Pre-Calculus Honors Summer Packet

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DearFuturePre-CalculusStudent,IhopeyouareexcitedforyourupcomingyearinPre-Calculus!Thepurposebehindthissummerhomeworkpacketistoreacquaintyouwiththenecessaryskillstobesuccessfulinthisyear’smathcourse.Atfirstglancethispacketmayseemoverwhelming.However,thereareapproximately9weeksofsummer.Paceyourself.Thereare7Partsofthispacket–completeoneparteachdayandyouwilleasilybeabletocompletetheassignmentbeforeyourreturntoschoolinthefall.PleasebepreparedtosubmitthisassignmentduringyoursecondPre-Calculusclass.Itwillbegradedforaccuracyaswellascompletion.Workneedstobeshowninaneatandorganizedmanner,anditisperfectlyacceptabletocompletethepacketonseparatesheetsofpaper.Justbesuretostapleanyextrapaperstothepacket.Also,donotrelyonacalculator!ShowALLworkforeachproblemandtakeyourtime.Remember,thiswillbeyourfirstimpressiontoyournewmathteacher,andyouwanttomakesurethatitisapositiveone!Seebelowfordirectionsandhelpfulwebsites.Wehopeyouhaveawonderfulsummer!Best,WarehamHighSchoolMathDepartmentAssistanceonthesummermathassignmentwillbeavailablefrom10:30AMto12PMAugust9th,11th,and17thatWarehamHighSchool.Feelfreetostopbywithanyquestionsyoumighthave.Additionally,youmayemailyourquestionstoMrs.Cavicchiatkcavicchi@wareham.k12.ma.us.Toensurethefastestresponse,pleaseincludeyourname,summerassignmentname,and(ifpossible)apictureoftheproblemandyouraccompanyingwork.

Part 1 Factoring Polynomials Factoring Trinomials https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/factoring-quadratic-expressions-core-algebra/e/factoring_polynomials_1

1. 2x2 + 5x + 3 2. 3n2 + 7n + 4

3. 4r2 + 5r +1 4. 6p2 + 5p +1

5. 11z2 + 2z − 9 6. 4y2 − 5y − 4

7. 15x2 − 2x − 8 8. 14m2 +m − 3

Example 1

Example 2

Factoring with quadratic patterns Perfect Square Trinomials https://www.khanacademy.org/math/algebra2/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/factoring-perfect-square-trinomials

9. a2 + 2a +1 10. b2 − 2b +1 11. x2 +10x + 25

12. x2 +16x + 64 13. x2 −12x + 36 14. 144 + 24 + x2

15. 16x2 + 8xy + y2 16. 144y2 −120y + 25 17. 81d 2 − 90cd + 25c2

Difference of Perfect Squares https://www.khanacademy.org/math/algebra2/polynomial-functions/factoring-polynomials-special-product-forms-alg2/v/u09-l2-t1-we3-factoring-special-products-3

18. b2 − 9 19. 4 − a2 20. 4x2 − 25

21. 16x2 −1 22. 36 − 25c2 23. 36x2 − 9y2

24. 3s2 − 24 25. −16n2 +12n 26. x2y2 − 4

Factoring Using a Cubic Pattern https://www.khanacademy.org/math/algebra2/polynomial-functions/advanced-polynomial-factorization-methods/v/factoring-sum-of-cubes

27. x3 + 8 28. y3 − 64 29. 125n3 + 216

30. 27a3 −1000 31. 27m3 +1 32. 8c3 + 343

33. 16z3 − 54 34. −5z3 + 320 35. 192w3 − 3

Part 2 Solving Equations Quadratic Equations by Inspection https://www.khanacademy.org/math/algebra/quadratics/quadratics-square-root/e/solving_quadratics_by_taking_the_square_root

36. x2 = 81 37. 3t 2 − 6 = 60 38. 3x2 − 5 = 55

39. y − 5( )2 = 9 40. x + 3( )2 = 5 41. 3 b − 4( )2 = 27

42. 2 x + 5( )2 = 32 43. 4 x − 2( )2 = 7 44. −4 z − 7( )2 = −72

45. 9 x − 4( )2 = 8 46. 12p + 4( )2 = 22 47. 1

7x + 6( )2 = 8

Zero Product Property https://www.khanacademy.org/math/algebra-basics/quadratics-polynomials-topic/solving-quadratics-factoring/v/example-1-solving-a-quadratic-equation-by-factoring

Example 1

Example 2

48. x − 4( ) x − 6( ) = 0 49. x + 4( ) 2x − 5( ) 3x +15( ) = 0 50. 8x x +15( ) = 0

51. 3 x +10( ) x − 8( ) 4x − 7( ) 52. 9x2 + 38x + 8 = 0 53. 10x2 = 39x + 27

Rational Equations https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/rational-equations

Example 1

Example 2

54. x + 22

= x + 64

55. c + 32

= c + 54

56. b − 28

= b + 424

57. 11− 3x4

= 6 − x6

58. 85y + 6

= 45y − 2

59. 32x

= 75x − 2

60. 25x

= x16

61. x − 2x − 6

= x + 2x − 4

62. 2x − 53x − 4

= 2x − 33x − 2

Part 3 Graphing Quadratics Graphing Quadratics from vertex form https://www.khanacademy.org/math/algebra/quadratics/graphing-quadratic-functions/v/graphing-a-parabola-in-vertex-form

Graph the function, label the vertex, axis of symmetry and at least one other point. 63. y = x + 2( )2 + 4 64. f x( ) = x − 3( )2 + 6

65. g x( ) = − x + 6( )2 +10 66. h x( ) = 3 x − 3( )2 − 4

Graphing Quadratics from intercept form. https://www.khanacademy.org/math/algebra/quadratics/graphing-quadratic-functions/e/graph-quadratic-functions-in-factored-form

Graph the function, label the vertex, axis of symmetry and x-intercepts. 67. f x( ) = x + 4( ) x + 3( ) 68. h x( ) = −3 x − 2( ) x − 4( )

69. g x( ) = 3 x +10( ) x − 8( ) 70. k x( ) = −12x x − 9( )