IB Mathematics SL: Analysis And Approaches Summer

IB Mathematics SL: Analysis and Approaches Summer HomeworkNameDear Future IB Mathematics SL Student,I hope you are excited for your upcoming year in IB Math SL! The purpose behind this summerhomework packet is to reacquaint you with the necessary skills to be successful in this year’s mathcourse.At first glance this packet may seem overwhelming. However, there are approximately 9 weeks ofsummer. Pace yourself. There are 13 Parts of this packet – complete two parts each week and you willeasily be able to complete the assignment before your return to school in the fall. Please be prepared tosubmit this assignment during your second IB Math SL class. It will be graded for accuracy as well ascompletion. Work needs to be shown in a neat and organized manner, and it is perfectly acceptable tocomplete the packet on separate sheets of paper. Just be sure to staple any extra papers to the packet.Also, do not rely on a calculator!Show ALL work for each problem and take your time. Remember, this will be your first impression toyour new math teacher, and you want to make sure that it is a positive one! See below for directions andhelpful websites. We hope you have a wonderful summer!Best,Wareham High School Math DepartmentNeed help with your Summer math packet?Feel free to email Mrs. Medina at mmedina@wareham.k12.ma.us with any questions you might have.To ensure the fastest response, please include your name, summer assignment name, and (ifpossible) a picture of the problem and your accompanying work.Directions: Before answering any questions, read through the given notes and examples for each topic.This packet is to be submitted during your second IB Math SL class period.All work must be shown in the packet or on a separate sheet of paper stapled to the packet.To avoid a penalty on your grade, final answers MUST BE BOXED or CIRCLED.1

Part 1 – FunctionsLet 𝑓 (𝑥 )1) 𝑥 ! , 𝑔(𝑥) 2𝑥 5, ℎ(𝑥 ) 𝑥 ! 1, find:ℎ( 2)3)2)𝑓.𝑔( 4)04)ℎ(𝑥 2)!.𝑔(𝑥 )0 2𝑓(𝑥)2

Part 2 – Intercepts of a GraphFind the 𝑥 and 𝑦 intercepts for each function below.5)6)𝑦 2𝑥 87)8)𝑦 𝑥 4𝑦 𝑥 ! 5𝑥 6𝑦 3" 93

Part 3 – Points of IntersectionFind the point(s) of intersection of the graphs for the given equations. Write each solution as an ordered pair.9)10)4𝑥 𝑦 1072𝑥 𝑦 87𝑦 3𝑥 4𝑥! 𝑦 64

Part 4 – Domain and RangeFind the domain and range of each function. Write your answer using interval notation.11)12)!𝑓 (𝑥) 𝑥 5𝑔(𝑥 ) 𝑥 313)2ℎ(𝑥 ) 𝑥 114)𝑓(𝑥) 4"#! 55

Part 5 – InversesFind the inverse of each function below.15)𝑓(𝑥 ) 2𝑥 117)ℎ(𝑥 ) 5𝑥 216) (Domain restriction: 𝑥 0)𝑔 (𝑥 ) 𝑥 ! 718)𝑓 (𝑥) 𝑥 4 319) If the graph of 𝑓(𝑥) has the point (2, 7), then what is one point that will be on the graph of 𝑓 !" (𝑥)?20) Explain how the graphs of 𝑓(𝑥) and 𝑓 !" (𝑥) compare.6

Part 6 – Transformation of Functions21) How is the graph of 𝑔(𝑥 ) (𝑥 3)! 1 related to the parent function 𝑓 (𝑥 )transformations that occurred from the parent function to the given function.22) Write an equation for a function, 𝑔(𝑥), that has the shape of 𝑓 (𝑥 )left and is reflected over the 𝑥 axis. 𝑥 ! ? Describe the 𝑥 , but is translated 6 units to thePart 7 – Vertical AsymptotesFind the vertical asymptote(s) of each rational function below.23)24)𝑓 (𝑥 ) 5𝑥 2𝑥 3𝑔 (𝑥 ) !𝑥 6𝑥 825)ℎ(𝑥 ) 𝑥 7𝑥 ! 497

Part 8 – Horizontal AsymptotesFind the horizontal asymptote of each rational function below.26)27)29)!𝑥 2𝑥 1𝑓 (𝑥 ) "𝑥 𝑥 728)3𝑔(𝑥) 𝑥 94𝑥 10𝑓(𝑥) 2𝑥 330)"! 5𝑥 2𝑥 8𝑔 (𝑥 ) 3𝑥 " 4𝑥 531)𝑥! 1ℎ(𝑥) 𝑥 210𝑥 !ℎ(𝑥 ) !2𝑥 18

Part 9 – Exponential EquationsSolve each exponential equation below.32)33)34)35)5!"# 5#%"&'(!1! 21663 "#( 9'"&)1 "!! 16# !%&49

Part 10 – LogarithmsThe logarithmic equation log % 𝑦 𝑥 can be written as an exponential equation 𝑏 "SAME thing. You can use this fact to evaluate logarithms.Recall the natural logarithmln 𝑥 log ' 𝑥 .Evaluate each logarithm below.36)39)The value of 𝑒 2.718281828 or37)log & 7They mean the !lim 1 !'! #38)log 2740)log !' 5 𝑦.log ! .1?1641)log ( 1log !& 910

Part 11 – Properties of LogarithmsUse properties of logarithms to evaluate each expression below.42)43)44) 'log ) 9log ! 246)50)𝑒 *. /47)48)7 ln 𝑒log34 25 log34 451)log !8 ln 𝑒 "45)2* ,2 )-49)ln 𝑒log 5 40 log 5 511

Part 12 – Factoring TrinomialsFactor the expression 2𝑥 ! 𝑥 6 using the box method.Steps to Factor Trinomials in the form 𝑎𝑥 ! 𝑏𝑥 𝑐 by Box Method:1) Multiply 𝑎 times 𝑐 .𝑎 𝑐 (2)( 6) 122) Find two numbers that multiply to 𝑎 𝑐 12 and add up to the coefficient of the middle term 𝑏 1.( 𝟑)(𝟒) 12 𝟑 𝟒 13) Rewrite the middle term with these two numbers, put the four terms in a box, and factor the GCF out of eachrow and column.2𝑥 ! 𝟏𝒙 62𝑥 ! 𝟑𝒙 𝟒𝒙 62𝑥 3𝑥 22𝑥 ! 3𝑥 4𝑥 62𝑥 ! 𝑥 6 (2𝑥 3)(𝑥 2)Factor each expression below by using the box method.52)53)!5𝑥 14𝑥 854)2𝑥 !55) 3𝑥 98𝑛! 10𝑛 36𝑥 ! 23𝑥 412

Part 13 – The DiscriminantUse the discriminant to determine the nature of the roots of each quadratic equation below.56)57)!4𝑥 12𝑥 9 07𝑥 ! 𝑥 2 58)3𝑥 !59) 18𝑥 5024𝑥 ! 5 14𝑥13

IB Mathematics SL: Analysis and Approaches Summer Homework Name _ Dear Future IB Mathematics SL Student, I hope you are excited for your upcoming year in IB Math SL! The purpose behind this summer homework packet is to reacquaint you with the