Geometry Honors Summer Packet

Name ________________________

DearFutureGeometryHonorsStudent,IhopeyouareexcitedforyourupcomingyearinGeometry!Geometryallowsustomeasuretheworldaroundusinaverypreciseandaccuratemanner.Itallowsustoformvalidargumentswithdeductivereasoning,andfindcounterexamples.Thisbranchofmathematicsisfoundationalforallotherareasofmath.YourlevelofsuccessinGeometrywilldirectlycorrelatetohowsuccessfulyouwillbeinyourfuturemathexperiences.Asyouprobablyknow,yourhighschoolmathematicsclassesarecumulative.Thismeansthatyouwillneedtoutilizeconceptspreviouslylearnedtobesuccessful.Thepurposebehindthissummerhomeworkpacketistoreacquaintyouwiththenecessaryskillstobesuccessfulinthisyear’smathcourse.PleasebepreparedtosubmitthisassignmentduringyoursecondGeometryclass.Itwillbegradedforaccuracyaswellascompletion.Workneedstobeshowninaneatandorganizedmanner,anditisperfectlyacceptabletocompletethepacketonseparatesheetsofpaper.Justbesuretostapleanyextrapaperstothepacket.Also,donotrelyonacalculator.ShowALLworkforeachproblemandtakeyourtime.Remember,thiswillbeyourfirstimpressiontoyournewmathteacher,andyouwanttomakesurethatitisapositiveone!Seebelowfordirectionsandhelpfulwebsites.Wehopeyouhaveawonderfulsummer!Best, Wareham High School Math Department Assistancewillbeavailablefrom10:30AMto12PMonAugust9th,11th,and17thatWarehamHighSchoolfrom.Feelfreetostopbywithanyquestionsyoumighthave.Additionally,youmayemailyourquestionstoMrs.Cavicchiatkcavicchi@wareham.k12.ma.us.Toensurethefastestresponse,pleaseincludeyourname,summerassignmentname,and(ifpossible)apictureoftheproblemandyouraccompanyingwork.Suggestionsfortimemanagement:StudentswhoareenrolledinBOTHGeometryHonorsandAlgebra2HonorsareexpectedtocompletetheGeometrypacketaswellasParts4-7oftheAlgebra2Honorspacket.Thereare5partstotheGeometrysummerpacket.Complete1parteachdayandyouwillbefinishedin5days.

Part 1 – Plotting Points http://www.virtualnerd.com/algebra-1/relations-functions/coordinate-plane/coordinate-plane-graphing/ordered-pair-definition Example:

Example:

Graph and label each point on the coordinate plane. Name the quadrant where each point is located. 1. T 2,5( ) Quadrant _____ 2. D 3,4( ) Quadrant _____ 3. R −3,−2( ) Quadrant _____ 4. B 5,−1( ) Quadrant _____ 5. S 2,0( ) Quadrant _____ 6. M −1,3( ) Quadrant _____ 7. P 1,−4( ) Quadrant _____ 8. L −4,−3( ) Quadrant _____ 9. A triangle with vertices 10. A polygon with vertices F 2,4( ),G −3,2( ),H −1,−1( ) J 4,2( ),K 1,−1( ),L −2,2( ),M 1,5( ) Part 2 Solving Equations

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–6 –4 –2 2 4 6x

https://www.khanacademy.org/math/algebra/one-variable-linear-equations#alg1-one-step-add-sub-equations Example 1:

Example 2:

11. r +11= 3 12. d − 7 = 8 13. 5t +1= −19

14. −4 − p = −2 15. 9 − 4g = −15 16. 8a +11= −37

https://www.khanacademy.org/math/algebra/one-variable-linear-equations#alg1-one-step-mult-div-equations Example 1:

Example 2:

17. p12

= 6 18. 125f = −18 19. 8

5a = −6

20. y7= −11 21. m

10+15 = 21 22. 7

4q − 2 = −5

https://www.khanacademy.org/math/algebra/one-variable-linear-equations#alg1-variables-on-both-sides 23. c −14 = −11 24. 3n + 7 = 28 25. 2p + 6 = 6p −10

26. 5c − 7 = 8c − 4 27. 8t +1= 3t −19 28. 9n + 4 = 5n +18

https://www.khanacademy.org/math/algebra/one-variable-linear-equations#alg1-equations-with-parentheses Example 1: Example 2:

29. −2 n + 7( ) = 15 30. 5 m −1( ) = −25 31. −3 d − 7( ) = 6

32. 6 3x − 5( )− 7x = 25 33. −2 5 + 6m( ) +16 = −90 34. 15 t + 2( ) + 9t = 6

Part 3 Graphing and Solving Systems of Equations https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/e/graphing_systems_of_equations

35. y = −x + 2

y = − 12x +1

36. y = 3x − 3y = x +1

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Graph by finding intercepts. https://www.khanacademy.org/math/algebra-basics/core-algebra-graphing-lines-slope/core-algebra-graphing-intercepts/v/x-and-y-intercepts

37. 4x − y = 82x − 3y = 3

38. x + 3y = 64x − 2y = −32

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Part 4 Square Roots and Simplifying Radicals Complete the Table of Perfect Squares 22 32 42 52 62 72 82 92 102 112 122 132

https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/square-roots-for-college/v/simplifying-radicals 39. 12 40. 32 41. 75 42. 108

43. 125 44. 60 45. 72 46. 216

4 27 = 4 9 i 3

4 9 i 3 = 4 i 3 i 3

12 3

47. 3 8 48. 2 60 49. 4 32 50. 2 150

51. 5 80 52. 8 18 53. 7 32 54. 3 48

55. 6 i 6 56. 16 i 25 57. 50 i 10

58. 12 i 20 59. 8 i 12 60. 5 i 15

Part 5 Writing Equations https://www.khanacademy.org/math/algebra/two-var-linear-equations/point-slope/v/idea-behind-point-slope-form 61. 2,4( ) with slope 5 62. 4,−1( ) with slope −3

63. −4,−5( ) with slope − 56

64. 0,0( ), 2,−6( ) 65. 2,3( ), 5,9( ) 66. −6,10( ), −2,−1( )