Gaithersburg Middle School. Algebra 1. Summer Packet

Transcription

1 Nme: Dte: Githersurg Middle School Alger 1 Summer Pcket Alger 1 Pge 1 Summer, 01

2 Der student, Hoory! Summer vction is lmost here nd the strt of the new school yer is just round the corner. We wnt you to e s prepred s possile for the school yer. It is importnt tht you hve smooth trnsition to your new mth clss right t the eginning of the school yer. With this in mind, we re providing prctice workook of previously tught skills for you to complete over the summer. It is your responsiility to complete the pcket efore the strt of the school yer. Plese look for the clcultor nd no clcultor symols throughout the pcket. Your new mth techer is expecting to see ll work necessry to solve the prolems in this pcket. Work spce is provided. However, if you use lined pper, plese ttch it to your pcket. Your signture t the ottom of the pge signifies tht you hve completed ll work to the est of your ility nd tried your est to complete the pcket. If you hve troule on some of the informtion, seek ssistnce from prent/gurdin or other dult who my e le to ssist you! Best wishes nd we will see you soon! Sincerely, GMS Mthemtics Deprtment Der Prent/Gurdin, It is importnt to us tht your child hs smooth trnsition into new mth course. With this in mind, we re providing prctice workook of previously tught skills for your child to complete over the summer. By doing so, it is our gol to increse your child s retention of mthemtics skills nd to ssure cler understnding of expecttions we hve for students in the upcoming yer in mth. Plese encourge nd monitor your child s completion of this workook. Plese mke sure tht ALL WORK IS SHOWN on ech pge or on ttched pper. Rememer, the gol is to work on it consistently throughout the summer nd not to rush to finish it quickly. Students re to sumit their workooks to their mth techers within the first week of school. The pcket will e ssessed for completion grde. Plese sign nd dte the ottom of this document stting tht your child hs completed the summer mth pcket to the est of his/her ility. A list of suggested supplies nd resources is lso ttched to this summer pcket. The mth deprtment will e using grphing clcultors for clssroom instruction, homework completion, nd MCPS ssessments. Students my choose to purchse their own to ring ck nd forth to school. It is recommended tht you purchse the grphing clcultor during the summer so tht your child cn ecome cquinted with it efore school strts in the fll. Thnk you for your support! Suggested Mth Supplies for Alger 1 Student: # pencils Binder Journl Protrctor- sic nd cler Compss TI-Nspire Sincerely, GMS Mthemtics Deprtment Plese fill in the following informtion when the summer mth pcket is complete: Student Signture Grde: Dte: Prent/Gurdin Signture Dte Alger 1 Pge Summer, 01

3 Protrctor Compss- Choice 1 Compss- Choice Cler Plstic Protrctors with smll hole re the esiest for the children to use. The protrctor ove is ville t most office supply stores. Metl compsses re the esiest for student to use. They won t move round s much s the plstic ones. Compsses with wheels in the middle re the most stle to use. The compsses ove re ville t most office supply stores. Sfety compsses hve unique slides tht re esy to djust nd esy to tighten, yet hold firm when students go to sketch figure. These compsses re ville online or t most techer supply stores. Cost- $0.0 Cost- $ - $10 Cost- $ - $ Clcultors SUGGESTED Texs Instrument TI-Nspire CX Scientific clcultors re helpful for frctionl opertions! Csio FX-00MS Plus 9 Texs Instrument TI-0X IIS Texs Instrument TI-II TI-Nspire will e utilized in the Alger 1 curriculum dily for instructionl purposes. The TI- Nspire cnnot e rented from GMS. However, students cn purchse their own clcultor to use in clss. The numer sentence stys on the top of the screen. The student cn scroll through previous opertions. It turns off utomticlly. This is one of the clcultors used y the GMS mth deprtment. The clcultor utomticlly simplifies frctions. It will lso turn off utomticlly s long s it hs solr pnel t the top of the clcultor. This is one of the clcultors used y the GMS mth deprtment. Cost: $160-$180 Cost- $1 Cost- $17 Cost- $ Resource Additionl Resources (Optionl) Glencoe: Alger 1 (00 Edition) The textook will e used s resource. If it is needed this textook will e issued t no cost to ech student y GMS mth deprtment. Alger To Go Alger To Go is gret resource to guide students through complicted tsks. The text is kid friendly nd esy to red. It closely mtches our IM nd Alger curriculums. ISBN #: Cost: $ Geometry To Go Geometry To Go hs kid friendly text tht guides students through complicted tsks. It is gret resource for the Alger 1 curriculum nd will lso e helpful for high school geometry. ISBN #: Cost: $ Alger 1 Pge Summer, 01

4 Note: All costs re pproximte. Decimls (All Opertions)- Help Pge Adding Decimls Write the prolem up nd down! Line up the deciml points Add. Rememer to crry when needed. Erse ny extr zeros t the end of your finl nswer Sutrcting Decimls Write the prolem up nd down! Line up the deciml points. Sutrct. Rememer to orrow when needed. Erse ny extr zeros t the end of your finl nswer Multiplying Decimls Write the prolem up nd down. DO NOT LINE UP YOUR DECIMALS!!!!! Multiply crefully! Plce the deciml in the finl nswer. Count the plces to the right of the deciml point in ech numer. Count the sme numer of plces from right to left in the nswer, then plce the deciml pt. Sometimes you ll need to fill plces with zeroes x x # fter deciml pt. # s fter deciml pt. Move deciml spces right..0 =. (Cut off ny zeros t the end fter the deciml point) Dividing Decimls Write the prolem cross. The first numer goes into the division symol. The second numer goes outside of the house. Dividing y Whole Numers 1) Bring up the deciml point. ) Divide until there is no reminder Dividing y Decimls 1) Move oth deciml points to the right until the outside numer is whole. ) Bring the moved deciml pt up. ) Divide until there is no reminder Prolem Answer 0.07 Alger 1 Pge Summer, 01

5 Decimls- All Opertions See Decimls All Opertions Pge for ssistnce (pge 1). 1) ) ) ) ) ) ) 6 x 0.0 8). x ) 8.90 (.1) Alger 1 Pge Summer, 01

6 10) ) ) Frctions, Decimls nd Percents Chnging Frctions to Decimls Chnging Decimls to Percents Chnging Percents to Decimls 1) Tke the top numer nd divide it y the Tke the deciml nd multiply it y 100. Tke the percent nd divide it y 100. ottom numer. ) Keep dding zeros until the deciml termintes or the numers repet. ) If the numers repet, drw repetition r over top. Terminting Repeting Trick: Move the deciml plces to the RIGHT Work 0. x x *. 0 0 % Trick 0.. % Trick: Move the deciml plces to the LEFT Work % Complete the chrt. Show ll work. Frction Deciml Percent Show work here or ttch lined pper with work Trick % % 6 1 Alger 1 Pge 6 Summer, 01

7 % Grphing on the Coordinte Plne Coordinte Plne Voculry Qudrnt Qudrnt 1 Qudrnt Qudrnt Helpful Hints for Grphing Steps to plot point. Strt t the origin (0, 0) 1. Move left or right to whtever numer x is. sign positive (+) negtive (-) direction right left. Move up or down to whtever numer y is. Definitions: sign positive (+) negtive (-) direction up down Ordered Pirs: set of numers. The first numer tells you to mover left or right. The second numer tells you to move up or down. Rememer: CRAWL efore you CLIMB!!! Origin: the center point You lwys strt from (0, 0) nd then move cross nd then up or down. 1) Give the coordintes of ech point. ) H f) Q ) A g) L c) T h) C d) M i) X e) F j) J Q H M X 1 F L T - - C - J A ) Stte which qudrnt ech point is in. ) (,-1) ) (-1,-) c) (18,10) d) (-,9) e) (,11) f) (-6,17) ) Descrie how to locte ech point. ) (,-11) - ) (-8,-6) Alger 1 Pge 7 Summer, 01

8 ) Plot nd lel ech point. ) J (,-) ) E (, ) c) W (-1,-) d) R (1,0) e) B (-, ) f) Z (,) g) P (-,1) h) G (-,-1) i) Y (0,-) j) S (,-) Alger 1 Pge 8 Summer, 011

9 Reltion- set of ordered pirs Function Tles Function- specil kind of reltion where set (output) of numers depends on nother set of numers (input) f(x)- the function of x Voculry to Know Liner Function- function with constnt rte of chnge nd grph tht forms single stright line Input- often x or n Output- often f(x), f(n), or y Function f(x) = x + Use the function to fill in the chrt! x work f(x) (x,y) - f(-) = (-) + - (-, -) -1 f(-) = (-1) + 0 (-1, 0) 0 f(-) = (0) + (0, ) 1 f(-) = (1) + (1, ) f(-) = () + 6 (, 6) Use the tle to plot the ordered pirs. Connect to form the function. Complete the function tles for ech rule. Grph the ordered pirs. Show ll work. 1) y = -x + 1 ) y = x ) y = 0.x + x f(x) (x, y) x f(x) (x, y) x f(x) (x, y) Work Are Work Are Work Are Alger 1 Pge 9 Summer, 011

10 Squre nd Squre Roots Squres When numer is multiplied y itself, the product is the squre of the numer. Fctor Form: 8 x 8 Write: 8² = 6 Sy: 8 squred is equl to 6 or 6 is equl to the squre of 8. Perfect Squre: the product of n integer multiplied y itself (no decimls or frctions) My numer is the squre of yours. Then my numer must e the squre root of yours. Squre Root When the product of two identicl fctors is second numer, the fctor is the squre root of the numer. Write: 6 = 8 Sy: The squre root of 6 is equl to 8. Rdicl Sign- used to indicte the squre root of numer 6 = 6 6 = -6 6 = +6 or -6 Hints: Estimting Squre Roots Find perfect squre tht is lrger nd smller thn the given numer. The given numer should fit in etween. Decide if the given numer is closer to the smll or lrge numer. The squre root will e very close to tht numer. Estimte the squre root of. Estimte the squre root of is the smller perfect squre. is the lrger perfect squre. is closer to which mens the squre root is out equl to is the smller perfect squre. 100 is the lrger perfect squre. 8 is closer to 81 which mens the squre root is out equl to 9. 1) List the perfect squres less thn or equl to 00 (in order). Hint: Follow the pttern. 1 = 1 = 9 = 16 = ) Estimte ech squre root to the nerest whole numer: No clcultor! Show work ) Solve (without the use of clcultor.) 9² ( )² ( 8)² (8 )² (9 1) ( 8 )(1 ) Alger 1 Pge 10 Summer, 011

11 Review of Exponents Positive Exponents Negtive Exponents Exponentil Form Expnded Form Stndrd Form ² x 7³ 7 x 7 x 7 x x x x ² x ³ x x x x RULE: Any numer to the power of zero is one. 1 1 RULE: Any numer to the power of one is itself. 8 Exponentil Form Frctionl Form Expnded Form Stndrd Form ) Fill in the chrt elow: Positive Exponents Exponentil Form Expnded Form Stndrd Form ) Fill in the chrt elow: Negtive Exponents Exponentil Frctionl Expnded Stndrd ) Write in stndrd form, if needed write s frction, not deciml. ) 8 = ) 9 - = c) 7 0 = d) 10 - = e) - = f) 6 = g) 1 = h) - = i) Alger 1 Pge 11 Summer, 011

12 Alger 1 Pge 1 Summer, 011 Lws of Exponents Multiplying ( Bses) Power of Power(1 Bse) Dividing Leve the se. Add the exponents. Leve the se. Multiply the exponents. Leve the se. Sutrct the exponents ) )( ( ) ( Simplify the following expressions using the lws of exponents. Keep your nswer in exponentil form. Do not multiply out. ) ) 7-7 c) (1 ) d) 9 e) f) 10 g) 1-6 h) x y x -8 y i) (d ) 7 j) (6 ) k) d (8d 6 ) l) (k 8 ) 10 m) - c ( 6 c -9 ) n) ( ) o) 7

13 Integer Opertions: Addition & Sutrction Integers- Addition Sme Sign: You dd Positive + Positive = Positive Negtive + Negtive = Negtive Different Signs: You sutrct The numer tht hs the igger solute vlue or looks igger determines whether the nswer is negtive or positive. Integers- Sutrction Keep the first numer. Switch the minus sign to plus sign Chnge the sign of the second numer to its opposite. Then follow the rules of dding. Adding Decimls Write the prolem up nd down! Line up the deciml points Add. Rememer to crry when needed. Erse ny extr zeros t the end of your finl nswer Sutrcting Decimls Write the prolem up nd down! Line up the deciml points. Sutrct. Rememer to orrow when needed. Erse ny extr zeros t the end of your finl nswer Add or sutrct. ) ) c) d) e) 1 f) g) h) 1. 9 i) j) k) l) Alger 1 Pge 1 Summer, 011

14 Integer Opertions: Multipliction & Division Multipliction ) Positive x Positive = Positive ) Negtive x Negtive = Positive c) Positive x Negtive = Negtive d) Negtive x Positive = Negtive e) Anything x zero = zero Division ) Positive Positive = Positive ) Negtive Negtive = Positive c) Positive Negtive = Negtive d) Negtive Positive = Negtive e) Anything zero = NOT POSSIBLE f) Zero Anything = ZERO ) (-) (6) ) (-1) (-) c) () (-) (-) d) 6 e) 6( ) 8 6 f) g) 0 x - h) - i) (-10)(-10) j) 80 - k) 90 6 l) 100 m) 0 n) ( ) o) Alger 1 Pge 1 Summer, 011

15 Order of Opertions with Integers Helpful Hints- Order of Opertions Exmple #1 Exmple # 1) Underline the step you re completing. ) Bring down ll other numers nd opertions. ()³ (10 ) ()³ (10 6) + 8 ()³ ( 1) (8) Go in order! Rememer: Plese Excuse My Der Aunt Slly! P E M D A S Prenthesis Exponents Multiply or Divide (Left to Right) Add or Sutrct (Left to Right) Simplify the following expressions using order of opertions nd integer rules. ) 6 (- - -6) ) -6 (9 11) 1 c) d) 8 1 e) f) g) (- + 7) (-16 + ) h) -1 + (²) (-1 + ) i) -(² - ) ² + -7 Alger 1 Pge 1 Summer, 011

16 Solving One Step Equtions Solving One Step Equtions Get the vrile (letter) y itself y doing the opposite opertion on oth sides of equl sign. Addition: x + 7 = 9 x + 7 = x = Exmples Sutrction: x 1 = 8 x - 1 = x = 0 Solve ech eqution using the steps ove. ) x + 8 = -1 ) t - -9 = c) -t = -1 d) r = e) y = - f) h + 8 = - g) 8 p = -16 h) -k = 0 i) -9 p = 17 Alger 1 Pge 16 Summer, 011

17 Solving Two Step Equtions Solving Two Step Equtions Steps: 1) Get rid of the numer tht is dded or sutrcted y doing the opposite opertion. ) Get the vrile y itself y doing the opposite of the multipliction or division. Exmples x + 7 = x = 6 x = x - 7 = x = 11 x = Solve ech eqution using the steps ove. ) -t 6 = ) m + -6 = - c) -r + = - d) x + -7 = 6 e) g + - = -1 f) y + - = 8 g) x = (9 ) h) x = 8(6 ) i) (d ) = 9(7 ) Alger 1 Pge 17 Summer, 011

18 Solving One & Two Step Inequlities Solving Inequlities Follow the sme steps tht you would use when solving equtions. However, there is one extr step. NOTE: If you multiply or divide oth sides of inequlity y sme POSITIVE NUMBER, direction of inequlity sign does not chnge. If you multiply or divide oth sides of inequlity y sme NEGATIVE NUMBER, direction of inequlity sign REVERSES. Chnge the Sign x - > + + x > 8 x > Don t Chnge the Sign -x - > + + -x > x < - Grphing Inequlities Look t the finl solved nswer. 1) If the finl solved nswer hs: < or > or Use n open dot ( ) Use n open dot ( ) ) If the finl nswer hs: < or or Arrow goes to left. Arrow goes right. x x -6 x - -x +10 < x < x > y - switch the > to < ) Solve nd grph. ) -d ) c 18 < - c) x > 7 ) Which of these grphs represents the solution set for the inequlity elow? x 10 A) B) C) D) ) Which of these grphs represents the solution set for the inequlity elow? A) B) C) D) x 9 ) Wht does ech sign men? ) < ) c) d) e) > f) = Word Bnk greter thn or equl to not equl to less thn or equl to less thn equl greter thn Alger 1 Pge 18 Summer, 011

19 Comining Like Terms Like Terms Terms tht hve identicl vrile prts. m nd m hve the vrile m, so they re like terms Unlike Terms Terms tht hve different vrile prts. 6x nd y hve the different vrile prts, so they re unlike terms m + m - m + m + m + m = m m m = m Comining Like Terms: the process of dding or sutrcting like terms c + d c + c + d + h g + g h h g + g h g c c = c. d nd re not like terms. h h = h -g + g = 1g = g Comine the like terms. 1) 7x + x ) 1x x ) x + x + 8 ) 10x x + 1 ) 9x + 8x 7x 6) 6x + x + 6x x 7) x 1 + x 8) x + x - x + 1 x 9) (x ) + 7x + 10) (x + 9) - 11) -11x + 6 x + + 1x 9 1) 1(x ) x Answer Bnk: 1 10x 1x 8x 9x 8 x + 0 9x + 1 1x + 6 x + 1 x + 8 x + 1 9x 6 Alger 1 Pge 19 Summer, 011

20 Percent of Numer Percent of Numer Formul is of % or 100 prt % whole 100 Key Words- Prolem Solving Tip: Find percent of # nd dd to originl cost Tx: Find percent of # nd dd to originl cost Discount: Find percent of # nd sutrct from originl cost Commission: Find percent of # only Find the missing vlue. Show ll work. Use lined pper if necessry. 6% of wht numer is 6.? Wht percent of 0 is 7.? Wht is % of 0? 8% of 78 is wht numer? Wht is 18% of 6? out of 7 students is wht percent? Answer the following word prolems. Show ll work. Set up proportions for ech prolem. Viny just ought pir of jens for $9.9, swetshirt for $.0 nd jcket for $8.9. The sles tx is %. Find the sles tx nd totl for ll of his items. Brndon ought set of golf clus for $ nd received discount of %. How much ws the discount? How much did Brndon py for the golf clus? Crlos wnts new video gme system. The regulr price for video gme system is $16.0 ut is on sle for 0% off. Wht is the mount of the discount? How much did Crlos py for the gming system? Djon erns 1% commission on ll sles. On Sturdy, he sold $98.0 worth of merchndise. Wht ws the mount of commission he erned on Sturdy? Alex, Adm nd Ym went out to dinner. Their mel cost $180.0 totl. They wnt to leve n 18% tip. How much tip should they leve? Wht is the totl cost of their mel including tip? Alger 1 Pge 0 Summer, 011