Summer Work
NAME_________________
For students to successfully complete the objectives of the Agassi Prep math curriculum, the student must demonstrate a high level of independence, capability, dedication, and effort. This summer packet will help you maintain/improve your skills. This packet is a requirement for those entering their math course for the 2016-2017 school year, and is due on the first day of class. Your attempt to complete this packet by the first day will be combined with an accuracy grade after the first week of school, along with a post-test on the material to form your first grade of the math course. Complete as much of this packet on your own as you can, then get together with a friend, or “Google” the topic (math.com and Khan Academy.com are good resources). SHOW YOUR BEST WORK. Requirements The following are guidelines for completing the summer work packet… • You must show all of your work on separate paper in PENCIL. All graphs must be done on graph paper. You can Google free graph paper or purchase some. • Be sure all problems are neatly organized and all writing is legible. • We expect you to come in with certain understandings that are prerequisite to this math course.
Finally, it is suggested to not wait until the last two weeks of summer to begin on this packet. If you spread it out, you will most likely retain the information much better. Once again this is due, completed with quality, on the first day of class. It is intended to help you be successful in the coming year. Enjoy the summer! Be safe and be mathematical!
For the first day of class: Ø Have your summer assignment, with the printed vocabulary, stapled and ready to turn in. Ø Have a binder ready with dividers, white lined paper and graph paper. It is recommended that you have at least a 2” binder. Ø Bring your graphing calculator. We recommend the TI-84, TI-83 Plus or InSpire. Ø Bring your pencils (not pen!).
Geometry SUMMER Assignment $
$
! This!assignment!is!to!be!completed!before!the!first!day!of!school.!These!are!all!skills!that!were! learned!in!algebra!1!and!are!going!to!be!used!in!geometry.!If!you!are!not!sure!on!how!to!solve!a! question,!research!it.!If!you!are!still!unsure,!then!ask!your!geometry!teacher!at!the!beginning!of!the! school!year.!You!will!be!assessed!on!these!skills!within!the!first!week!of!school.! $ Evaluate$ 1.!!
3
!2 ! + !5(4)!!
!
!
!
!
!
2
2.!!
2
(8!– !5) ! + ! (9!–!(−3)) !
For$questions$3@6,$use$the$coordinate$plane$below$
! 3.!!Name!the!ordered!pair!for!point!A! 4.!!Name!the!ordered!pair!for!point!C.! 5.!!Plot!the!point!Z(I2,!I8)! 6.!!What!quadrant!is!point!F!in?! Simplify.$ 7.!
! ! − 8! + 2 − (−5! ! + 7! + 3)!
!
8.!
!
!
10.!!
!!6!! + !5! + !2!!– !11! = !90"
!
!
12.!
24 = ! + 4!
6! + 4! − 2 + (−3! − 8! + 2)!
Solve$ 9.!
!8!!– !10! = !6!!!
!
! ! 11.!
!!18! + !7!! = !10!! + !39!
! !
!
!
Solve$and$Graph! 13.!!!! + !13! < !41!
!
!
14.!!!!– !6! > !2!!
!
!
15.!!8!! + !15! ≥ !9!!– !26!
!
!
!
17.!!
!(!) ! = !3!! + !11!!!"!!! = ! −3"
!
!
!
!
19.!!
!(I3,!I5)!and!(I3,I1)!
!
!
!
Slope:!!__________!
!
!
!
Parallel!Slope:!!__________!
!
!
Perpendicular!Slope:!!__________!
! ! ! ! ! $ Evaluate$ 16.!!
2
!5! – !3!!!!!"!!! = !2! !
! $ $ Find$the$following$slopes$ 18.!
!!(I2,!3)!and!(1,!I3)!
! ! Slope:!!__________!
!
Parallel!Slope:!!__________!
Perpendicular!Slope:!!__________!
Rewrite$each$equation$so$!$is$a$function$of$!.$ 20.!
7! + ! = 10!
!
!
!
!
!
21.!
3! + 5! = 15!
!
!
!
!
23.!
2! + 8 = ! − 3!!
$ $ 22.! $
5! = ! − 2! − 3!
Solve$each$proportion! 24.!
!
!
!
!
!
!
!
25.!
!!!!!!!!!!!!!!!!
x 3 = ! 4 2
!
!
!
!
!
!
7 x−4 ! = 3 6
!
!
!
!
!
27.!
−3!" + !18!!
!
!
!
!
29.!
!!! ! + !!!– !20!
!
!
!
!
31.!
!!4! – !36=0!
!
!
!
!
33.!
−4! ! − 8! − 3 = −3 − 5! ! !
$ $ Factor$ 2
26.!
!!2! !– !4!!
28.!
!!! ! + !7!! + !12!
2
2
2
$ Solve$by$factoring.$ 2
30.!
!! – !16 = 0!
!
32.!
!2! – !!!– !15 = 0!
2
2
!
$ $ Find$the$product$ 34.!
2!! + !5 3!!– !4 !
!
!
!
!
35.!
! !+1 !−3 !
36.!
! + 2 (! − 2)!!
!
!
!
!
37.!
4!(3! + 9)!
!
!
!
!
39.!
(2! − 3)! !
38.!
(! + 4)! !
!
! ! Solve$the$linear$system$by$using$elimination$or$substitution.$ 40.!
! = −3! + 5 !! 5! − 4! = −3
!
!
!
!
41.!
−4! − 2! = −12 ! 4! + 8! = −24
5! + ! = 9 ! 10! − 7! = −18
!
!
!
!
43.!
2! − 3! = −1 ! !+1=!
! 42.!
!
!
Solve$the$following$linear$systems$by$graphing.$ ! = −! + 5
44.!
!
!= !−2
!
!! !
!
!
!
!
45.!
!
!= !−1 !
2! + ! = −1
!
! ! Simplify$each$radical.$Leave$answer$as$a$radical.$No$decimals.$ 46.!
45!
!
!
47.!
2 18! !
!
48.!
!" !"
!
!
!
49.!
!"
!
! ! Simplify!each!expression.!Make!sure!your!final!answer!is!completely!simplified.! 50.! 52.!
8 ∙ 3 6!
!
7 2 + 8 2 − 3 3!
!
!
!
!
51.!
5 2 ∙ 10 24!
!
!
!
!
53.!
− 5 − 4 45 + 5 20!
!
!
!
!
55.!
! Solve!the!following!equations.! 54.!
2 5! − 4 = 6! !
!
!
13! − 3 = 6!
!
!
!
The skills below are crucial to your success in Geometry. You will need to be able to recall and apply these skills throughout the year. Complete the problems on separate paper, not on this packet. Rewrite each problem and show all work! Box/Circle your final answers.
Solving Linear Equations - Solve each equation. Write your answer as a fraction, if necessary. 1. 2x + 5 = 11
4. x ! 3( x ! 7 ) = 4 ( x ! 7 ) ! 2x
2. 2 ( x ! 3) = 84
x 5. ! + 7 = 5 8
3. 3x ! 4 ( x ! 4 ) + 4 = 13
6. 12x + 8 = 6x ! 5
Solving Inequalities - Solve each inequality. 7. 4c + 23 ! "13 8.
a !8 11
9. !3b < 48
10.
8 x + 1 > !5 3
11. 7q + 3 ! "4q + 25 12. !3w + 1 " 8
Solving Systems of Equations using Elimination - Solve each system of equation. Write your solution as an ordered pair, using fractions if necessary. 13.
2x ! 3y = 2 5x ! 3y = 14
15.
11x ! 3y = !39 6x + 12y = !19
14.
x ! y = 39 x + y = 1785
16.
2y ! 3x = 51 11x ! 7y = !187
Solving System of Equations using Substitution - Solve each system of equation. Write your solution as an ordered pair, using fractions if necessary. 17.
2x + y = 21 7x ! 2y = 90
19.
2x ! 4y = 40 8x ! 3y = 82
18.
2x + 7y = !20 x ! 5y = !10
20.
2x + 3y = 8 9x ! 3y = 14
Simplifying Radicals - Simplify. NO Decimals!!! 21.
80
24.
675
27.
98x 3 y 6
22.
243
25.
50 ! 10
28.
56a 2b 4 c 5
23.
40
26.
6! 6
29.
63 8
Solving Equations using Quadratic Formula - Solve each quadratic equation. Write your answers using decimals. 30. x 2 + 5x + 4 = 0
32. 4x 2 + 8x + 2 = 0
31. x 2 ! x = 6
33. !8x + 3x 2 = !1
Solving Equations by Factoring - Solve. Write your solutions as fractions, if necessary. 34. x 2 ! 10x ! 24 = 0
37. 24x ! 35 = 4x 2
35. x 2 = 2x + 48
38. !9x 2 + 15x = 4
36. x 2 ! 9x = 2x + 12
39. 6x 2 = 2 (13x + 10 )
Multiplying Polynomials - Find each product.
9 40. !# x $& ( 8x 5 ) "2 %
42. ( a + 3) ( a ! 6 )
41. 8y ( 5y ! 2y + 1)
8 43. !# t + $& " 3%
2
3
2
Graphing Lines - Graph each linear equation. 44. y = !2x + 3 45. y =
1 x !1 2
46. 2y ! x = !2 47. 4x + y = 4
Writing Equations of Lines - Write an equation in slope-intercept form of the line with the given information. 48. m = !4 , through ( 0, 3) 49. m = 2 , through ( 5,!7 ) 3
50. through ( !5,!3) and (10,!6 )