SUMMER PACKET PREPARING FOR ALGEBRA II

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SUMMER PACKETPREPARING FOR ALGEBRA IIMoorestown High SchoolMoorestown, New JerseyThis packet will be reviewed the first day of school. All work must beshown and final solutions should be circled.You will be tested on the concepts covered in this packet during the1st week of school. The test will be NO CALCULATORS!Student’s Name0

HIGH SCHOOL Calculator RequirementsAll High School Math courses require the use of a TI-84 Plus graphingcalculator. This is the same calculator that was required for Geometry.If you need to purchase another one, many local stores carry this calculator,including Staples, Best Buy, and Walmart. This calculator can also bepurchased online (hyperlinks are included above for those stores). It costsapproximately 115.You should NOT use a graphing calculator to complete this packet,unless the directions note that you can use one.1

Preparing for Algebra IIThe purpose of the packet is to help you review and reinforce concepts/topicsthat are necessary for Algebra II. This packet has been designed to provide areview of Algebra I skills that are essential for student success in Algebra II.Completion of this packet over the summer will be of great value to helpingstudents successfully meet the academic challenges awaiting them in AlgebraII.Instructions:Complete all sections of this packet. You will show this completed packet to your AlgebraII teacher the first day of school. All work must be shown and final answers shouldbe circled.Students must show work that supports their understanding. Students will betested on the concepts covered in this packet during the 1st week of school.It may be necessary to seek assistance on some questions/concepts.that is fine!Websites that may be of assistance:www.mathforum.org/dr.math Use this web site if you have a math questions that youneed answered.www.allmath.com This website will provide you with links to games, reference, generalmath help and resources.www.mathforum.com This online community includes teachers, students, researchers,parents and educators who have an interest in math and math education. The siteincludes Ask Dr. Math, Problems of the Week, discussion groups and much more.www.AAAmath.com. Customized by grade level and topic, AAA Math featuresexplanations of various mathematical topics, practice problems and fun, challenginggames.www.coolmath.com This fully interactive site and allows the user to sharpen basic mathskills, play games and explore new math concepts.www.figurethis.org Created by the National Council of Teachers of Mathematics, this sitehelps families enjoy mathematics outside school through a series of fun and engagingchallenges.The more math you explore the more prepared you will be in September!2

Algebra I TopicsEquationsVariables and ExpressionsSolving Equations by Adding or SubtractingSolving Equations by Multiplying or DivingSolving Two-Step and Multi-Step EquationsSolving Equations with Variables on Both SidesSolving for a VariableSolving Absolute-Value EquationsRates, Ratios, and proportionsApplications of ProportionsPrecision and AccuracySolving Linear InequalitiesSolving Systems of Linear InequalitiesInequalitiesGraphing and Writing InequalitiesSolving Inequalities by Adding or SubtractingSolving Inequalities by Multiplying or DividingSolving Two-Step and Multi-Step InequalitiesSolving Inequalities with Variables on Both SidesSolving Compound InequalitiesSolving Absolute-Value InequalitiesFactoring PolynomialsFactors and Greatest Common FactorsFactoring by GCFFactoring x2 bx cFactoring ax2 bx cFactoring Special ProductsChoosing a Factoring MethodFunctionsGraphing RelationshipsRelations and FunctionsWriting FunctionsGraphing FunctionsScatter Plots and Trend LinesArithmetic SequencesLinear FunctionsIdentifying Linear FunctionsUsing InterceptsRate of Change and SlopeThe Slope FormulaDirect VariationSlope-Intercept FormPoint-Slope FormSlopes of Parallel and Perpendicular LinesTransforming Linear FunctionsSystems of Equations and InequalitiesSolving Systems by GraphingSolving Systems by SubstitutionSolving Systems by EliminationSolving Special SystemsExponents and PolynomialsInteger ExponentsRational ExponentsPolynomialsSpecial Products of BinomialsMultiplying PolynomialsAdding and Subtracting PolynomialsQuadratic Functions and EquationsSolving Quadratic Equations by FactoringCharacteristics of Quadratic FunctionsGraphing Quadratic FunctionsTransforming Quadratic FunctionsSolving Quadratic Equations by GraphingIdentifying Quadratic FunctionsSolving Quad Equ by Using Square RootsNonlinear SystemsThe Quad Formula and the DiscriminantCompleting the SquareExponential FunctionsGeometric SequencesExponential FunctionsExponential Growth and DecayLinear, Quadratic, and Exponential ModelsComparing FunctionsData Analysis and ProbabilityOrganizing and Displaying DataFrequency and HistogramsData DistributionMisleading Graphs and StatisticsExperimental ProbabilityTheoretical ProbabilityIndependent and Dependent Events3

Solve each equation.1. 3d 8 2d 172. 2n 7 5n 103. v 5 6v 1 5v 3 4. 5(r 1) 2(r 4) 6Solve for the indicated variable.5. 4c d for c7. 10 xy z for x6. 2p 5r q for p8.h 4 k for jjSolve each equation.9. x 1210. x 1 211. 3 x 2412. 4 x 5 1213. How many solutions does the equation x 7 1 have?14. How many solutions does the equation x 7 0 have?15. How many solutions does the equation x 7 1 have?4

Solve each inequality and graph the solutions.16. b 8 1517. 9 m 918. 7y 2119. 2s 3382k 3 7 520. c 921.22. 3a 10 1123. 6(n 8) 1824. 2x 30 7x25. 5s 9 2(s 6)Write the compound inequality shown by each graph.26.27.5

Solve each compound inequality and graph the solutions.28. 12 4n 2829. x 3 3 OR x 3 330. 2 3b 7 1331. 5k 20 OR 2k 8Solve each inequality and graph the solutions.32. x 2 333. x 3 - 1.5 2.534. x 17 2035. 2 x 2 3Evaluate each function for the given input values.36. For f(x) 5x 1, find f(x)when x 2 and when x 3.37. For h(x) x 3, find h(x)when x 3 and when x 1.6

Use intercepts to graph the line described by each equation.38. 3x 2y 6Find the slope of the line.39.40.41.42.Find the slope of the line that contains each pair of points.43. (2, 8) and (1, 3)44. (0, 2) and (4, 7)Find the slope of the line described by each equation.45. 3x 4y 2446. 8x 48 3yWrite the equation that describes each line in slope-intercept form.147. slope 4; y-intercept 348. slope ; y-intercept 637

49. slope 2, (10, 3) is on the line.51350. slope , (-6, 0) is on the line.Write each equation in slope-intercept form. Then graph the line described by the equation.51. y x 352. 5x 2y 10Write an equation in point-slope form for the line with the given slope that contains the given point.53. slope 3; ( 4, 2)54. slope 1; (6, 1)Graph the line described by each equation.255. y 2 (x 6)356. y 3 2 (x 4)Write the equation that describes the line in slope-intercept form.57. slope 4; (1, 3) is on the line58. (2, 1) and (0, 7) are on the line8

Find the intercepts of the line that contains each pair of points.59. ( 1, 4) and (6, 10)60. (3, 4) and ( 6, 16)Identify which lines are parallel.61. y 3x 4;y 4;y 3x;y 3Identify which lines are perpendicular.162. y 2;y x 4;y 4 2(x 3);2y 2xTell whether the ordered pair is a solution of the given system. x 3y 6 4 x 5 y 763. (3, 1); 3 x 2y 14 5 x y 3264. (6, 2); 9

Solve each system by graphing. y x 465. Solution : y 2x 1Solve each system by substitution. y x 267. y 4x 1 2 x y 6 x y 369. 2x y 0 5 x 3 y 1171. y x 6 y 3 x 666. Solution : y x 4 y x 268. 2 x 3 y 0 x 2y 170. 72.1 1 2 x 3 y 5 1 x y 10 410

Solve each system by elimination.2x 3y 1473. 2x y 103 x y 1774. x 3y 775. x 3y 1476. y 3 x 11 10 x y 078. x 2y 877. 2 y x 2Solve each system of linear equations. y 2x 379. y 2x 3 4 x 2y 20 2x 4y 32 5 x 3 y 7 y x 3 0 x y 380. Tell whether the ordered pair is a solution of the given inequality.81. (1, 6); y x 682. (5, 3); y x 211

Graph the solutions of each linear inequality.83. y x 484. 2x y 2Write an inequality to represent each graph.85.86.Tell whether the ordered pair is a solution of the given system.y x 2y x 387. (2, 2); 88. (1, 3); y 4x 1 y x 1Graph the system of linear inequalities.a. Give two ordered pairs that are solutions.b. Give two ordered pairs that are not solutions.y x 489. y 2 x 1 90. y 2 x 1 x y 312

Simplify.91. 3092. 3 393. 8 394. 4.2 0Evaluate each expression for the given value(s) of the variable(s).95. 2t for t 2 496. 2x 0 y 3 for x 7 and y 4Simplify.97. 3k 4x1098. 3df 499. 6g100.p 7 q 113

Simplify each 9.121336 13481 3632106.108.110.1481 81251132334Simplify. All variables represent nonnegative numbers.111.x4 y 2112.x6 y 614

113. 12 a 2a2114.Add or subtract. 13 z z23115.13x2 9 y 2 6 x 2116. 8m 5 16 11m117. 9x118. 3.7q119. 2r 5 5r 6 120. 7k4 x3 2 x 4 6 x3 8 x 4 x3 Multiply.22 8q 3.7 4.3q 2 2.9q 1.6 3 2k 2 5k 1 121. 5mn 4m n 122. 2 pq 5 p q 3q 123. 3x x 2 4 x 6 124. y 3 y 5 322322415

125. m 2mn 3mn n2 126. 3x 4 x 2 5 x 2 127. 4 x 6 2 x3 x2 1 128. a b a b b a 129. 2 x 130. 2x 6 131. 2a 7b 132. x 2 134.13q 4 and 2 p 2136. 4 x 2 6 x22222Find the GCF of each pair of monomials.133.6x 2 and 5x 2Factor each polynomial. (GCF)135.10 g 3 3g16

137.3x 2 9 x 3138.14n3 7n 7n2140.4 x 3 x y 2 Factor each expression.139.5 m 2 m m 2 Factor each polynomial by grouping.141.6 x3 4 x 2 3x 2142.2m3 4m2 6m 12143.3r r 2 2r 6144.6a3 9a 2 12 8ax2 13x 36146.x2 10 x 16Factor.145.17

147.x2 11x 24148.x2 7 x 6149.x 2 3x 88150.x2 6 x 27151.x2 x 2152.x 2 4 x 45153.2 x2 9 x 10154.5x2 7 x 6155.7 x2 3x 10156.2 y 2 11y 14157. 4n2 16n 9158. 6 x2 13x 218

159.x2 4 x 4160.9 x2 12 x 4161.x2 2 x 1162.x2 6 x 9163.1 4x 2164.81x 2 1165.4 x4 9 y 2166.x8 50Factor each polynomial completely. Check you answer.167.2 4 x3 3x 2 8 x 168.4 4 p 4 1 169.3x5 12 x3170.8 pq 2 8 pq 2 p19

171.mn5 m3n172.6 x 4 3x 3 9 x 2173.p5 3 p3 p 2 3174.2 z 2 11z 6176.2 x 2 y 3x 1178. 10,15 , 9,17 , 8,19 , 7, 21 , 6, 23 Tell whether each function is quadratic. Explain.175.y 6 x 14177.Tell whether the graph of each quadratic function opens upward or downward. Explain.179.y 3x 2 4 x180.y 2 x2Identify the vertex of each parabola. Then give the minimum or maximum value of the function.181.182.20

Find the domain and range.183.184.Find the zeros of each quadratic function from its graph. Check your answer.185.186.Find the axis of symmetry of each parabola.187.188.For each quadratic function, find the axis of symmetry of its graph.189.y 3x2 18x 1190.y 2 x 2 3x 4192.y Find the vertex.191.y 5x 2 10 x 31 2x 2x221

Order the functions from narrowest graph to widest.3194.193.f x x 2 , g x 2 x 2 , h x 8 x 24f x 5x 2 , g x 5x 22Compare the graph of each function with the graph of f x x .195.g x x2 6196.1g x x2 24Solve by graphing.197.y x2 2x 3198.y 2x2 2x 4199.8x 4 x2 4200.x2 6 x 7Use the Zero Product Property to solve each equation. Check your answer.201. x 6 x 5 0202.x x 11 022

Solve each quadratic equation by factoring. Check your answer.203.x2 4 x 12 0204.x2 5x 6 0205.x2 10 x 16206.x2 8x 16 0207.x2 36 12 x208.2 x2 7 x 6 0Solve using square roots. Check your answer.209.x 2 49210.x 2 400211.16 x2 10 131212.0 81x2 25213.3x 2 81214. x 9 2 2523

Solve by completing the square.215. x 2 6x 5216.x 2 x 30217.x2 10 x 9218. x2 5x 5219. 6 x 3x2 9220. x2 8x 6 0Solve using the Quadratic Formula.221.x2 5x 4 0222.x2 6 x 7 0223.x2 7 x 2 0224.x2 4 x 7 0225.3x 2 2 x 8226.2 x2 6 024

Solve each system by graphing. Check your answers. y 2x 2 7 x 6227. 228. y x y x 2 2x 5 y 2x 8Solve each system by substitution. Check your answers. y x 2 4x 3229. 230. y x 3 y 2x 2 5 x 3 y 3 x 15Solve each system by elimination. Check your answers. y x 2 3231. 232. 4 x y 6 y x 2 7 x 12 3 x y 525

Tell whether each set of ordered pairs satisfies an exponential function. Explain your answer.233. 1, 1 , 0,0 , 1, 1 , 2, 4 234. 0,1 , 1,4 , 2,16 , 3,64 Graph each exponential function.235. y 5 x237.y 4 2 239. 1 y 3 xx236.y 5 2 x238.y 2 3 x240.y 2 0.25 xWrite an exponential growth function to model the situation. Then find the value of the function afterthe given amount of time.241. The cost of tuition at a college is 12,000 and is increasing at a rate of 6% per year; 4 years.26

Write a compound interest function to model the situation. Then find the balance after the given numberof years.242. 1500 invested at a rate of 3.5% compounded annually; 4 years.Write an exponential decay function to model the situation. Then find the value of the function after thegiven amount of time.243. The value of a car is 18,000 abd is depreciating at a rate of 12% per year; 10 years.Graph each data set. Which kind of model best describes the data?244. 1, 4 , 2,0.8 , 0, 20 , 1,100 , 3,0.16 245. 2, 7 , 2, 9 , 0, 8 , 4, 6 , 6, 5 FORMULASExponential Function: f x ab xExponential Growth: y a 1 r tExponential Decay: y a 1 r t r Compound Interest: A P 1 n ntHalf-Life: A P 0.5 tQuadratic Formula: b b2 4ac2a27

Preparing for Algebra II The purpose of the packet is to help you review and reinforce concepts/topics that are necessary for Algebra II. This packet has been designed to provide a review of Algebra I skills that are essential for student success in Algebra II. Completion of this

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