Practice 'lest

1 Using the equation an = a1 + d(n - 1), findthe 12th term of the series-3 + - 6 + -9 + - 12 + -15+. ..

A -39B 36C -36D -30

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2 Which of the following arithmetic serieswill yield a sum of 257

6A 2:= [13 - 3(n - 1)]

n=l

5

B 2: [-:-3+ 4(n - 1)]n=l

4

C 2:= [-8 + 2(n - 1)]n=l

4D 2: [25 - 7(n - 1)]

n=l H2.cDOK2

3 Solve: 39 + 11Ox·- 81 > 41

A x > 1or x < ~B x < ~3eX> 1

D ~<x<lDl.aDOK2

4 Which one of these is a valid equation forall values of a and b7

A .ja+b=va+VbB .ja+h=vaxVbC Val) = va + VbD vOJ; = va x Vb

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Part 1

35 Evaluate: 92

A 812

B08C 27D 729

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6 A spherical water tank holds 15,000 ft3of water. Find the diameter of the tank.TT _ 'Trd3Vsphere - 6"

A 30.6 ftB 23.0 ftC 15.5 ftD 121.8 ft G1.gDOK2

-5 -4i :i i

~ !

.!.__ "' __ .J.""_~ _~ J

What is the solution to the equationx3 - 3x2 + 2 = 07

A x = -4, 2, and 1B x = -3,0, and 1C x = - 2, 2, and 0D x = -0.75,1, and 2.75

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8 What is 15x4 + x3 -52$2 +20x, + 16writterr'as:'productofitS'factors?>:.;~~):..

A (x + 1)(2x - 3)(5 - x)

B (x - l)(x + 2)(3x - 4)(5x + 2)

C (2x + 5)(x + 2)(3x + 4)(x + 1)

D 2x(5x + 2)(x + 2)(x - 1)F2.bDOK3

9 A circle has a center at the point (5,0) andan area of 3n units". Find the equation ofthe circle.

A x + 52 + y2 = 3

B (x + 5)2 + y2 = V3 .c (x - 5)2 + y2 = 3

D X2 + (y - 5)2 = J3E3.d DOK2

10. Which of the following is the ordered pairfor one of the foci of the ellipse?

(x + 1)2 (y + 8)2 _ 1169 + 36 -

A (-1, -8)

B (-1 - V133, -8)

C (-1- V133,8)

D (1+ V133, 8)E3.c DOK2

11 Solve this system of equations.

4x - 2y + 3z = 1x + 3y - 4z =-73x + y + 2z = 5

A x = -31 Y = -21 Z = -2

B x = 3, y = 2, z = -1

C x = 2, y = --1, z == -3'

12'- Which inequalities are, represented. by the.graph?'>;

y

x

A Y > 5 and y ::; _·x - 1

B Y < 5x and y > -x - 1

C Y ~ x - 2 and y < 2x + 2

D Y S; x - 2 and y > 2x + 2D2.aDOK3

13 Suppose that bamboo grows at a rate of 2feet per day. Determine how long it wouldtake an 8-foot stalk of bamboo to triple itsheight.

A 4 days

B 9 days

C 8 days

D 48 daysH2.dDOK3

14 Solve: 14x - 51 > 19

A _1 < x < 62

B x < _1 or a: > 62

C x>_12

D. x <6.DLiIDOK2~' .

15 Choose the system of linear inequalities thatdefines the shaded region.

y.-----6 ~-T-rT------f

! . 1 I

A u > Ixl and y < Ix I - 4B x + y = -1 and y = 1C Y < Ixl and y :2: [z] - 4D Y < x and y :2: x - 4 D1.b DOK 2

16 Given f(x) =ft and g(x) = x - 2, find(f 0 g) (x) and its domain.

A (f 0 g)(x) = x2 - 2, domain is x :2: 0B (f 0 g)(x) = Jx - 2, domain is x :2: 2C (f 0 g)(x) = ft, domain is x :2: 0D (f 0 g) (x) = ft - 2, domain x < 2

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17 Determine the domain and range of thefollowing function.

y = J-2x+3.

A domain: x < 1.5, range: y :::;:0B domain: y < 0, range: x ::; 1.5C domain: x ::; 1.5, range: y :2: 0D domain: x < 1.5, range: y < 0

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18 Use the quadratic formula to solve2x2 - 4x - 3 = O.Round your answer totwo decimal places.

A x = 0.58, x = -2.58B x = 3.18, x = -4.18C x = -0.58, x = 2.58D x = -3.18, x = 4.18 E1.aDOK2

19 Study the figure below and decide betweenthe law of cosines and law of sines to find y?

A 42.55 emB 18.66 emC 12.33 emD 8.71 em G3.aDOK2

20 For the triangle shown, find the value of bOto the hundredths place.

A 43.04B 21.25C 14.66D 59.37 G3.bDOK2

21 What trigonometric function does the curvein the graph below best represent and whatrange does it show?

y

':xo!-11-----+-

1

-i-! -""-+", = --t-j---tI--11

-2-~--!_---.L ~~l~'

A sine function; -1 :s: y < 1 rangeB cosine function; -1 :::;:y ::; 1 rangeC tangent function; -1 < Y ::; 1 rangeD sine function; 0 ::; y ::; 6 range

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22 Solve the following matrix problem.r: f FT; {J'nrrcA d = 4, e = 3, f = 2, 9 = 1

B d = 1, e = 2, f = 3, 9 = 4

C d = 8, e = 1, f = 2, 9 = 2

D d = 3, e = -1, f = 0,9 = 111.aDOK I

23 The area of a triangle with vertices at thepoints (a, b), (c, d) and (e, f) is ~Idet AI,

[

a b 1]where A = e d 1 .e f 1

IfdetA = ad + be + cf - ed - af - beand the vertices of a triangle are the points(-7,5), (3, -6) and (1,9), what is the areaof the triangle?

A -64

B 64

C 32

D 128

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24 What is the inverse of [~4

A [-=-~o =;]B [~O ;]

7 ]?-10 .,I,I,

c [=~=!JD [~ !]

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318

25 What is another way o6<vritinga:;,ca.Y.?/ ..

A x = logaYB x = logaaC Y = logaxD Y = log; a

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26 The local hardware store has four differentstyle grills for the summer sale. The priceof the four grills are listed from the leastto greatest and are represented in the 2 x 2matrix below.

[$120 $155]$160 $230

If the store is having a sale where everythingis 20% off, what is the new price of the grillthat is the second most expensive?

A $32B $124C $184D $128

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27 Use a calculator to find the inverse, A-}, ofthe matrix given below.

[1 0 2]A = -2 1 -4

120

A [~2 r ~4]B [X r -tJc [~ -5 ~]4

2

n3 0 =~r11

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28 A restaurant that has 5 sandwiches and 4sides to chose from. You would like to pickone sandwich and one side.: How manydifferent meals can you order?

A 25B 20C 16D 9

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29 The probability that Mike passes Science is

~, and the probability that he passes Social

Studies is ~. If the probability that he will

pass at least one subject is ~, what is theprobability that he passes both subjects?

A 32135

B 2890

C 1027

D 1445

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30 From the Venn diagram, find the value of(G n D n sv.

u

s

A 125B 108C 35D 143

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31 Two cards are to be drawn, withoutreplacement, from a deck of playing cards.What is the probability of drawing 2Kings in this manner, from a deck of cardscontaining 52 cards?

1A -

131

B -221C

2-53

D 1Hl.fDOK2

32 You go to a movie theater and can buyequally priced candy bars, bottles of soda,and popcorn. Three scenarios of thecombinations of the three items are listedbelow with their total purchase price.

2 candy bars, 2 sodas, and 1 popcorn for$6.73.

1 candy bar, 2 sodas, and 2 popcorns for$8.08.

3 candy bars, 1 sodas, and 3 popcorn for$11.24.

What was the price of each candy bar, soda,and popcorn?

A candy bar: $2.35; soda: $1.19; popcorn:$1.00

B candy bar: $1.00; soda: $1.19; popcorn:$2.35

C candy bar: $2.35; soda: $1.00; popcorn:$1.19

D candy bar: $1.19; soda: $1.00; popcorn:$2.35

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1 Given the sequence {21, 40, 59, 78,97, ... },use the formula given below to find the 10thterm of the series.

The nth term: an = al + (n - l)d

A 186B 192C 230D 428

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2 Find the angle between 0 and 21f radians471f

that corresponds to 3'71f

A 3211'

B 3

C51f3

Dll1f-3

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3 The graph below is that of either anexponential or logarithmic function.

y4~~--~-'---~--~~

I!:X

4 $ I+__ -+-_-j--I ---i--~

I, I ii J

Which of the functions could it be?

A Y = log; xo

B y = log, X

C y= GtD y = 5x

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Part 2

4 Randomly select 4 digits from 1,2,3, ...7,without replacement, to form a 4 digitnumber. What is the probability that thisnumber is even?

A 11

B -2

C3-71

D -4

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5 What is the solution set to the followinginequality: 0 :::; Ixl < 3?

A (-3,3)B [-3,3]

C (0,3)

D [0,3)Dl.aDOK 1

6 Solve the following compound inequality.List and graph your solution set.-x - 6 -4x -27 - x--->-->---3 - 3 3

A -1 < x:::; 5+--$ • •

-1 5

B -9 < x <-2~

-9 -2

C 3<x<7~

3 7

D 2:::;x<9of. $ •2 9

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Copyright © American Book Company 321

7 Which of the following graphs representsthe inequalityy >..2x + 1?A y'

B y

c y

D y

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8 What is the solution to the system ofequations below?

2x - 3y + 7z = - 23- 2x + 5y - z = 293x + y + 4z = -18

A x = 132, Y = 314, and z = 413B x = -7, y = 3, and z =.0C x = 20, Y = -7, and z = -12D x = 7 y --:--3 and z = 0

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9 Which set of inequalities corresponds to theshaded region below? .

y

A Y < x, x ~ 1

By> x + 2, y 2: 2x + 3

C Y < ax - 2 x > 1.- 3 ' 3

D y < _1.x + 1 Y > ~x + 2- 3 ' 3

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10 Which of the following system ofinequalities has a solution set that is bestrepresented by the graph shown below?

y... ....\ 7 I

<>

1\ f!\1\ ~. I

I ~)II 1 1

1! X·5 r'I 3 ., LJ 0 pp 13 4

i

-1 ,..?-I

A y> _2x2 + 5y < _2x2 + 1

B Y 2: _2X2 + 5v : _2x2 + 1

C y < _2x2 + 5y> _2X2 + 1

D y:::; _2:;;2'+ 5'y 2: X2 + 1

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322 Copyright © American Book. Company

11 Which system of inequalities defines theshaded region below?

y

A y < -1, y ~ -2xB y < -x,y ~-2C y> -2x, y ::; -1D Y < -x, Y ~ -2x

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12 What is the maximum value in the graphbelow in the given region: -1 ::; x ::;1?

y

I I1<00 iiso l- I120 !

/ so -, I4U \ i

-5 -4 3 • /"1 I

"-Y -'" I~ I

I ~" \\ / -ov

\ ~u I-lOU

I -2UU

x

A (90,0)B (-1,0)C (0,90)D (1,75)

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13 Using your knowledge of discriminants,how many solutions would b2 - 4ac < 0result in?

A 2 Real solutionsB 1 Real solutionC 0 Real solutionsD Infinitely many Real solutions

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14 What is the equation of a circle whosediameter is 10, and its center has beentranslated 3 units to the left and 4 units upfrom the point (-2, -3)?

A (x + 5)2 + (y - 1)2 = 25

B (x - 5)2 + (y + 1)2 = 25

C (x + 5)2 + (y - 1)2 = 100

D (x + 2)2 + (y + 3)2 = 25E3.d DOK 2

15 Clive graphed the quadratic equationy = x2 + 4 and came to the conclusion thatthe graph has no solutions. Alex used thequadratic formula on the same equation andcame to the conclusion that the zeros are(2i,0) and (-2i, 0). Who is correct andwhy?

~ 1-8

\ 7 /\ 6 /

"- 5/4

3

2

1

-4 -3 -2 -1 ~ 1 2 3 4

A Alex is correct because the equationy = x2 + 4 has two imaginaryx-intercepts, which she found correctly.

B Clive is correct because the equationy = x2 + 4 never intersects the x-axiswhich is seen by the graph, and so thereare no x-intercepts.

C Alex and Clive are both incorrectbecause the x-intercept occurs at (4,0).

D Alex and Clive are both incorrectbecause the x-intercept occurs at (0,4).

El.d DOK3

Copyright © American Book Company 323

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16 Solve the following quadratic equationusing completing the square method.

7x2 - 14x - 56' 0

A x = -2 and-8B x = -2 and 4C x = 2 and-8D x = 2 and-4

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17 The area of a television screen is (40 - 12i)inches-, and the length of the screen is(30 + 54i) inches. What is the width ofthetelevision?

A30 + 54i40 - 12i

B 768 + 1800i

C15 + 140i. 436

D23 - 105i

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18 Using the general formula for transforma-tion of graphs y = a(x - h)2 + k, then howhas the graph of the quadratic below beentransformed from its parent graph, y = X2?, y ,t

\ 8

1+ 7 If\ \ 6 I I\ \ 5 /

\ -, 4j I\ 3 I\ 2 iJ\. V

-4 -3 -2 -1 ~ 1 2 3 4 x

A y - a(x - 3)2 + kB Y = a(x + 3)2 + kC y = a(x~h)2+3'D y = a(x - h)2 - 3

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19 Simplify the following polynomial:2(x3-5x2 '- 2}-3(x3,,- 2x).~ (x2,_ 8)and evaluate·:y()Nr:solution:when:x:~-:--"~2.;i,;,

A -x3 + llx2- 6x+4; -36

B -x3 -llx2 + 6x+4;-44C x3 + 11x2 - 6x + 4; -44D x3 - llx2 + 6x + 4; -36

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20 Using the graph below, find all the rationalzeros of the polynomial function.

y

I I t25 I I

/' <,12U I/ ~ I

I 1,\ I1

5 f4 -3 2 -J 0 '\ 2 3 14 /5

I -, \ III -10 \ II

I ["" "'- •.. ./I r-v I

ft 2S II i I

x

A (-3,0), (1,0), and (5,0) -B (0, -3), (0,1), and (0,5)C (-3,0), (1,0), (0,0), and (5,0)D (0, -3), (0,1), (0,0) and (0,5)

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21 Use the graph shown below to determine therange of the function.

yI

1 I JI •.I I 6-4 1-3 r2 -I 0 1 2 3 14

I -6 Ii / -12 f\1 f -18 \

I -24 \-30 \-se +-1

1 -4L 1! 1 I

f

x

A (-00, -12)B (-00, -12}C [-00, -12]D [-12, -00) F2.dDOK 1

324 Copyright © American Book Company

22 Simplify the following expression:(p3 - 10p2 + 20p + 26) -7 (p - 5)

A p2 - 5p- 5

2 1B P +5p-5---p-5

2 1C p -5p-5+ p-5

D p2 + 5p + 5 __ 1_p-s

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23 The graph below represents a cubicfunction. This function has 3 real solutions.Use your knowledge of polynomialsand their x-intercepts to write a possiblecomplete factorization of this function.

y

A (x + 2)(x - 2)(x - 1)B (x-2)(x-2)(x+1)C (x + 2)(x - l)(x - 1)D (x - 2)(x + l)(x - 1)

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24 List all the possible rational zeros of theexpression: 2x3 + 5x2 - 7x - 4

A ±~, ±1, ±2, ±4

B ±~,±~,±1,±2,±4C 0

D There are no possible rational zeros.F2.bDOK 1

25 Use a matrix to determine the solution set tothe following system of equations.

-4x - 5y - z = 18-2x - 5y - 2z = 12- 2x + 5y + 2z = 4

A [~~ 1

B [~~]

C [T]D [~:]

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26 Jason can paint a fence in 3 hours. It takeshis friend Brian 4 hours to paint the samesize fence. How long will it take the boys topaint the fence if they work together'? Roundyour answer to the nearest minute.

A 1 hour and 4 minutesB 2 hours and 4 minutesC 1 hour and 43 minutesD 2 hours and 43 minutes

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27 Lamar made an 82 on his math test. Thefollowing week Lamar made an 87 on hismath test. What is the relationship betweenthe first and second test score?

A There is not enough information given todraw any conclusions.

B Each test represents dependent events.C Each test represents independent events.D The two tests are not mutually exclusive

events.H1.dDOKl

COll'Yright © American Book Company 325

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28 Simplify the following expression:yt128 + .y32 - ~A ?'2+ 2B yt182 + 2C -vm+2D yt2+6~

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29 Simplify the following expression:

(:~~)- (:~~)1+ 0A

(4 - v5)(4 - v5)

22+ 11v5 + 80 + 2V1OB11

12 + 3v5 - 8\1'2 - 2v1OC

113- 2\1'2

D11

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30 A website for chocolate candy is holding acontest. They are asking voters to choosewhat the next new color of their candyshould be. The results are shown below.

Color Voted %Cream 38%Teal 36%Purple 16%Other 10%

If two voters were picked at random what isthe probability that both voters chose teal?Round your answer to the nearest wholepercent.

A 3%B 13%C 48%D '72%,

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31 Find the twenty-second term in thissequence:

2, 2.8, 3.9~ 5A8'8; 7.6832;:.:

Round your answer to the nearest wholenumber.

A 2,343

B 2,433

C 3,423

D 4,323H2.bDOK2

32 To keep students busy, Karl's teacher askedthe class to find the sum of the first 1000whole numbers. Karl found the solutionalmost instantly. What solution did Karlcome up with?(Note: This problem is based off of themathematician Karl Gauss, but Karl'steacher asked him to find the first 1000numbers, not the first 100.)

A 5,050

B 500,000

C 500,500

D 5,005,000H2.dDOK2

33 Evaluate the following:7

E(-1)n+l(n2 +3n)n=l

A 25

B 37

C 40

D 65H2.e, DOK.2.·,.

326 Copyright © American Book Company

34 Find the amplitude of the following sinefunction.

y

3

y\:l.n :n: f ()

~ :n: Iln 21t2 2

-I \J2

x

A -2B 2C 7r

D 4G3.fDOK 1

35 Go-cart A and go-cart B are racing, andeach has a tire with a pebble stuck in thetread. The following graph shows thedistance of each of the pebbles above theground as the tires of the two go-carts arerotating:

y'".,t 24~!~"'-rT'-rT~rT'-"'-"''-''''~ 1-+1·~·'~'.~~+4~4"~~4-~!+4I~~~+4~~ 21 , .1 ! Ie ~l/~~4-~4-h+4-~~rl~+.~1-~~1.:1 18 /, i II , ,( \ I "

.s 151'+~-it-+H/+- - '--1--- ~r-"+"-i-~ 111- 1\ 'v i J\,' t 'i'

~ 12 "i , !., I I 'i I 1\ I I! I:g 9, i I ~ i I j

~ ' ! h J

"i5 6 r-+' 4-fH--+'J.+-'+4'-l-~H-+rt-++-I++-t-\t';+-t-l~ 3 l-++fH-t~fJ;\i-i +~+-It+-f-H--':I, -t-, l+ltl+-HI-~+ITM~ H--t-i--\t-I./! I, " i \ I -rt-f\lTQ LL~~~~7~5~A~U-~~~15~O~.8-L~-D~~X

Distance Travelled by Pebble (lnches)

I

-~~f-"-'

A --- B ------

Which of the following statements about thetwo go-carts can be determined from thegraph?

A A and B are traveling at the same speed.B B is going faster than A.C A has bigger tires than B.D B has bigger tires than A.

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