NAME: __________________________________

BRICK TOWNSHIP PUBLIC SCHOOLS ALGEBRA 1 HONORS

SUMMER PACKET !! This!packet!covers!the!material!that!you!should!be!competent!in!at!the!beginning!of!

Algebra! 1! Honors.! You! are! to! complete! each! problem! during! the! summer.! The! summer!

packet!will! be! collected!on! the! first! day!of! class! and!will! count! as! your! first! 3!homework!

grades.! Packets! that! are! not! turned! in! will! receive! a! zero! for! all! 3! homework! grades.!

Additionally,!there!will!be!a!test!on!this!material!during!the!first!week!of!the!semester.!

!

! It! is! your! responsibility! to! know! the!material! covered! in! this! packet.! If! there! is! a!

topic! with! which! you! are! not! confident,! you! should! find! someone! who! can! help! you! or!

search!for!resources!as!part!of!your!summer!preparation.!!

!!

The!following!are!a!list!of!resources!you!may!want!to!refer!to!when!completing!the!packet:!!

• https://www.algebra.com!• http://www.math.com/homeworkhelp/Algebra.html!• http://www.algebrahelp.com!• http://www.coolmath.com!• https://www.khanacademy.org!

!!!Have%a%great%summer.%See%you%in%September!%

% %

1. Which!equation!does!not!belong!with!the!other!three?!

!(a) ! + 3 = 7!(b) !! = 2!(c) ! − 5 = 9!(d) 4! = 16!

! !2. Solve:!−8! = 56!

!!!!!

3. Solve:!!! ! = 15!!!!!!

4. A!basketball!costs!$15.00.!If!the!sales!tax!is!6%,!which!equation!can!be!used!to!find!the!amount!of!tax?!

!(a) ! = 0.06 ∙ 15!(b) 0.06! = 15!(c) 15 + 0.06 = !!(d) ! = !"

!.!"!!

5. If!the!volume!of!a!cone!is!24!!!".!,!which!of!the!following!are!possible!dimensions!of!the!cone?!Choose!all!that!apply.!!

!(a) ! = 2!&!ℎ = 4!(b) ! = 3!&!ℎ = 8!(c) ! = 6!&!ℎ = 2!(d) ! = 4!&!ℎ = 18!

!6. Solve:!12! + 2 = 26!

!!!!!

7. Solve:!6 ! − 4 + ! = 5(! − 2)!!!!!!!

8. Translate!the!equation!4! − 5 = 3(! + 2)!into!a!verbal!sentence.!

!(a) Four!times!the!difference!of!x!and!five!equals!three!times!the!sum!of!x!and!two.!(b) Four!times!x!less!than!five!is!the!same!as!three!times!x!plus!two.!(c) The!sum!of!four!times!x!and!five!is!three!times!the!sum!of!x!and!two.!(d) The!difference!of!four!times!x!and!five!is!three!times!the!sum!of!x!and!two.!

!9. Solve:!!! 6! + 30 = 4! + 2(! − 7)!

!!!!!

10. Solve:! 3! + 6 = 21!!

(a) ! = ±5!(b) ±9!(c) ! = −9!&!5!(d) No!Solution!

!11. Translate!5! + 7 ≥ 2!into!a!verbal!sentence.!

! !(a) Five!times!the!sum!of!x!and!seven!is!greater!than!two.!(b) Five!times!x,!increased!by!seven,!is!less!than!or!equal!to!two.!(c) The!product!of!five!and!x,!increased!by!seven,!is!greater!than!or!equal!to!two.!(d) Seven!more!than!the!product!of!five!and"x!is!greater!than!two.!

!12. Which!inequality!is!different?!!

!(a) x!is!no!more!than!12.!(b) x!is!less!than!or!equal!to!12.!(c) x!is!at!most!12.!(d) x!is!no!less!than!12.!

!13. Translate!“seven!is!greater!than!the!difference!of!twice!a!number!and!nine”!into!an!

inequality.!Solve!the!inequality.!!!!!!!

14. Solve:!2! − 1 > 15!!!!!!!

15. An!error!was!made!while!solving!the!inequality!−4 2! − 3 > 5! − 14.!Choose!the!

step!where!the!error!was!made.!!

(a) −8! + 12 > 5! − 14!(b) −13! + 12 > −14!(c) −13! > −26!(d) ! > 2!

!16. The!table!shows!the!cost!per!hour!to!rent!a!canoe.!Which!function!represents!the!

situation?!!

Number'of'hours,'h' Rental'fee,'f'

1! 15!2! 20!3! 25!4! 30!

! !(a) ! ℎ = 5ℎ + 10!(b) ! ℎ = 10ℎ + 5!(c) ! ℎ = 5ℎ + 15!(d) ! ℎ = 10ℎ + 15!

!17. Which!of!the!following!equations!are!equivalent?!

!(a) 15 − 2! = 3!!(b) ! + 2 = 5!(c) 4 ! − 2 = 3! − 5!(d) !! ! = 9!

!18. The!formula!for!the!volume!of!a!cylinder!is!! = !!!ℎ.!

!(a) Solve!the!formula!for!h.!

!!!!!!!

(b) Use!the!formula!from!part!(a)!to!find!the!height!of!the!cylinder!with!a!radius!of!!3!centimeters!and!a!volume!of!45!!!"!.!

!!!!!!

19. You!permitted!a!50\pound!check!bag!for!free!on!your!flight!to!Florida.!Your!bag!!

weighs!32!pounds.!(a) Write!and!solve!an!inequality!that!represents!how!much!weight!you!can!add!to!!

your!bag.!!!!!!

(b) Can!you!add!your!5\pound!algebra!book!and!your!6\pound!biology!book!without!going!over!the!weight!limit?!Explain!your!reasoning.!

!!!!!

20. You!want!to!average!at!least!90%!on!your!algebra!quizzes.!So!far,!you!have!scored!93%,!97%,!81%,!and!89%!on!your!quizzes.!!!(a) What!must!you!score!on!your!next!quiz!to!have!at!least!a!90%!average?!

!!!!!

(b) Is!it!possible!for!you!to!raise!your!quiz!average!to!97%!if!only!one!more!quiz!is!added?!!Explain!your!reasoning.!

!!!!!

21. Which!equations!are!equivalent!to!! = !" + !?! !!

(a) ! − ! = !"!(b) ! = !!!

! !(c) ! = !!!

! !(d) ! = ! −!"!(e) !!!! = !!(f) !!!! = !!

!22. One!cell!phone!plan!charges!$17.50!per!month!plus!$0.17!per!minute!used.!A!second!

cell!phone!plan!charges!$32!per!month!plus!$0.07!per!minute!used.!Write!and!solve!an!equation!to!find!the!number!of!minutes!you!must!talk!to!have!the!same!cost!for!both!calling!plans.!

!!!!

23. Find!the!slope!and!the!y\intercept!of!the!graph!of!the!linear!equation!! = !

! ! + 1.!Then!sketch!its!graph.!

!

!!

24. The!equation!3.5! + 1.5! = 21!represents!the!cost!for!a!family!to!attend!a!play!where!x!is!the!number!of!adults!and!y!is!the!number!of!children.!Find!the!intercepts!and!interpret!the!meaning!of!each!one.!

!!!!!!!!!

25. Write!an!equation!of!the!line!passing!through! 0,2 !!"#!(1,−1)!in!slope\intercept!form.!

!!!!!!!!!

26. Solve!the!system!of!equations:!! = !

! ! + 2! − !

! ! =!!!

!!!!!!!!!!

27. It!costs!$0.07!to!send!a!text!message!and!$0.12!to!send!a!picture!on!your!cell!phone.!

You!spend!$3.38!and!send!twice!as!many!text!messages!as!pictures.!How!many!text!messages!did!you!send?!

!!!!!!!

28. Simplify:!(−3!)!!!!!!!!

29. Simplify:!12!" ∙ 12!!"!!!!!!

30. Simplify:!(!!)!

(!!)!!!!!!!

31. Multiply!(4.0×10!!)×(2.5×10!!)!and!write!the!answer!in!scientific!notation.!!!!!!

32. Simplify:!− 225 + 4.8!!!!!!

33. Simplify:!3 −343! + 8!