Name: Date: Period:

Semester Exam Review - Spring 2015

State the solution to each system below, ,1. ( a,-ÿ 2. tÿ ÿ 1 /

lUJ t fN, Iiÿ I =4i.I

it-- 5 .......... -V

y = 4x+1

4. Determine the solution to the system: t.Y = x + 4

?.... " i)

................. L I ..ÿ

Solution

__J

•

5. Create a table of values for the two equations in the system:-2x + 4

x y=x-S y= -2x+4

Row 1 -) 0 .- S"

Row 2 -> Z ÿ

Row 3 -> 2 ÿ7

C,£ow 4 --> 3 --ÿ.

Rows -) 4 -ÿ

<4

©6. Which row in the table shows the solution?

What is the solution?

Solve the following linear systems by using either substitution, elimination or graphing.

7. y=3x-4

y=3x+2r[TTT'''rrH

:::::::::::::::::::::::::::::: ::::i:!,

f-ÿ7i -(" f !" 7 :Lf2[212Llf2iZi2fk:...Lÿ_i i ii ti il

- b.ca. i. &.L:a...i_.ÿ..,ii ÿ I!i /liff{'7:? 212 : I3ZILT"Zi i i t ! { I I "i.................. L., ....ÿ.....ÿ:ÿ .....L..1 1 .... L,. 21 ..

i: i:ki::i: f ?ÿi iÿL...L.L.i.L..i,...IL,L&ÿ

gb

FTTTÿTr !7ÿ .....

iE[T '"FTTT"T'"i ......... ÿ"!-r-T" -T" 1":F q ÿ'i ! " tii .......... r" Tr r "i ? " i "ÿ "ÿ

:V'ÿI IBm7 -].1 [ÿC:I.....L......L<....ÿ,£ÿ(:i::]....L.LI.i..I..3T/-ii ÿ ÿ'-.-ltl ...................

..L.g ;4..44..¢-l...a4ah,..LLL..L4.-L....L..L..L..ÿ .....k4-L ÿi t ..... LI.ki iÿi i If . .:" "T"T'",.-""T7 .............. r" ""l:r ? i " i " -i ........... ?ÿ

: Li i:i { ;21:i;i ;I

Substitution/Elimination

_l

8ÿ 2y = -7 ° q::::::i: :Fi::-"!2 ÿ DL?2 ÿL..i2LLIÿ L3_i.J_...:,..L.L--ÿ-:-i

i [-'. i ÿ I' lj.oj ÿ,.4F'ÿ'Tÿ".-'ÿ'Tÿ"'-n'ÿT']%-ÿV-Iÿ' ÿ"T' f" r Iÿ"ÿ ....I....f..-i..-.!--l-..ÿ-.ÿ--..f.-..ÿ-- b'l-"i'"i" "i"v-i"' '"r'i-l'|

i_ . L.L ' . L,.. *-!- i2-ÿL i-i-4-'ÿ4 .i-4- i_ -i..-i- _ ÿ .ÿ- ÿ- ÿ i_L._:,.-.ÿi - I i i t " i i - i - i .

-I0 ÿ81 .Iÿ-o:iL:-.--ÿ..'..-.L..L..2.-.,...K..i-.6..-,...&.d.i0.L.,_L..I_L_Lÿ_.....L,iÿL..L.L i- - .; .i - ,'..l.Li i I" I i L.L i ( .ÿ I i ! I:'"i ............. ÿ, ............... i'T'T-'ÿi->.l"i .................... f-i .................

! i i I i ! ! . i i t ! ! I . iI ,H--...i--.+-l-..r-.4@.4s.I-..l--t-+:..++-,r.-......ÿ-.-i;-i,.4-.--:"-4,,,I-M-.H-+,.,%.¢d- i,.-!.+.*--ÿI tl I I+i / ÿ-L..!.J i I t - ii I i

U.LTJPff_EZ 7 3-_".--'%iL2CE£Z.i2iT72L-..i..' iS ÿ .--'I-" I / i j..-'ÿ fillL .............. ÿ-.ÿ&4,0.L!...,.A ................................

--ÿbsÿ/Elirnination

9, xN6y=20x + 2y = 12 • r-r-,---Tr-[r' r-r !% TTTÿrT r r-r-r.-ÿ

[ T ÿ ............ i .......'TT.T"-FT , ÿ .-" 1 .ÿ ..'i-m-ip"tT..@iÿ;Fl-:: i-r-i-,-rr-ÿ-

-_ ÿ...ÿ.ÿ....ÿ..-ÿ..ÿ .m.ÿ..-ÿ.r_[].-_l_.,._..ÿ.....r .r...T..T.ÿ

"/ i , I/ i i i / i ÷....... :-+..,:-f.+..:@..÷4.1--....+..- ..,...+..f +3...¢_:

.'-'ÿ'"'''-,"-'-'i"-ÿ" ""i'-" 'ÿ'-"-"w'l,"-ÿ-""-'l-"."-"-I"i " = "-" : : • . ! t: i 1I, IIÿ1, 11 !|ii lil i ÿl!!

-1i0i ,iil !.Aÿ .L,!I.L:i:i..L.i i. !/1_ &J ÿ.LÿI3.-" I I I I iÿ/ ÿ il ,t

1...LI...-ÿ-.,.-ÿ.-4---!.--:.-D....ÿ-.L...L.ÿ,,4,¢,ÿ.-.I4 .......... i-s---4-.ÿd-.i...--i-.ÿ-:..-ÿ-uÿi. j t i I i I i+l., i i i i 1 ii°" i°Y-i-T-l-i'i--i,:h" I"-TTT°f"f T,."i .... r"T"ÿ'"r'"'. = i ['**"r--r"i "'I""I','ÿo'ÿ'''T'" "-"'T't'"r'"r"'r-'l . i , f ""'I

L.L_ÿa..I.Z..L]2ÿi0.E]_LL.u.-_L_L..L.-Lÿ

Substitution@.

]K÷ÿ v. 740

b..t I_l., ÿ'Z,O

x--ÿ'

Write a system of linear equations to represent each situation.rdrdÿ ÿ, • o5 ÿ.'r. ÿAÿ I.ÿ,,ÿ

!0. Jason has 18 coins in his pocket valued at $1.60. He only had nickels and dimes. Which of these is a system ofuations that could be used to solve for the number of each type coin?n + d = 18 I ÿlg) n + d =ÿ Tÿ' 5n+10d =ÿB ÿ:ÿ + d =:18 Mg:ÿ-'ÿ + 0.10d =/ÿ0 5n+ 10d= 18 8n+10d=160"-15 n+ 10d = 160'k._J ÿ.-J

11, Suppose that you bought supplies for a party. Three rolls of streamers and 15 pa_rty.hats cost $30. Later youbought 2 rolls of streamers and 4 party hats for $11. How much did each roll of streamers cost? How much did

hat cost?+ ÿ5H=30 ÿ,"

+ 4H = 11

12, Which of the follow system of linear"

2S+4H=303S + 15H =(ÿ

K'Jÿ (3_ÿ_ÿ)ÿ 15H = 303S + 4H = 11 "

.-ÿ S ÿ ÿ,SH-_3o •

.'2,,3 YH H ÿ- t!

quality graphs contains the point (8,-3)as a solution?

c).

Simplify the following, there should be no NEGATIVE exponents.

15. ?,17 16.a6D4c

a2bc2

Find the area of each figure in simplest exponential form

:l.3x2y9

Find the volume of the following figure in simplest exponential from.

18. 3x2y IÿTxÿD ) ( % ÿ 3ÿ ÿ " 9)

2xySz

Write an exponential function to model the situation and find the amount for the specified time.Ciÿ--,z. ÿ" )

19. The population of a city of 450,000 people increases 2.5% per year. Determine what the population of the citywill be after 6 years. ÿj, ÿ ÿa

Equation: ÿ): wsÿ ccC t,oÿa')ÿ

20. John purchased a car for $25,000 and decreases in value 12% per year. How many years will it take before thecar is less than half of its original value?Equation: >: vosÿ:ÿ (, ÿg)'ÿ

Tell whether the following tables are linear or exponential. If the table is exponential, also tell whether it is

a growth or decay,

21. 22. 24.x y0 8001 12002 18003 27004 4050

H

23.x y1 22 43 6 tÿ.

4 85 10

x y x y0 2 1 20481 5 2 5122 8 3 1283 11 4 325 17

q

Identify whether the following graphs are exponential growth, decay or neither.

.......... ' ........ w !

Chapter 9 Review QuestionsFind the sum, difference or product. Write your answers in descending order.

28. 4

30. 5m3(m+6)..__.

32. (3y+8)(5Y+6)

31. 3(4x2 -5)+4(x2 +6)

Write an expression to solve the following word problems.

33. A triangle has sides Of 2x + 6, 6x-12 and-x +7. What is the perimeter of the triangle?

-Iÿ +q

34. A swimming pool has a length of 2x2 - 2x + 5 and a width ofx ÷ 4. What is the area of the swimming pool?

_ÿ- zÿyXÿ+qÿ ÿÿ, 3,ÿ7.rÿl

35. What is the area of the following triangle?

x-+ .'42ÿ, ft

Factor the following polynomials.36. x2 +3x-18 -ÿ9.>ÿ

" 't ÿ °}

37. x2 +15x+56 .......................

x/ÿ}×l d * ÿ).x#ÿ)2{` i-

38. 25X2 + 40x + 16t-, ^

(ÿ--ÿ .ÿ0 <ÿ ÿ;o1

39. 7x2 +20x-3 .ÿ.i ÿ ÿ

) X

40. 24a2b4c +18a4b2c

a} 6(4a2b4 c + 3a 4b2c) b)a2b2c(4b2 + 3a2) c} 6abc(4bÿ- +3a2) (d})6a2b2c 4b2

Use the fiÿureto answer the following questions.

41. What is the area of the figure?k

t}- 42. What are the factors of the figure?

7",\

43. Tammy drew a floor plan for her kitchen, as shown below. Which expression represents the area of Tammy's

kitchen? (ÿ ÿ ÿ-':ÿ(t ÿ ÿ.ÿ

Sx unitsa} 6x2 +30x+5 ÿ'}ÿx2 +13x+5 ÿ× ÿ ÿ

2x+lunits c} 10x + 12 d} 5x + 6 .+ ÿ ÿ, ÿ 5.ÿ

44. What is the perimeter of the following triangle?

Chapter 10 Review Questions

45, How does the graph ofy = x2+ 2 compare to the graph ofy = x2- 17

b-

46, How does the graph ofy = -4x2 compare to the graph ofy = 4x27

47. If the graph of the functiony = x2 - 3 is moved up 4 spaces, what is the new equation?

48, What are the x-intercepts of the parabolay = xz + 4x?

49, What are the solutions to the equation 5x = x2 - 6 ?

50. Which of the following is the graph of the quadratic parent function? What is the equation?

B) c) ÿ D)

.... H-ÿ-EIEL

I I

51. Find thesolutions of the following equation: 0 -- xÿ + 3x + 2

71 .....

52, For each: What is the axis of symmetry? What is the vertex? Is it a maximum or minimum? What isthe y-intercept?

lA) f(x) =-xÿ -3x-2 B) ÿ ÿ (, {ÿ ._ ÿ) .ÿ,ÿ.

)L%

,i\ I

\ Lÿr

\ ,.L

Use the quadratic formula to solve the following questions.53. 9xa+6x=15 54. r2-7r=-3

Identify whether the equations are linear, qÿ

f'ÿ_ -'}r ÿ3-='JI)(Iÿ

ic or exponential.

L I" .......

56. y=2= 57. y=2x+6 58. y=5

Identify whether the following graphs are linear, quadratic or exponential.59. 60. 61.

-5

...... .+ ..........

• .-ÿ I-i I J ÿ_-x

--+I

-i

1_[z:?-I

Decide if the data in the table shows direct, inverse variation, or neither. If it is either direct or inversevariation, determine the value of the constant (k}, and write the corresponding equation.

62.m.

: x 8 12 16

Y i 2 3 4

Constant? k"

Equation ÿ q *

63. x -2 3 10

6 -4 -1.2

Constant? "

Equatfon ,- ,ÿ

64. A farmer uses a lever [o move a large .rock, The force required :to move the rock variesinversely with the distance from the pivot point to the point the force is applied, A forÿ;e of50 pounds applied to the tever 36 inches from the pivot point oF the lever wii! move the rock,Which function models the relationship betÿ,ÿeen F, the amount of force applied to the tever,and d, the distance of the applied force from the pÿvot point?

F

ii

1ÿ800

G d= .......

" " 1,800

d

dtÿ ÿ ÿ,ÿ.ÿ

86

Identify whether the function is linear or quadratic. Identify the reference point.

65. y- 5 = -2(x+3)2 (°°'}. ÿ ,i0

66. y+ 7= 3(x-6) I, (ÿ .--ÿ? }

Fill in the missing information.

67.

Table

/

Graph Algebraic (write an equation)

y÷ 8 :-3(X-7)2

Verbal (describe the transformaUonsfrom ÿhe pajeÿ)ÿt function)

Complete the Square.

68. xz + 8x + ÿ :ÿ:ÿi 69. xz - 9x + 70, 4xz - 16x + ÿ-ÿ;

Solve for x by completing the square.

71. x2 + 8x + 6 = 0

/4 ' "

72. xz - 4x - 8 = 0k

' /

73. xz + 9x = 19 74. xz - 14x + 44 = 4

\i

STAAR Review Questions

75.

76,

A Iawn is shaped like a parallelogram witlf abase of ÿ2 feet, and a height of 18 feet,.Coverilÿg fl-te lawn with grass ÿlI cost $2.60per sqÿtare 1bat. HOw mÿtctl money wilt if. cÿ)stto cover t.he taÿvn with grass?

Record your answer and fflI in the bubbles onyottr answer documenL Be sure to uÿ ttxecorre@ place value.

Look aÿ the drawdng shown beloÿ

A ,,7@®

M P

9in.

®®@®®®®®®®®

:!

® ® ® ® ®,,2)® ® ® ® ®®@®® ® ®®® ® ® ® ®®®®® ® ®@® @ ® ® ®®®®® ® ®®® ®@ ® ®®®®® ® ®®® ®® ® ®®®®® ® ®®

J77. Describe the effect, on the m'ea of a drcle wherÿ

the radgus is doubled,

% / 1The area is reduced by ÿ.

The area rsmainis constant,

iI' The area fÿ doubledÿ

;J The area is ÿlcreased four times.

IfAKMP is a right tHangie formed by the placement of 3 squm'es, what is the area of the shadedsquare?

A 135 in, 'ÿ

B 24imÿ ÿ:2,:c ÿi,,,ÿ ÿ .:,,'t, -

D 81 in,ÿ 'f

78.

H -8.96

If @/-3ÿ2) is a solution to t:he equation&ÿ= 5y - 17, whatds t, he value of x?

F 0,84 ",, "- s ÿ '

X%

79.Wllich equation could be used torepresent file graph of tiffs fimctioff?

! !l I' 14 tl

80.What is file slope of the line flintcontains the coordinate points(6,-9) ÿd (ÿ, 9)?

/

x

,:B v=-3x+6/,- 2

'D" v=3x+6

2C y=---x+6

3

A y =-3x+2

i i

.... ! ......... i .....

.... I .....

.......... i ....

1to

+t+t+t

/ '; ,i

-1A --2

'B -2

C 2

81.An amusement park chm'ges anadmission tee of $5.50 plus 75¢ perride ticket. Which eqnation bestrepresents e, the total cost for aperson to ÿnter the amusement parkand ptu'chase r ride tickets?

e = 0.75+5.50r

B r = 5.50+0.75c .,,

iC" e = 5.50 + 0.75r

./D r = 0.75 +5.50eÿ

1D -

2

82. 83.Yunlmy Bakery sells appte andbiuebeny pies each Satm'day. Applepies cost $8 each andbluebeny piescost $I2 each. Last Saga-day, thebfikery sold 4 nmre app!e pies thanbluebeny pies for total sales of$232. Which system of equationscan be used to find a, |he number ofapple pies mÿd b, the number ofbluebenT pies sold?

A 8a+12b=232

B 8a+12b=232 *ÿa=b+4

C 8a+12b=232 ÿ"cr÷b =4

The amoÿmt of leather needed towrap around a baseball bestrepresents the. ball's -

A perimeter

B circnnfference

C Sm'Nce,area

D vohane

84.

V,qÿich monomial represents thearea of a rectangle with a length of

33a-bc milts and a width of

5able4 units ? ;:ÿ ..... :

A 8aÿbÿc7 ÿ " ÿ :ÿ

B 15abe

C 15a3bÿc7

D 8abe

D 8a+12b=232=b-?4

85.

Mike is packing a rectangular box that contains 8 tightly packaged bars of Spanish soap,called Jabdn, shaped like rectangular prisms, as shown below.

1.5 in:

2.5 in.

/

J'> iÿ ?

i ÿ, • .... A 450

86.

What is the approximate volume in cubic inches of this rectangular box?

A 13in.3

B 30 in.3

,4"C, 105 in.3

D 221 in.3

The water wheel of a mill makes 45revolutions per milmte. How manyrevolutions wil the wheel make hi1- hour?2

B 600

C 900

D, 1350

87. In a particular town, there is a smallpark in the shape of a triangle, asshmÿm below.

. r Depot RoadMain Street

The side of the park facing FirstAvenue is 110 feet tong and the sideof the park facing Marl1 Street is130 feet long. Which of thefollowing is closest to the length ofthe side of the park facing AirDepot. Road? i ':

A 20 feet

B 70 feet\

C 140 feet

D 4800 feet