incoming algebra 2 summer work - duxbury.k12.ma.us

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!"#$%&"' )*'+,-. / 01%%+- 2$-3 450 6.78+%.7&#9 4+:.-7%+"7 /;<<=/;</ Dear Incoming Algebra 2 Students, To better prepare for your Algebra 2 Course, summer work is assigned to ensure a smooth transition into higher-leveled mathematics. The expectation is that all students bring the completed assignment to their first math class in the Fall 2011. If resources are needed to complete the problems, the Duxbury Free Library has a copy of each text for reference. Please allow yourself sixty to ninety minutes of time to complete the packet. Please keep in mind that non-calculator problems need to be completed without the use of any type of calculator. All answers must be justified by showing all work. A TI-83(plus)/84(plus) graphing calculator will be necessary to complete the calculator section. All high school mathematics courses will use of this type of calculator. Therefore, it is essential that every student obtain one. If you are enrolled in Course 234(College Algebra 2) next year, Only complete Section A and Calculator Section A. If you are enrolled in Course 233(Honors Algebra 2) next year, Complete the entire packet except for Section C and Calculator Section C. If you are enrolled in Course 220 (Accelerated Algebra 2) next year, Complete the entire packet.

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Page 1: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

!"#$%&"'()*'+,-.(/(01%%+-(2$-3(450(6.78+%.7&#9(4+:.-7%+"7(

/;<<=/;</((

Dear Incoming Algebra 2 Students, To better prepare for your Algebra 2 Course, summer work is assigned to ensure a smooth transition into higher-leveled mathematics. The expectation is that all students bring the completed assignment to their first math class in the Fall 2011. If resources are needed to complete the problems, the Duxbury Free Library has a copy of each text for reference. Please allow yourself sixty to ninety minutes of time to complete the packet. Please keep in mind that non-calculator problems need to be completed without the use of any type of calculator. All answers must be justified by showing all work. A TI-83(plus)/84(plus) graphing calculator will be necessary to complete the calculator section. All high school mathematics courses will use of this type of calculator. Therefore, it is essential that every student obtain one.

If you are enrolled in Course 234(College Algebra 2) next year, Only complete Section A and Calculator Section A. If you are enrolled in Course 233(Honors Algebra 2) next year, Complete the entire packet except for Section C and Calculator Section C. If you are enrolled in Course 220 (Accelerated Algebra 2) next year,

Complete the entire packet.

Page 2: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

Name_________________________________________ Course #__________________________(Math class taken in 2010-2011) Part I Non-Calculator Section: Show all work to justify your answers Section A 1. Solve each equation for the variable by using algebraic methods: (a) 2r =12 (b) 3! 2g = !1 (c) 9t + 6 = 3t (d) !3w – 4 = !w ___________ ___________ ___________ ____________ 2. Solve each equation for the variable, y. (a) x + 2y = 8 (b) 10y – 5x = 0 ____________________ ______________________ 3. Use the formula D = rt for distance traveled to solve for the missing variable. Label your answer correctly.

(a) Given: D = 84 !miles (b) Given: D = 3!miles t = 2!hours r = 10!miles! per !hour

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Page 3: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

>)!!*+,-.!./01!0+?:+3$%!#$.23/,#45!65!#$0,3%#$7!/!8+,34#+$!8.4!/$%!/!,#$.!79/:1!+;!41.!8+,34#+$)!!</=!!!3< x + 2 " 4 ! ! ! <6=!! x < 0!or !x !1 > 2 ! ! <0=!! !3x + 4 ! > 2 !!!!!!!!!'''''''''''''''''''! ! ! !!!''''''''''''''''''''! ! ! !!''''''''''''''''''''!!!!@)!!"+9!./01!+;!41.!;+,,+A#$7!9.,/4#+$8B!./01!8.4!9.:9.8.$48!:+#$48!+$!/!039-.)!!C$%#0/4.!#;!#4!#8!/!;3$04#+$!+9!$+4)!!</=!!<DEB!F=B!<EB!DF=B!<DGB!F=B!<GB!DF=! ! ! <6=!!<DEB!F=B!<GB!D@=B!<DEB!>=B!<(B!DH=!!!''''''''''''''''''''''''''''''''''''! ! ! '''''''''''''''''''''''''''''''''''''!!I)!!"#$%!41.!8,+:.!+;!./01!,#$./9!9.,/4#+$81#:!7#-.$)!!!

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<%=!! y ! 2 = 12(x + 3) ! ! ! ! ! ! ! ! 8,+:.!J!'''''''''''''''''''''!

!<.=!! 4x ! 5y = 2 ! ! ! ! ! ! ! ! 8,+:.!J!'''''''''''''''''''''!!K)!!L9#4.!41.!.23/4#+$!+;!./01!,#$.!7#-.$!41.!0+$%#4#+$8!,#84.%)!!M+3!?/5!38.!/$5!;+9?)!!</=!!N1.!,#$.!:/88.8!419+371!41.!:+#$4!<FB!DE=!/$%!1/8!/!8,+:.!+;!G)! ''''''''''''''''''''''''''''''!!!<6=!!N1.!,#$.!:/88.8!419+371!41.!:+#$4!<GB!>=!/$%!1/8!/!8,+:.!+;!O.9+)! ''''''''''''''''''''''''''''''!!!

<0=!!N1.!,#$.!1/8!/!5D#$4.90.:4!+;!DF!/$%!/!8,+:.!+;! !14)! ! ! '''''''''''''''''''''''''''''!

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H)!!P9/:1!./01!.23/4#+$!+$!41.!0++9%#$/4.!/Q#8!:9+-#%.%)!!R#84!41.!QD!/$%!5D!#$4.90.:4!;+9!./01)!!</=!! y = !x + 2 !!!! ! :;,-#.!6.3#)<<<<<<! ! <6=!! 2x – y = 4 ! ! :;,-#.!6.3#)<<<<<<!" " " " =;,-#.!6.3#&''''''! ! ! ! ! ! =;,-#.!6.3#&''''''!

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ES)!!P9/:1!./01!+$!41.!0++9%#$/4.!/Q#8!:9+-#%.%)!!!!</=!! x + 2y > 3 ! ! ! ! <6=!! 3y + 2x ! "2 ! ! ! <0=!!!! y = ! !x + 3! ! 2 !

!!!!!! !! ! !! ! !!!

EE)!!M+3!/9.!?./839#$7!/!6#T.!9/?:!A1#01!#8!E>!;..4!A#%.!/4!#48!6/8.!/$%!EG!;..4!4/,,!/4!#48!4/,,.84!:+#$4)!!!!</=!!L1/4!#8!41.!8,+:.!+;!41.!6#T.!9/?:U!

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</=! ! ''''''''''''''''''''''! ! ! <6=! !'''''''''''''''''''''!

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Page 5: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

!

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#$

%&'!+$!41.!$3?6.9!,#$.!:9+-#%.%)!

!!!!E()!!M+3!A+9T!(!1+398!/$%!./9$!WF@)!!L1/4!#8!5+39!./9$#$7!9/4.U! ! '''''''''''''''''''''''!!!E>)!!M+3!49/-.,!;+9!G)>!1+398!/4!>S!?#,.8!:.9!1+39)!!V+A!;/9!%#%!5+3!7+U!!! ''''''''''''''''''''''''!!!!E@)!!X-/,3/4.!/$%!8#?:,#;5!./01!.Q:9.88#+$!0+?:,.4.,5)!!</=!! 5x(x ! 2)!when!x = 6 ! ! <6=!! 3y2 ! 4y!when!y = !2 ! ! <0=!! z + 3( )3 !when!z = 1 !!!!!!'''''''''''''''''''''''''''''! ! ''''''''''''''''''''''''''''! ! '''''''''''''''''''''''''''!!EI)!!*#?:,#;5!./01!$3?.9#0/,!.Q:9.88#+$!0+?:,.4.,5)!!</=!!!26 ! ! <6=!! !2( )6 ! ! <0=!! 169 ! ! <%=!!1! 3(5 ! 33)2 ! <.=!! 8 ! 6( )2 !!!!!'''''''''''''! ! '''''''''''''! ! ''''''''''''''! ! '''''''''''''''! ! ''''''''''''''''!!EK)!!*#?:,#;5!./01!/,7.69/#0!.Q:9.88#+$)!!</=!!16c !10d + 3d ! 5c ! ! <6=!! 2m2 ! 5n2 + 6n2 ! 8m ! ! <0=!! 3(x2 ! y) + 9(x2 + 2y) !!!!''''''''''''''''''''''''''''! ! '''''''''''''''''''''''''''''! ! ''''''''''''''''''''''''''''''!!EH)!!L9#4.!/!8#?:,#;#.%!.Q:9.88#+$!;+9!41.!:.9#?.4.9!+;!41.!;#739.)!!!!

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Page 6: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

Section B !GS)!!X-/,3/4.!/$%!8#?:,#;5!./01!.Q:9.88#+$!0+?:,.4.,5)!!

</=!!x ! yx + y

!when!x = 10!and !y = 8 ! <6=!! 25 + 4x !when!x = 6 ! ! <0=!!n3 ! 4n +10!when!n = !3 !

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</=!! 4x(x + 2)(1! 3x) !! ! <6=!!x2yx!3y4

! ! <0=!! x + 2( )2 !! ! <%=!5(x + 9) ! 2(4 ! x) !

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</=!!45x + 8 = 20 ! ! ! ! ! <6=!! 3(5x ! 8) = !2(!x + 7) !12x ! ! !

!!!!!'''''''''''''''''''! ! ! ! ! ! '''''''''''''''''''!!<0=!!!4(2x + 5) = 2(!x ! 9) ! 4x ! ! ! <%=!! x2 ! 4x + 4 = 0 !!!!!!!'''''''''''''''''''! ! ! ! ! ! ''''''''''''''''''!!GF)!!M+3!/9.!+9%.9#$7!ND81#948!;9+?!/!0/4/,+7)!!X/01!ND81#94!0+848!WE>)!!N1.!0+84!+;!81#::#$7!#8!W@!$+!?/44.9!1+A!?/$5!5+3!+9%.9)!!N1.!4+4/,!0+84!#8!WEEE)!!!</=!!*.4!3:!/$!.23/4#+$!A1.9.!N!J!Y!ND81#948!+9%.9.%!/$%!41.!.23/4#+$!?+%.,8!/$!.23#-/,.$4!9.,/4#+$81#:!A#41!41.!7#-.$!#$;+9?/4#+$)!!<6=!!*+,-.!;+9!N!4+!;#$%!1+A!?/$5!ND81#948!A.9.!+9%.9.%)!

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Section C !G()!!Z%%!:/9.$41.8.8!4+!?/T.!/!493.!84/4.?.$4)!!*1+A!/,,!84.:8!4+!/99#-.!/4!41.!/$8A.9!+$!41.!9#714D8#%.)!!</=!!H![!EG!\!F!]!E!J!E>! ! ! ! <6=!!F!^!( 2 ]!G 3[!F 2 J!GF!!G>)!!*+,-.!;+9!41.!-/9#/6,.)!!

</=!!23x +

56= x !

12! ! ! ! ! <6=!! 3x2 !10x ! 8 = 0 !

!!!!''''''''''''''''''! ! ! ! ! '''''''''''''''''''''!! !<0=!! ! ! ! ! ! ! <%=!

! ! ! ! !!!!!!!''''''''''''''''''''''! ! ! ! ! '''''''''''''''''''''!!G@)!!*#?:,#;5!0+?:,.4.,5&!! 240 ! ! ''''''''''''''''''!!!!!GI)!!Z!8/,.8:.98+$!/4!/!0/9!%./,.981#:!1/8!/!6/8.!8/,/95!+;!WG>BSSS!:.9!5./9!/$%!./9$8!/!>_!0+??#88#+$!+$!4+4/,!8/,.8)!!V+A!?301!?384!41.!8/,.8:.98+$!8.,,!4+!./9$!W>SBSSS!#$!+$.!5./9U!!!!!GK)!!M+39!;9#.$%!6+3714!/!4+4/,!+;!ES!`a8!/$%!aba8!/8!7#;48!;+9!WEHH)!!N1.!:9#0.!:.9!`a!A/8!WE>!/$%!41.!:9#0.!:.9!aba!A/8!WGG)!!L9#4.!/$%!8+,-.!/$!.23/4#+$!4+!;#$%!1+A!?/$5!`a8!/$%!1+A!?/$5!aba8!5+39!;9#.$%!6+3714)!!V+A!A+3,%!5+39!/$8A.9!01/$7.!#;!41.!4+4/,!0+84!A/8!WEK>U!!XQ:,/#$)!!!!!

Page 8: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

GH)!!M+3!/9.!A+9T#$7!+$!41.!,/5+34!+;!/!5./96++T)!!N1.!:/7.!#8!H!#$01.8!A#%.B!1/8!12!?/97#$8B!/$%!1/8!

419..!0+,3?$8!+;!.23/,!A#%41)!!</=!!L9#4.!/$%!8#?:,#;5!/$!.23/4#+$!41/4!9.,/4.8!41.!0+,3?$!A#%41B!0B!/$%!41.!7/:B!7B!6.4A..$!0+,3?$8!4+!41.!4+4/,!A#%41!+;!41.!:/7.)!

!<6=!!`+?:,.4.!41.!4/6,.!65!83684#434#$7!41.!7#-.$!-/,3.!#$4+!5+39!.23/4#+$!;9+?!:/94!</=!/$%!8+,-#$7!4+!;#$%!41.!3$T$+A$!-/,3.)!

!!!!!!!FS)!!"/04+9!./01!+;!41.!;+,,+A#$7!0+?:,.4.,5)!!</=!! 4x2 !16 ! ! ! <6=!!3x3 + 3x2 ! 2x ! ! <0=!!2x2 !11x ! 6 ! ! <%=!! x3 ! 25x !!!!!!!!!!!'''''''''''''''''''''''! ! ''''''''''''''''''''''! ! '''''''''''''''''''''''''! '''''''''''''''''''''''!!!!

Page 9: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

Part II Calculator Section: Show work when necessary to justify your answers !Calc Section A E)!!M+3!%9#-.!(>!?#,.8!:.9!1+39)!!L1/4!#8!5+39!8:..%!#$!;..4!:.9!8.0+$%U! ''''''''''''''''''''''''!$%0#.)""#2.!."/!.">?@AB"7..#",-"0-."C,+."!!!G)!!X-/,3/4.!41.!.Q:9.88#+$8)!!

</=!!>S)G!]!E>!\!F! ! <6=!!DEE<GS=!]!@@! ! <0=!9.2 !15.9!19 +14

!! <%=!! 7(44.5!!!82 ) !

!! '''''''''''! ! ! ''''''''''! ! !!!!!!!''''''''''! ! !!!!!!!!!!'''''''''''!!3. Graph each of the following equations accurately.

(a) y = 34x + 5 (b) 2x + 3y =1 (c) y !1= 3

2(x + 2)

4. Graph: y = ! !x + 3! ! 2 5. Graph: 3y + 2x > !2 6. Write an equation for the graph

shown below:

____________________________

! ! !

! !!

Page 10: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

Calc Section B

7. Graph the linear system and find the solution: 8. Graph the linear system and find the solution:

y = 2x !1y = !x +1

!x + y = !22x ! 2y = 4

________________________ ________________________ 9. Which system of inequalities is represented by the graph below?

(a) x + y < 3!4x + 2y >1

(b) x + y ! 3"4x + 2y #1

(c) x + y ! 3"4x + 2y >1

(d) x + y ! 3"4x + 2y #1

10. A scuba diver is returning to the surface from a depth of 165 feet. The safe ascent rate for a diver is 30 feet per minute. How many minutes will it take for the diver to return to the surface? _______________ 11. Which equation represents the table at the right? (a) y = 5x + 7 (b) y = 7x + 5 (c) y =12x ! 5 (d) y = 7x +12

!!

!

!

Page 11: Incoming Algebra 2 Summer Work - duxbury.k12.ma.us

Calc Section C

!12. The student council is having a bake sale. They spend $40 for the ingredients to make brownies and cookies. It costs $1.25 to make a dozen brownies and $1.50 to make a dozen cookies. The brownies sell for $6 per dozen and the cookies sell for $7.50 per dozen. The student council sells a total of $195 in baked goods.

(a) Write a system of linear equations with two equations and two variables to represent the situation. What do the variables represent?

(b) Solve the system for the two variables by using any method.

(c) What profit did the student council make for the brownies sold? For the cookies sold? 13. Look for a pattern in the table. Then write an equation that represents the table.

________________________ 14. Write and solve an equation to find x.

________________________ 15. A tutor charges a fee for the first lesson that is 1.5 times the fee for later lessons. You spend $315 for 10 lessons. How much does the first lesson cost? How much does a later lesson cost? _______________________ _______________________

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ALGEBRA 2 REFERENCE SHEET

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