identity 42.Fill in the property that justifies each step. 48 = 6(x + 3) Given 6(x + 3) = 48 6x + 18 = 48 6x (-18) = 48 + (-18) 6x + 0 = 30 6x = 30 1x = 5 x = 5

7 43.Using the axioms of inequality and the properties of real numbers, justify each step in the solutions given below. Solution Justification 3( x + 7) > 27 Given 3x +21 > 27 3x (-21) > 27 + (-21) 3x + 0 > 6 3x > 6 (3x) >( )(6) 1x > 2 x > 2 Solve each word problem. 44.Allison earns $7.25 per hour waiting tables at Red Robin. In a weekend, she can also earn $200 in tips. How many hours will she need to work next weekend in order to make $270? Round your answer to the nearest tenth. 45. A man stands next to the Cape Hatteras Lighthouse in North Carolina. The sun s rays strike the lighthouse, casting a shadow 83.2 feet. If the man is 5.8 feet tall and his shadow is 2.5 feet, find the approximate height of the lighthouse. Round your answer to the nearest hundredth. 46. You need to have at least $250 in your checking account to avoid a low balance fee. You have $900 in your account now and you make withdrawals of $35 per week. Which inequality below can you use to determine the possible number of weeks that you can withdraw money and avoid paying the fee? A w 250 B w 250 C w 250 D w 852

8 Graphing and Functions Decide if each relation is a function. Then list the domain and range. 47. {(7, 5) (8, 5) (9, 5) (10, 5)} 48. x y Determine if the graphs shown are functions. Then state the domain and range. A. B. y x 50. Which equation matches the line graphed at right? A. y = -3x + 1 B. y = 3x + 1 C. y = ⅓x +1 D. y = -⅓x What are the x and y intercepts of the graph?

9 Graph the lines below using the method indicated. 52. y = 2x x 4y + 1 = -11 Method:slope intercept form. Method: x and y intercepts 54. y = 55. 2x y = 2 Method: slope intercept form Method: x and y intercepts Find the slope (8,3) (-3, -2) 58. y = -3x (-1, -5) (6, -5) 60. A vertical line 61. 4y = 2x 8

10 Find the zeros (roots) of each function. 62. f(x) = 3x x 63. y = -3x Draw a line with a slope of and a root at -3. Use f(x) = 2x + 5 and g(x) = 3x² + 2 to evaluate each expression. 66. f(-1) 67. g(-2) 68. g(f(0)) 69. Find the range for f(x) = -5x + 3 if the domain is {-4, -1, 6}.

List two points that are part of the solution set. 72. y > -3x + 4 73.

11 Find each solution. 70. y = y = - 2x + 3 4x + 4y = 8 y = Graph each system of linear inequality. List two points that are part of the solution set. 72. y > -3x y < - x + 1 3x 6y < -12 x > - 4 (, ) (, ) (, ) (, ) 74. Which system of inequalities matches the graph below?

12 Writing Equations of Lines Write the equation of the line in slope intercept form using the information given. 75. slope = -⅝ 76. slope = 3 y intercept = (0, -2) y intercept = m = m = ¼ (1, -3) (-3, -5) 79. (1, -3) (4, 2) 80. f(-3) = -2 f (1) = m = m = 3 (5, 1) (0, 6)

13 Write each equation in standard form. 85. y = ½x y = 2x 4 Write an equation in standard formfor the line satisfying the given conditions. 87. m = m = ¾ b = 6 (5, 2) 89. Write the equation of a line in slope intercept form that is parallel to the graph of y = 3x 5 and passing through the point (-1, 4). 90. Write the equation of a line in slope intercept form that is perpendicular to the graph of y 4x = 2 and passing through the point (2, -6). 91. Determine if the lines given are parallel, perpendicular or neither. and 5x 4y = 8

14 Variation Decide if the graphs below represent direct variation. If it does, state the constant of variation Assuming that x and y vary directly, write the direct variation equation. 95. x = 9, y = x y Assume that x and y vary inversely. Find the missing variable. 97. If x = 3 and y = 3, find x when y = If x = 2 and y = ½, find y if x = 4. Assuming that x and y vary inversely, write the inverse variation equation. 99. x = 7, y = x y

15 SEMESTER 1 EXAM REVIEW PACKET ANSWERS Equations and Inequalities 1. x x (8 + x) = x 2 + 8x x 2 2x x x x = All Real Numbers 16. x > x = x < x < x = x = x = z = x = x = x < x x > 4 or x < x -4 or x > F 35. D 36. E 37. B 38. G 39. C 40. A 41. Substitution Property Distributive Property Subtraction Prop. Of Equality Division Prop. Of Equality 42. Symmetric Property Distributive Property Addition Prop. Of Equality Additive Inverse Additive Identity Mult. Prop. Of Equality Multiplicative Inverse Multiplicative Identity 43. Distributive Property Addition Prop.of Inequality Additive Inverse Additive Identity Mult. Prop. of Inequality Multiplicative Inverse Multiplicative Identity x = 270 x = 9.7 hours 45. Lighthouse = ft 46. B Graphing and Functions 47. Yes D: {7, 8, 9, 10} R:{5} 48. Yes D: {-3, -2, -1, 0} R:{2, 9, 16, 23} 49. No D: { R: { } B. Yes D: { } R:{-2} 50. D 51. x = 2, y = 3 or (2,0) and (0,3) 52.

53. x-int: -4 y int: 3 71. (3, -3) 54. 72. (1,3) (1, 4) 55. x-int: 1 y-int: -4 73. (0, 0) (1, 0) 56. m = 57. m = 58. m = -3 59. m = 0 60. m = undefined 61.

y = 76. y = 3x 4 77. y = -2x 1 78. y = 79. y = 80. y = 81. y = 4x 19 82. y = 3x + 6 83. y = - x 5 84. y = 85. x + 2y = 6 86. -2x + y = -4 87. x + y = 6 88.

16 53. x-int: -4 y int: (3, -3) (1,3) (1, 4) 55. x-int: 1 y-int: (0, 0) (1, 0) 56. m = 57. m = 58. m = m = m = undefined 61. m = 62. x = 63. x = 64. x = -3 and f(-1) = g(-2) = g(f(0)) = R :{-27, 8, 23} 70. (3, - 1) 74. Writing Equations of Lines 75. y = 76. y = 3x y = -2x y = 79. y = 80. y = 81. y = 4x y = 3x y = - x y = 85. x + 2y = x + y = x + y = x + 4y = y = 3x y = 91. Parallel Variation 92. No 93. No 94. Yes k = y = -4x 97. x = y = 99. xy = 14 or y = 100. xy = 12 or y =

SEMESTER 1 EXAM REVIEW PACKET

SEMESTER 1 EXAM REVIEW PACKET Expressions, Equations, and Inequalities: - Translating and evaluating - Solving equations, proportions and inequalities - Literal equations (rearranging for a given variable) - Justifying the steps in