chapter 13 practice test 2content.randomhouse.com/.../pdfs/practicetest-2.pdf · 2018. 2. 6. ·...

Chapter 13 Practice Test 2

4 4 4 | Cracking the SAT Subject Test in Math 2

MATHEMATICS LEVEL 2—Continued

USE THIS SPACE FOR SCRATCHWORK.

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GO ON TO THE NEXT PAGE

MATHEMATICS LEVEL 2

USETHISSPACEFORSCRATCHWORK. 1. If xy ≠0and3x=0.3y, then

y

x =

(A)0.1(B)1.0(C)3.0(D)9.0(E)10.0

2. If f(x) = 3 42

x( )− ,thenhowmuchdoesf(x)

increaseasxgoesfrom2to3?

(A) 1.43(B) 1.37(C) 1.00(D) 0.74(E) 0.06

Foreachofthefollowingproblems,decidewhichistheBESTofthechoicesgiven.Iftheexactnumericalvalueisnotoneofthechoices,selectthechoicethatbestapproximatesthisvalue.Thenfillinthecorrespondingovalontheanswersheet.

Notes: (1)Ascientificorgraphingcalculatorwillbeneces-saryforansweringsome(butnotall)ofthequestionsonthistest.Foreachquestion,youwillhavetodecidewhetherornotyoushoulduseacalculator.

(2)Forsomequestionsinthistestyoumayhavetodecidewhetheryourcalculatorshouldbeintheradianmodeorthedegreemode.

(3)Figuresthataccompanyproblemsonthistestarein-tendedtoprovideinformationusefulinsolvingtheproblems.TheyaredrawnasaccuratelyaspossibleEXCEPTwhenitisstatedinaspecificproblemthatitsfigureisnotdrawntoscale.Allfigureslieinaplaneunlessotherwiseindicated.

(4)Unlessotherwisespecified,thedomainofanyfunctionfisassumedtobethesetofallrealnumbersxforwhichf(x) isarealnumber.Therangeoffisassumedtobethesetofallrealnumbersf(x),wherex isinthedomainoff.

(5)Referenceinformationthatmaybeusefulinansweringthequestionsonthistestcanbefoundbelow.

THEFOLLOWINGINFORMATIONISFORYOURREFERENCEINANSWERINGSOMEOFTHEQUES-TIONSONTHISTEST.

Volumeofarightcircularconewithradiusrandheighth:

V = 1

32≠r hπr2h

Lateralareaofarightcircularconewithcircumferenceof

thebasecandslantheight: S = 1

2c

Volumeofaspherewithradiusr: V = 4

33≠rπr3

Surfaceareaofaspherewithradiusr: S = 4πr2

VolumeofapyramidwithbaseareaBandheighth:

V = 1

3Bh

Practice Test 2 | 4 4 5



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3. Whatistheequationofalinewithay-interceptof3andanx-interceptof–5?

(A) y=0.6x+3(B) y=1.7x–3(C) y=3x + 5(D) y=3x–5(E) y=–5x+3

4. Forwhatpositivevalueofadoesa– 5 18a + equal–4?

(A) 0.56(B) 1.00(C) 1.12(D) 2.06(E) 4.12

5. Ifthesecondterminanarithmeticsequenceis4,andthetenthtermis15,whatisthefirstterminthesequence?

(A) 1.18(B) 1.27(C) 1.38(D) 2.63(E) 2.75

6. If g(x) = 5 2 3x x− , then g(6) =

(A)–54(B)–36(C)36(D)216(E)396




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7. Whichofthefollowinggraphsoffunctionsis symmetricalwithrespecttotheliney = x ?(A)

x

y

(D)

x

y

(B)

x

y

(E)

x

y

(C)

x

y

8. If0°°≤ A ≤90°and sin sin A= °1

375 , then A =

(A)12.9º(B)18.8º(C)25.0º(D)32.2º(E)45.0º




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9. Iff(x) = 12

6 112x x− ,thenwhatisthemini-

mumvalueoff(x) ?

(A) –8.0(B) –7.0(C) 3.2(D) 6.0(E) 11.0

10. x y y x− −

(A) 0

(B) x–y

(C) y–x

(D) 2 x y−(E) 2 x y+

0° ≤ A ≤90°0° ≤ B ≤90°

11. IfsinA=cosB,thenwhichofthefollowingmustbetrue?

(A) A = B(B) A = 2B(C) A = B + 45(D) A=90–B(E) A = B+180




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Total Units Production Flawed Units

April 569 15

May 508 18

June 547 16

Figure1

12. Eachmonth,someoftheautomobilesproducedattheCarcoplanthaveflawedcatalyticconvert-ers.AccordingtothechartinFigure1,whatistheprobabilitythatacarproducedinoneofthethreemonthsshownwillbeflawed?

(A) 0.01(B) 0.02(C) 0.03(D) 0.04(E) 0.05

3θ

Figure2

13. Adamsvilllebuildingcodesrequirethatawheel-chairrampmustriseatanangle(θ)ofnolessthan5°andnomorethan7°fromthehorizontal.Ifawheelchairramprisesexactly3feetasshowninFigure2,whichofthefollowingcouldbethelengthoftheramp?

(A) 19.0feet(B) 24.0feet(C) 28.0feet(D) 35.0feet(E) 42.0feet




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150

100

–10 –5 5 10

–50

50

x

y

Figure3

14. Figure3representsthegraphofthefunction y=–x4–4x3 + 14x2 + 45x–n.Whichofthefol-lowingcouldbethevalueofn ?

(A) –50(B) –18(C) 50(D) 100(E) 150

15. Whatvaluedoesx x

x

2 63 6+− −

approachasx approaches–2?

(A) –1.67(B) –0.60(C) 0(D) 1.00(E) 2.33




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16. InTitheland,thefirst1,000florinsofanyinheri-tanceareuntaxed.Afterthefirst1,000florins,inheritancesaretaxedatarateof65%.Howlargemustaninheritancebe,tothenearestflorin,inordertoamountto2,500florinsaftertheinheri-tancetax?

(A) 7,143(B) 5,286(C) 4,475(D) 3,475(E) 3,308

17. Inanengineeringtest,arocketsledispropelledintoatarget.Ifthesled’sdistancedinmetersfromthetargetisgivenbytheformulad=–1.5t2+120,wheretisthenumberofsecondsafterrocketigni-tion,thenhowmanysecondshavepassedsincerocketignitionwhenthesledis10metersfromthetarget?

(A) 2.58(B) 8.56(C) 8.94(D) 9.31(E) 11.26

18. 1

10

k=

(3k – 2) =

(A)25 (B)28 (C)145 (D)280 (E)290

19. Ifex = 5, then x =

(A) 0.23(B) 1.61(C) 1.84(D) 7.76(E) 13.59




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20. Ifthegreatestpossibledistancebetweentwopointswithinacertainrectangularsolidis12,thenwhichofthefollowingcouldbethedimen-sionsofthissolid?

(A) 3×3×9(B) 3× 6 ×7(C) 3× 8 × 12(D) 4 ×7×9(E) 4 × 8 × 8

21. RunnerAtravelsafeeteveryminute.RunnerBtravelsbfeeteverysecond.Inonehour,runnerAtravelshowmuchfartherthanrunnerB,infeet?

(A) a–60b(B) a2 –60b2

(C) 360a–b(D) 60(a–b)(E) 60(a–60b)

22. Arighttrianglehassidesintheratioof5:12:13.Whatisthemeasureofthesmallestangleinthetriangle,indegrees?

(A) 13.34(B) 22.62(C) 34.14(D) 42.71(E) 67.38




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23. If f xx

( )=+1

1,andg x

x( )= +

11, then g (f (x)) =

(A) 2

(B) x + 2

(C) 2x + 2

(D) x

x

++

2

1

(E) 2 1

1

x

x

++

24. If f(x) = (x–π)(x–3)(x–e),thenwhatisthegreatestpossibledistancebetweenpointsatwhichthegraphofy = f (x)intersectsthex-axis?

(A) 0.14(B) 0.28(C) 0.36(D) 0.42(E) 0.72

25. x

x

!!( )−=

2

(A) 0.5(B) 2.0(C) x(D) x2–x(E) x2–2x + 1




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(0, 5) (7, 5)

(0, 0) (7, 0)

AB

C

D

B C

A Dx

y

Figure4

26. WhatisthevolumeofthesolidcreatedbyrotatingrectangleABCDinFigure4aroundthey-axis?

(A) 219.91(B) 245.00(C) 549.78(D) 769.69(E) 816.24

27. Iff(x, y) = x xy y

x y

2 2

2 22−−

, then f(–x,–y) =

(A) 1

(B) 1

x y+

(C) +

x y

x y

−

(D) x y

x y−

−

(E) x y

x y+−




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28. Inordertodisprovethehypothesis,“Nonumberdivisibleby5islessthan5,”itwouldbeneces-saryto

(A) provethestatementfalseforallnumbersdivisibleby5

(B) demonstratethatnumbersgreaterthan5areoftendivisibleby5

(C) indicatethatinfinitelymanynumbersgreaterthan5aredivisibleby5

(D) supplyonecaseinwhichanumberdivis-ibleby5islessthan5

(E) showthatastatementtrueofnumbersgreaterthan5isalsotrueofnumberslessthan5

29. Aparallelogramhasverticesat(0,0),(5,0),and (2,3).Whatarethecoordinatesofthefourthvertex?

(A) (3,–2)(B) (5,3)(C) (7,3)(D) (10,5)(E) Itcannotbedeterminedfromtheinformation

given.

30. Theexpressionx x

x x

2

23 4

2 10 8+ +−

isundefinedfor

whatvaluesofx ?

(A) x={–1,–4}(B) x={–1}(C) x={0}(D) x={1,–4}(E) x={0,1,4}




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31. Forwhichofthefollowingfunctionsisf (x)>0forallrealvaluesofx ?

I. f(x) = x2 + 1 II. f(x)=1–sinx

III. f(x) = π(π x–1)

(A) Ionly(B) IIonly(C) IandIIIonly(D) IIandIIIonly(E) I,II,andIII

x

y

O

Figure5

32. Thegraphofy = f(x)isshowninFigure5.Whichofthefollowingcouldbethegraphofy=–f(–x) ?

(A)

xO

y

(B)

x

y

O

(C)

x

y

O

(D)

x

y

O

(E)

x

y

O




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33. Awireisstretchedfromthetopofatwo-foot-tall

anchortothetopofa50-foot-tallantenna.Ifthe

wireisstraightandhasaslopeof2

5,thenwhatis

thelengthofthewireinfeet?

(A) 89.18(B) 120.00(C) 123.26(D) 129.24(E) 134.63

34. If3

22

π π< <θ andsecθ =4,thentanθ =

(A) –3.93(B) –3.87(C) 0.26(D) 3.87(E) 3.93

35. CircleOiscenteredat(–3,1)andhasaradiusof4.CirclePiscenteredat(4,–4)andhasaradiusofn.IfcircleOisexternallytangenttocircleP, thenwhatisthevalueofn ?

(A) 4.00(B) 4.37(C) 4.60(D) 5.28(E) 6.25




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36. IntriangleABC, sin

sin

A

B=

7

10and

sin

sin

B

C=

5

2. If

anglesA, B,andC areoppositesidesa, b,andc,

respectively,andthetrianglehasaperimeterof

16,thenwhatisthelengthofa ?

(A) 2.7(B) 4.7(C) 5.3(D) 8.0(E) 14.0

x h (x)

-1 0

0 3

1 0

2 3

–1

37. Thetableofvaluesaboveshowsselectedcoor-dinatepairsonthegraphofh(x).Whichofthefollowingcouldbeh(x) ?

(A) x(x + 1)(x–1)(B) (x + 1)2(x–1)(C) (x–1)(x + 2)2

(D) (x–1)2(x+3)(E) (x–1)(x + 1)(2x–3)

a + b + 2c=7a–2b = 83b+2c=n

38. Forwhatvaluesofndoesthesystemofequationsabovehavenorealsolutions?

(A) n ≠–1(B) n ≤0(C) n ≥ 1(D) n>7(E) n=–15




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12

5

θ

125

Figure 6

Note: Figure not drawn to scale.

39. InFigure6,whatisthevalueofθindegrees?

(A) 62.00(B) 65.38(C) 65.91(D) 68.49(E) 68.70

40. If

l m n

p q r

s t u

A= , then

2 2 2

2 2 2

2 2 2

l m n

p q r

s t u

=

(A) 2A(B) 4A(C) 6A(D) 8A(E) 18A

41. Inthefunctiong(x) = A[sin(Bx + C)] + D,con-stantsarerepresentedbyA, B, C,andD. If g(x) istobealteredinsuchawaythatbothitsperiodandamplitudeareincreased,whichofthefollow-ingconstantsmustbeincreased?

(A) Aonly(B) Bonly(C) Conly(D) AandBonly(E) CandDonly




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42. AlloftheelementsoflistMandlistN arear-rangedinexactly20pairs,suchthateveryele-mentfromlistM ispairedwithadistinctelementfromlistN.Ifineachsuchpair,theelementfromlistMislargerthantheelementfromlistN, then whichofthefollowingstatementsmustbetrue?

(A) Themedianoftheelementsin MisgreaterthanthemedianoftheelementsinN.

(B) AnyelementofMisgreaterthananyele-mentofN.

(C) ThemodeoftheelementsinMisgreaterthanthemodeoftheelementsinN.

(D) TherangeoftheelementsinMisgreaterthantherangeoftheelementsinN.

(E) ThestandarddeviationoftheelementsinM isgreaterthanthestandarddeviationoftheelementsinN.

43. If3,5,8.333,and13.889arethefirstfourtermsofasequence,thenwhichofthefollowingcoulddefinethatsequence?

(A) a0=3;a

n + 1 = a

n + 2

(B) a0=3;a

n + 1 = 2a

n–1

(C) a a an n0 13 409

= = +; −

(D) a a an n0 13 53

= =; −

(E) a a a an n n0 1 13 73

409

= =; − −−

44. If 02

nπ≤ ≤ andcos(cosn)=0.8,thentann =

(A) 0.65(B) 0.75(C) 0.83(D) 1.19(E) 1.22




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45. Theheightofacylinderisequaltoone-halfofn,wherenisequaltoone-halfofthecylinder’sdiameter.Whatisthesurfaceareaofthiscylinderintermsofn ?

(A) 3

2

2πn

(B) 2πn2

(C) 3πn2

(D) 22

2π πn

n+

(E) 2πn2 + πn

46. If(tan θ–1)2=4,thenwhichofthefollowingcouldbethevalueofθinradianmeasure?(A) –0.785(B) 1.373(C) 1.504(D) 1.512(E) 3

47. Whichofthefollowingexpressestherangeof

valuesofy = g(x),ifg(x) = 5

4x + ?

(A) {y: y ≠0}(B) {y: y ≠1.25}(C) {y: y ≠–4.00}(D) {y: y>0}(E) {y: y ≤–1ory ≥1}



USETHISSPACEFORSCRATCHWORK.

2 2 2 2 22 2 2 2

48. If csc θ =1

3t,thenwheredefined,cosθ =

(A) 3t

(B) 1 3 2t−

(C) 1 9 2t−

(D) 3

1 3 2

t

t−

(E) 3

1 9 2

t

t−

49. Iff(x, y) = xy y

x y

++ ,thenwhichofthefollowing

statementsmustbetrue?

I. If x=0andy ≠0,thenf(x, y) = 1. II. If x = 1, then f(x, x) = 1.

III. f(x, y) = f(y, x)

(A) Ionly(B) IIonly(C) IandIIonly(D) IandIIIonly(E) I,II,andIII

50. Atriangleisformedbythex-axis,they-axis,andtheliney = mx + b. If m=–b3,thenwhatisthevolumeoftheconegeneratedbyrotatingthistrianglearoundthex-axis?

(A) π9

(B) π3

(C) π

(D) 3π

(E) 9π

S T O PIFYOUFINISHBEFORETIMEISCALLED,YOUMAYCHECKYOURWORKONTHISTESTONLY.DONOTWORKONANYOTHERTESTINTHISBOOK.

chapter 13 practice test 2content.randomhouse.com/.../pdfs/practicetest-2.pdf · 2018. 2. 6. ·...

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