precalculus summer packet 2020...1 precalculus summer math packet 2020 dear students, the teachers...

1

Precalculus

Summer Math Packet 2020

Dear Students, The teachers in the math department are very excited about the upcoming school year. We look forward to working with you and helping you to become successful in your math classes. The problems in this packet are a review of concepts that you have learned in your previous math classes. A strong knowledge of this material will help you in your future math classes. Here are some suggestions for the summer math packet:

• Print the packet or get a printed copy from the school

• Work on one page at a time

• Do NOT wait until the end of the summer to complete the whole packet

• Use your notes from previous math courses or watch videos online for extra help if needed (https://www.khanacademy.org/, http://patrickjmt.com/)

Please show all of your work and circle your final answers for each question. You will turn the completed packet into your teacher on the first day of school. The packet will be your first grade of the year. Students who follow all instructions and turn their packets in with all work shown on the first day of school will receive a homework pass. Email us if you have any questions. We will answer emails when we can over the summer. Becky Mullis, bmullis@lee-scott.org 7th grade math and 10th grade Algebra 2 Michele Merrett, mmerrett@lee-scott.org 8th grade math and 12th grade Finite Math Sara Whorton, swhorton@lee-scott.org 9th grade Geometry and 10th grade Algebra 1 Katie Wilson, kwilson@lee-scott.org, PreCalculus and Calculus

Thank you and have a great summer!

LSA Math Department

2

Showallworkandcircleyourfinalanswers. Name___________________________________1)Evaluate: ( ) 2 2 4f x x x= − − + for 3x = − . 2)Solve: ( )2 3 7 1x x− − = + .

3)Solve: 2 412 7x x− +

+ = − . 4)Solve: y = 30v

3 forv.

5)Solve: ( )40 42 6 5 3x x− − ≤ − − . 6)Solve: 6 4 or 2 6x x+ > − > .

3

ForQuestions7&8Grapheachfunction.Statethedomainandrangeinintervalnotation.

7) 1 43

y x−= − 8) 24 4 3y x x= − −

Domain: Domain:Range: Range:9)Findtheslopebetween ( ) ( )2, 5 and 3,8− − . 10)Findtheslopeofalinethatis

perpendiculartotheline5 3 8x y+ = .

11)Findtheequationofthelinethroughthepoint ( )2,0− andwithslope 18

− .

4

12)Determinewhethertherelationisdefinedasafunctionandstatethedomainandrange. ( ) ( ) ( ) ( ) ( ){ }2,4 , 1, 9 , 5, 7 , 9, 3 , 12, 3− − − − − .Function:YESorNO Domain: Range:Forquestions13&14solvethesystem.

13)2x −5y = −5−2x +3y =11

. 14)3 4 105 9 24x yx y− = −

+ = −.

15)Simplify: ( ) ( )7 6 6 7 59 1 9 4 6 3 9x x x x x− − − − + + − 16)Simplify: ( )28 3a y− .

5

Forquestions17&18usesyntheticdivisiontosimplify.17) ( ) ( )4 32 3 12 11 4x x x x− − − ÷ − . 18) ( ) ( )3 23 8 100 2x x x− − ÷ + Forquestion19–24factorCOMPLETELY19) 3 2 2 310 25 12 30a a b ab b− − + . 20) 3 3 316 4x y xy− + 21) 2 18 81g g− + 22) 23 3 18x x− − 23) 27 33 10y y+ − 24) 3 3108 4x y+

6

24)Forthefunctions ( ) ( )2 3 23 3 and 5 2 3f x x g x x x x= + = + − − ;find

( )( ))a f g x− b) g / f( ) x( ) c) fg( ) x( )

25)Acertainrectangle’slengthis7feetlongerthatitswidth.Iftheareaoftherectangleis330square

feet,findthedimensions.

26)Thedomainoftherationalexpression 2

33 14 8

xx x

−

+ +isallrealnumbersexcept.

7

27) Simplify;9 3

7 4

219x y zxy z

−

−. 28)Solve; 24 23 6 0k k− − = .

29)Simplify;2

2

4 2149

x xx− −

−. 30)Simplify;

2 2

2 2

10 24 611 28 56

z z z zz z z z+ + +

÷+ + − −

.

31)Simplify; 2 2

3 53 2 1y y y

+− + −

. 32)Solve;4+ 2x= 5 .

33)Solve; 2

8 3 153 3 9x x x− =

+ − −. 34)Simplify:8 3 4 45 5 243− +

8

35)Completethesquare.Thenfactorthepolynomial; 22 20 _______x x− .35b)SolvebyCompletingtheSquare: 2 5 3 0x x− − =

36)Simplify; 3 22 754a b− . 37) Simplify; 2 52 5+

−.

38) Findthedomain;answerinintervalnotation; ( ) 5 2f x x= − .

9

39)Solve; 2 6 1 2x x+ − − = . 40)Simplify; 25ii

+

−.

41)Simplify; ( )22 8i− . 42Solve; ( )23 4 36x+ = − .

43) Basedonthediscriminantofthefollowingquadraticequation,determinethenumberandnature

ofthesolutions: 24 12 9x x− = − .

10

44)Solve; 2 6 0x x+ + = . 45)Solve; 4 25 36 0x x− − = .

46)Convert 23 12 7y x x= + − tovertexformandlabelthevertex ( ),h k .

47)Findthex-interceptsof: ( ) 2 12f x x x= − − .

48) Determinewhetherthefunctionhasamaximumoraminimum.Thenfindthemaximumor

minimumvalue. ( ) 24 16 3h x x x= + − .

11

Usethegraphofthefunction ( )f x showntoanswerquestions49–56.

49.Find ( )3f .

50.Is ( )4f − positiveornegative?

51.Forwhatnumber(s)xis ( ) 0?f x = 52.Inintervalnotation,whatisthedomainof ?f 53.Inintervalnotation,whatistherangeof ?f 54.Whatarethex–intercept(s)?

55.Whatarethey–intercept(s)?

56.Forwhatnumberxis ( ) 5?f x = −