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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
F1.b DOK 2
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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
G3.dDOK2
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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 [~ !]
Il.dDOK I D
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
Dl.c DOK 3
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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
Dl.b DOK 3
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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
, , Dl.cDOK 2
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
D2.aDOK2
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
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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
159C.lcDOK3
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
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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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