1 * * Algebra 2 CP Summer Packet RAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT* DearRamapo*IndianHillsStudent: Pleasefindattachedthesummerpacketforourupcomingmathcourse.Thepurposeof thesummerpacketistoprovideouwithanopportunittoreviewprerequisiteskillsand conceptsinpreparationforournetear smathematicscourse.whileoumafind someproblemsinthispackettobeeas,oumaalsofindotherstobemoredifficult; therefore,ouarenotnecessarilepectedtoanswereverquestioncorrectl.rather,the epectationisforstudentstoputforththeirbesteffort,andworkdiligentlthrougheach problem. Tothatend,oumawishtoreviewnotesfrompriorcoursesoron*linevideos (www.khanacadem.com,www.glencoe.com,www.outube.com)torefreshourmemor onhowtocompletetheseproblems.werecommendoucircleanproblemsthatcause oudifficult,andaskourteacherstoreviewtherespectivequestionswhenoureturnto schoolinseptember.again,giventhatmathbuildsonpriorconcepts,thepurposeofthis packetistohelpprepareouforourupcomingmathcoursebreviewingthese prerequisiteskills;therefore,thegreatereffortouputforthonthispacket,thegreaterit willbenefitouwhenoureturntoschool. PleasebringourpacketandcompletedworktothefirstdaofclassinSeptember. Teacherswillplantoreviewconceptsfromthesummerpacketsinclassandwillalsobe availabletoanswerquestionsduringtheiretrahelphoursafterschool.teachersma assessonthematerialinthesesummerpacketsafterreviewingwiththeclass. Ifthereareanquestions,pleasedonothesitatetocontacttheMathSupervisorsatthe numbersnotedbelow. Enjooursummer RamapoHighSchool MichaelKaplan mkaplan@rih.org 201*891*15002255 IndianHillsHighSchool AmandaZielenkievicz azielenkievicz@rih.org 201*337*01003355
Adding/Subtracting Fractions No Calculators Permitted. ALL work must be shown 1. Convert to a mied # 11 3 2. Convert to a mied # 25 13 3. Convert to an improper fraction 3 2 5 4. Convert to an improper fraction 5 4 11 Add the following fractions. Make sure ou have a common denominator 5. 2 5 9 9 6. 3 1 1 4 4 7. 2 1 5 10 8. 5 5 3 Subtract the following fractions. Make sure ou have a common denominator 9. 1 2 3 3 10. 3 2 1 7 7 11. 1 2 1 3 6 12. 4 5 9 13. 3 1 5 2 Reduce, Multipl, or Divide the following fractions. Make sure to reduce all answers. 14. 6 15. 5 3 16. 4 2 1 3 17. 2 1 18. 3 2 8 3 16 9 3 3 2 2 7
Order of Operations No Calculators Permitted. ALL work must be shown ** Make sure all fractions are reduced Use order of operations (PEMDAS) to simplif the following 19. 102 10 8 4 20. 2(5 8) 18 3 21. 22. 2 23. 2 8 6 2 4 4 36 17 5 5 2 2 2 4 Answer: Evaluate the following when 24. 12 z 2 25. 2, 1, z 3 z 3 26. 3 7 27. z 28. 2 3z
Plotting Points Plot each ordered pair on the given graph. 1. (1, 2) 2. (3, 5) 3. (5,1) 4. ( 1, 1) 5. (0,6) 6. ( 1,3) 7. (7, 0) 8. (2, 3) 9. ( 5, 7) 10. (5, 1) 11. ( 2,0) 12. (0,0)
G. Graphing Lines I. Finding the Slope of the Line that Contains each Pair of Points. Given two points with coordinates ( ) and ( ) 1, 1 the line containing the points is 2 m = 1. 2 1 2, 2 E. (2, 5) and (4, 1) E. (-3, 2) and (2, 3) 1 5 4 3 2 1 m = = = 2 m = = 4 2 2 2 ( 3) 5 1 The slope is -2. The slope is 5, the formula for the slope, m, of PRACTICE SET 8 1. (-1, 4) and (1, -2) 2. (3, 5) and (-3, 1) 3. (1, -3) and (-1, -2) 4. (2, -4) and (6, -4) 5. (2, 1) and (-2, -3) 6. (5, -2) and (5, 7) 5
II. Using the Slope Intercept Form of the Equation of a Line. The slope-intercept form for the equation of a line with slope m and -intercept b is 3 E. = 3 1 E. = + 2 4 3 Slope: 3 -intercept: -1 Slope: -intercept: 2 4 = m + b. Place a point on the -ais at -1. Place a point on the -ais at 2. Slope is 3 or 3/1, so travel up 3 on Slope is -3/4 so travel down 3 on the the -ais and over 1 to the right. -ais and over 4 to the right. Or travel up 3 on the -ais and over 4 to the left. PRACTICE SET 9 1 1. = 2 + 5 2. = 3 2 Slope: -intercept: Slope: -intercept: 6
3. 2 = + 4 5 4. = 3 Slope: Slope: -intercept: -intercept 5. = + 2 6. = Slope: Slope: -intercept: -intercept 7
A. Simplifing Polnomial Epressions I. Combining Like Terms - You can add or subtract terms that are considered "like", or terms that have the same variable(s) with the same eponent(s). E. 1: 5-7 + 10 + 3 5-7 + 10 + 3 15-4 E. 2: -8h 2 + 10h 3-12h 2-15h 3-8h 2 + 10h 3-12h 2-15h 3-20h 2-5h 3 II. Appling the Distributive Propert - Ever term inside the parentheses is multiplied b the term outside of the parentheses. E.1: 3(9 " 4) 3# 9 " 3# 4 27 "12 E. 2 : 4 2 (5 3 + 6) 4 2 " 5 3 + 4 2 " 6 20 5 + 24 3 III. Combining Like Terms AND the Distributive Propert (Problems with a Mi) - Sometimes problems will require ou to distribute AND combine like terms E.1: 3(4 " 2) +13 3# 4 " 3# 2 +13 12 " 6 +13 25 " 6 E. 2 : 3(12 " 5) " 9("7 +10) 3#12 " 3# 5" 9("7) " 9(10) 36 "15+ 63" 90 " 54 + 48 8
PRACTICE SET 1 Simplif. 1. 8 9 + 16 + 12 2. 14 + 22 15 23 2 + 3. 5n (3 4n) 4. 2 (11b 3) 5. 10 q(16 + 11) 6. ( 5 6) 7. 3(18z 4w) + 2(10z 6w) 8. ( 8c + 3) + 12(4c 10) 2 9. 9(6 2) 3(9 3) 10. ( ) + 6(5 + 7) 9
I. Solving Two-Step Equations B. Solving Equations A couple of hints: 1. To solve an equation, UNDO the order of operations and work in the reverse order. 2. REMEMBER Addition is undone b subtraction, and vice versa. Multiplication is undone b division, and vice versa. E.1: 4 " 2 = 30 + 2 + 2 4 = 32 4 4 = 8 E. 2 : 87 = "11 + 21 " 21 " 21 66 = "11 "11 "11 " 6 = II. Solving Multi-step Equations With Variables on Both Sides of the Equal Sign - When solving equations with variables on both sides of the equal sign, be sure to get all terms with variables on one side and all the terms without variables on the other side. E. 3: 8 + 4 = 4 + 28 " 4 " 4 8 = 4 + 24 " 4 " 4 4 = 24 4 4 = 6 III. Solving Equations that need to be simplified first - In some equations, ou will need to combine like terms and/or use the distributive propert to simplif each side of the equation, and then begin to solve it. E. 4 : 5(4 " 7) = 8 + 45+ 2 20 " 35 =10 + 45 "10 "10 10 " 35 = 45 + 35 + 35 10 = 80 10 10 = 8 10
PRACTICE SET 2 Solve each equation. You must show all work. 1. 5 2 = 33 2. 140 = 4 + 36 3. 8 (3 4) = 196 4. 45 720 + 15 = 60 5. 132 = 4(12 9) 6. 198 = 154 + 7 68 7. 131 = 5(3 8) + 6 8. 7 10 = 18 + 3 9. 12 + 8 15 = 2(3 82) 10. ( 12 6) = 12 + 6 IV. Solving Literal Equations - A literal equation is an equation that contains more than one variable. - You can solve a literal equation for one of the variables b getting that variable b itself (isolating the specified variable). E.1: 3 =18, Solve for. 3 3 = 18 3 = 6 E. 2 : 5a "10b = 20, Solve for a. +10b =+10b 5a = 20 +10b 5a 5 = 20 5 + 10b 5 a = 4 + 2b 11
PRACTICE SET 3 Solve each equation for the specified variable. 1. Y + V = W, for V 2. 9wr = 81, for w 3. 2d 3f = 9, for f 4. d + t = 10, for 5. P = (g 9)180, for g 6. 4 + 5h = 10 + u, for 12
I. Reviewing the Distributive Propert D. Binomial Multiplication The distributive propert is used when ou want to multipl a single term b an epression. E 1: 8(5 8 " 5 40 2 2 2 9) + 8 " ( 9) 72 II. Multipling Binomials the FOIL method When multipling two binomials (an epression with two terms), we use the FOIL method. The FOIL method uses the distributive propert twice FOIL is the order in which ou will multipl our terms. First Outer Inner Last E. 1: ( + 6)( + 10) FIRST OUTER First " ------> 2 ( + 6)( + 10) Outer Inner 10 -----> 10 6 ------> 6 INNER LAST Last 6 10 -----> 60 2 + 10 + 6 + 60 2 + 16 + 60 (After combining like terms) 13
Recall: 4 2 = 4 4 2 = E. ( + 5) 2 ( + 5) 2 = ( + 5)(+5) Now ou can use the FOIL method to get a simplified epression. PRACTICE SET 5 Multipl. Write our answer in simplest form. 1. ( + 10)( 9) 2. ( + 7)( 12) 3. ( 10)( 2) 4. ( 8)( + 81) 5. (2 1)(4 + 3) 6. (-2 + 10)(-9 + 5) 7. (-3 4)(2 + 4) 8. ( + 10) 2 9. (- + 5) 2 10. (2 3) 2 14