Honors Algebra 2 Summer Assignment

Transcription

1 Hoors Algera Summer Assigmet Dear Future Hoors Algera Studet, Cogratulatios o your erollmet i Hoors Algera! Below you will fid the summer assigmet questios. It is assumed that these cocepts, alog with may others, have ee mastered y you, the icomig Hoors Algera studet. There will e a assessmet o this material withi the first five days of school. This assessmet will e a idicator of your foudatio for the course, hece your success with the ew material Hoors Algera offers. It is strogly suggested that you take this assigmet seriously. This assigmet should e completed prior to the first day of school. Waitig to start it the ight efore the first day of school is ot a wise idea. Whe you fid yourself uale to aswer a questio, do ot skip it research it. That research ca e i the form of a paret, a fried, free o-lie help like rightstorm.com ad kahacademy.org, or your old Algera 1 oteook. The wesites are user-friedly ad offer excellet explaatios. Defiitely check them out as a resource. Whe you retur to school i Septemer, we expect that you will have goe through all of the questios. Feel free to ask specific questios pertaiig to the summer assigmet withi the first few days of school. The Hoors Algera teachers are here to help. Ejoy your summer ad we look forward to meetig you i Septemer. Go Kights!

2 Name Date Hoors Algera Summer Assigmet The followig prolems will help to prepare you for your Hoors Algera course. You should e ale to complete all of these prolems without the assistace of a calculator. May of the tests ad quizzes you will take i Hoors Algera are calculator-free assessmets, so this gives you a opportuity to sharpe your metal math skills. There will e a i-class calculator-free assessmet o these skills withi the first five days of school. Good luck! ORDER OF OPERATIONS A umerical expressio must have exactly oe value, to e determied y the order of operatios. Groupig Symols: Evaluate expressios iside groupig symols, such as paretheses, rackets a, races, ad fractio ars, such as i. c Expoets: Evaluate all powers. Multiplicatio ad Divisio: Perform these operatios with equal importace from left to right. Note: a commo miscoceptio is that multiplicatio is always performed efore divisio. These operatios rak equally, ad oly the order i which they appear determies the order i which they are performed. For example, the expressio 18 simplifies to 7. Additio ad Sutractio: Perform these operatios with equal importace from left to right. Simplify each expressio Evaluate each expressio if a, 0., c, d, ad e a c c 10. a cd 11. ae a c 1. c d d 1. ac 1. cd a

3 SIMPLIFYING EXPRESSIONS Simplify each expressio. 1. m m 6m x 1x 17. x 9 x 18. x x x a a 1. a a 7 7 a. xy x y x y 9 Simplify each expressio usig the laws of expoets. No egative expoets i your fial aswer. m m m m a a m m 1, m m m m, 0 1 a a a. a 1 1x y z x y z. 6a 8a c c a a a 8. a 9. x x x y x y 0

4 SOLVING LINEAR EQUATIONS AND INEQUALITIES Solve each of the followig equatios. Report your aswers i simplest form u 1. c c 1 c. x x 7 x a 1 a 7. 8x 1 6 x 8. 7 x x 8 Solve each of the followig iequalities. Report your aswers i simplest form. 9. 7x x 1 7x 0. 1x 1 18x m 1. a ad a ad m. x 7 or x 0. x 7 x or x x. h 1 6. x 0. Solve each equatio for the give variale. 7. P w l, for w A 1 h, for C F, for F 1 0. A h, for h 9 1. A P Ptr, for P. ax y cx dy, for x

5 SOLVING ABSOLUTE VALUE EQUATIONS AND INEQUALITIES The asolute value of a umer is its distace away from 0 o the umer lie. Sice distace is oegative, the asolute value of a umer is always oegative. uits uits For example, if x the we kow that either x or x. - 0 Solve each of the followig equatios. Report your aswers i simplest form.. x. x 8. x x x x 1 To solve a asolute value iequality, we ca still use the defiitio of a asolute value from aove. For example, if x the we kow that Ad if x the we kow that x is less tha uits away from 0. x is more tha uits away from 0. uits uits uits uits x ad x x x or x Solve each of the followig iequalities. Report your aswers i simplest form. 9. x 60. x x x x 6. x x x 1

6 SLOPE AND WRITING EQUATIONS OF LINES Fid the slope of each lie. 67. through, 6 ad, through, 17 ad, through, ad, 70. through, 6 ad, y x 8 7. y 7. x y x Determie the value of r so the lie through the give poits has the required slope. 77., r ad, 11 ; m 78. r, ad 1, r; m Write a equatio i slope-itercept form y mx for each of the followig sets of coditios. 79. Passig through, 80. Passig through, with a slope of. 7 ad,. 81. A vertical lie passig through 1,. 8. Parallel to x y 18 passig through 10,. 8. Perpedicular to 7x y 16 passig through 7,. 8. Has a x-itercept of 1 ad is parallel to the lie that passes through 19, 1 ad 17, 1

7 GRAPHING LINES AND INEQUALITIES Graph each of the followig liear equatios or iequalities x 86. y 6x 1 y 87. x 1 y x y x y x

8 SYSTEMS OF EQUATIONS AND INEQUALITIES Solve each system y graphig. Descrie it as cosistet ad idepedet, cosistet ad depedet, or icosistet. Type of System The Graph Solutio cosistet ad idepedet itersectig lies oe solutio, (x, y ) cosistet ad depedet coicidig lies ifiitely may solutios icosistet parallel lies o solutio 91. x y x y 9. x y y x 9. x y 6 y x Solve each system algeraically. You may use either sustitutio or elimiatio. 9. x y 1 1 x y 9. y x 1 x y x y x y x y 16 6x y 8

9 FACTORING POLYNOMIALS Guidelies for Factorig: Always look for a GCF efore doig aythig else. Cosider the umer of terms i the polyomial. Two Terms: Try factorig as a differece of two squares. a a a Three Terms: Triomials of the form ax x c ca e factored ito the product of two iomials. (Use a method that your Algera 1 teacher taught you.) More Tha Three Terms: Try factorig y groupig. Make sure the polyomial is factored completely. This meas that each remaiig factor is prime. Factor each of the followig expressios completely. 98. x 8x 99. x 1x x 0x x 0x x x a x x 9x x x x 1x ac ad c 6d x 7x 109. x x x 1x a a

10 QUADRATIC EQUATIONS AND SQUARE ROOTS Solve each of the followig quadratic equatios. You may use ay of the methods (factorig, quadratic formula, or completig the square) you leared i Algera 1. Please ote: ot all of the equatios ca e factored. 11. x 6x 11. x x 11. 1x 9 x 11. x x x x 1 0 x 117. x 118. x 1 6x x x 0 Simplify each of the followig x