ALGEBRA II HONORS REVIEW PACKET NAME This packet contains all of the material that you should have mastered in Algebra I. You are responsible for reviewing this material over the summer and expect an assessment on ALL of these topics within the first couple weeks of school for one of your first assessment grades. If you are having difficulties with any of these topics then you will need to attend after school help sessions at the start of the school year as well as utilizing other resources. You are EXPECTED to come in with a strong understanding of even the later topics of Algebra 1: including: factoring (ALL types), quadratics (SOLVING AND GRAPHING), and RADICAL EXPRESSIONS. What you completed in Algebra 1 WILL NOT be retaught. Directions: Please do all work on a separate sheet of paper. All answers should be in fractional form and in lowest terms. It is strongly recommend that these problems be completed without the aid of a calculator. I. ORDER OF OPERATIONS Simplify the expression on each side of. Make a true statement by replacing the with the symbol or. 1.. 19 54 9 7 1 4 81 16 1 7 108 4. 6 6 0 (6 ) 6 4. (7 4) 6 7 4 6 Use order of operations to simplify each expression 5. 7. 6 [5 ( ) ] 6. 6( ) 4 ( 4) 8. (6 1) [(0 ( 5) ] 4 7( 1) ( ) 9. 1 4 8 9 4 ( 8) 10. 0 1 ( ) 1( ) Evaluate each expression if 1 a 5, b 0.5, c, d 4, e.6 11. ae d c 1. d( b c) ac
II. SIMPLIFYING EXPRESSIONS--Use distributive property to simplify. 1..4t 1.6 s ( 1.9t 4. s) 14. [ 7( x y) x] ( x y)5 15. 50 [(1 f) ( f)] 16. 5 x(x 5) 7 x(1 5 x) 17. 1 xy (9x 6 xy y ) 18. [ 7( ) ] ( ) r s r s r 19. 4[( 5 x y) y] 10( y 4 x) 0. 15 [( g 7) (1 g)] III. SOLVING EQUATIONS-- Solve the following equations. Be sure to check your solutions. 1. 4 9 ( ) 1 5 u. ( ) 1 d. 1 [4( k ) ( k)] 4 4. ( c ) c (1 c) 5 5. n 8n6 6. 4 5 1 n n 7 4 7. 4( a ) 14 ( a) 8. ( g ) 4 ( g ) 9. 1 9 x (4 x) (4x 5) 0. 6 1 1 4( x 7) x (9 6 x) 1. 5 t t t. 4 ( x ) x ( x 1) 5 5 4 Solve for the given variable:. Solve for W: P W L 4. Solve for P: A P Pr t 5. Solve for F: C 5 ( F ) 9 1 b A b1 b h 6. Solve for : IV. WORD PROBLEMS 7. Jim s weekly pay is two thirds of Alicia s. Together they earn $600 per week. What is each person s weekly pay?
8. Bob is 4 years younger than his father. In years, he will be half as old as his father. How old is each now? 9. The length of a rectangle is 15 cm more than the width. A second rectangle whose perimeter is 7 cm is 5 cm wider but cm shorter than the first rectangle. What are the dimensions of both rectangles? 40. Lizzy bought several apples at 0 cents each, ate two of them, and sold the rest for 0 cents each. She made a profit of $.0. How many apples did she buy? 41. In a collection of coins worth $9.1, there are twice as many dimes as quarters, four more nickels than dimes, and twice as many pennies as nickels. How many of each kind of coin are in the collection? 4. Inga invested part of her $6000 savings in common stock and the rest in rare stamps. At the end of the year, she realized a gain of 9% on the stock and 1%on the stamps. If her savings now amounts to $6615, how much did she invest in stamps? 4. A car travels 418 km in 6 hours. One hour of the trip is in the city, where the average speed is just half of what the car averaged on the turnpike for the rest of the trip. What was the car s average city speed? 44. Laura can run at 8 m/s and Mary at 7.5 m/s. On a race track, Mary is given a 5 m head start and the race ends in a tie. How long is the track? 45. A local radio station is having a drawing to win tickets to see Nickelback in concert. The winners will be driven in a limousine that holds 8 passengers. Concert tickets cost $ for adults and $19 for students. After renting the limousine, the radio station has $167 left in their giveaway budget to buy the eight tickets. How many adult tickets and student tickets can the station buy? 46. Consuela walks from her house to the recreation center at 6 km/h, stays for 45 minutes and then gets a ride back home at 48 km/h. If she arrives home 1.5 hours after she started out, find the distance from home to the recreation center. 47. Joshua is doing a chemistry experiment that calls for a 0% solution of copper sulfate. He has 40 ml of 5% solution. How many milliliters of 60% solution should Joshua add to obtain the required 0% solution? 48. How many kilograms of water must be evaporated from 1 kg of a 0% salt solution to produce a 60% solution? V. IDENTIFYING NUMBERS Determine whether each statement is true or false. If false, give an example of a number that shows the statement is false. 49. Every real number is irrational. 50. Every integer is a rational number. 51. Every rational number is an integer. 5. Every irrational number is a real number. 5. Every natural number is an integer. 54. Every real number is either a rational number or an irrational number.
VI. ABSOLUTE VALUE EQUATIONS 55. x 9 0 56. 8 4x 64 57. 7 9 4 x 58. 1 7 9 7 4 x VII. SOLVING INEQUALITIES. Graph on a number line to find the solution and write your answer in interval notation. (look up what interval notation is if necessary) 59. (x 5) (x 5) < 5x + 1 60. 4x 0.04 5 61. x 6( x1) 6. 4m 5 7 or 4m 5 9 5 10 6. 5 45 10 ( 1 x) or x 64. 14 h 7 1 65. 4 y 7 y 1 11y 66. x 7 x 5 x 11 5 4 67. 4 n 6 or 17 5n1 7 68. 5x 7 x 4 or x 4 4x 69. (7 h) 8 h or 7h 9 ( h 5) 70. 0 8 x 7 and 7 6x1 41 VIII. SOLVING ABSOLUTE INEQUALITIES 71. 1 6 4 x 1 7. 1 1 y 8 4 4 IX. PROBLEM SOLVING USING INEQUALITIES Express each statement in terms of an inequality involving absolute value. Do not solve. 7. The diameter of the lead in a pencil p must be within 0.01 millimeters of 1 millimeter. 74. The cruise control of a car set at 55 mph should keep the speed s within mph of 55mph.
Write an inequality to describe each situation and then solve. 75. The three sides of an equilateral triangle are increased by 0 cm, 0 cm, and 40 cm, respectively. The perimeter of the resulting triangle is between twice and three times the perimeter of the original triangle. What can you conclude about the length of a side of the original triangle? 76. The telephone company offers two types of service. With plan A, you can make an unlimited number of local calls per month for $18.50. With Plan B, you pay $6.50 monthly, plus 10 cents for each min of calls after the first 40 minutes. At least how many minutes would you have to use the telephone each month to make Plan A the better option? 77. A subway train make six stops of equal length during its 1 km run. The train is actually moving for 0 minutes of the trip. At most how long can the train remain at each station if the average speed for the trip, including stops, is to be at least 6 km/h? 78. Find all triples of consecutive integers such that 11 times the largest of the integers is at least 46 more than the product of the other two. X. POLYNOMIALS Perform the given operation. 79. 80. 81. Factor completely. State if you used a special case or grouping. 8. 8. 84. 85. 86. Solve the following by factoring. Identify all double roots. 87. y 6y 7y 88. 4r 8r 0 89. 5x 64 0 90. ( u )( u ) 8u 91. y 5y 4 0 9. 4 1x 4x 4x 9. 94. 95.
Solve the following by using the quadratic formula. 96. v 5 v 0 97. p p 0 Solve the following by completing the square. 98. x 4x 0 99. n 8n Graph the quadratic function. State what form it is in, the axis of symmetry, and the vertex. 100. y ( x 4)( x 1) 101. y x x 18 4 10. y ( x ) XI. SLOPES OF LINES XI. LINES Find the slope of each line. 10. (-,6) and (4,-1) 104. 5, 4 and 4 1, 5 Find the x-intercepts and y-intercepts of each line. 105. 4xy 7 106. x 1 y 0
Graph the following lines. 107. x 7 108. x y x y 4 109. Graph a line through (, 1.5) that is perpendicular to the graph of y. 110. Graph a line through (-4,-) with an undefined slope. 111. Graph the line perpendicular to the graph of xy 4 that intersects it at its y-intercept. 11. Graph the line that passes through (-,-1) and has a slope of.75. 11. Write an equation of a line using point slope given the point 1 4 1,, m 5 and rewrite in standard form. 114. Write an equation of a line using point slope given the point (, 4), m = 0.4 and rewrite in standard form. 115. Find an equation in standard form that passes through the points (, ) and (, 6). 116. Find an equation in standard form that passes through the origin and has slope 0. 117. Find an equation in standard form that has a y-intercept of 6 and is parallel to the x-axis. 118. Find an equation in standard form that has an x-intercept of 4 and is perpendicular to the x-axis. XII. LINEAR SYSTEMS Solve. 119. x + y = 1 10. x + y = 6 x + y = 1 5x 6y = 15 11. 6x = 4y + 5 1. x + 4y = 16 6y = 9x 5 1 4 x y
Graph each system of inequalities. y x1 1. 1 y x 14. 5 x y 6 5xy4 XIII. RADICALS Simplify each expression completely. 15. 16. 17. 18. 19. 10. 11. 1. 1. 14. 15. 16.