SAT Mathematics Level 2 Practice Test

There are 50 questions on this test. You have 1 hour (60 minutes) to

complete it.

1. Themeasuresoftheanglesof�QRSarem∠Q=2x+4,m∠R=

4x−12,andm∠S=3x+8.QR=y+9,RS=2y−7,andQS=3y−13.

Theperimeterof�QRSis

(A)11 (B)20 (C)44 (D)55 (E)68

2. Giveng(x)=xx

5 13 2-+ , g

43-c m=

(A)–1___2 (B)1__

9 (C)1___

11 (D)7___

16 (E)1__

2

3.7 103 81x y =

(A) 3539 xyx (B) 2 3 39x y xy (C) 2 3 33 9x y xy

(D) 2 3 33 3x y xy (E) 3533 xyx

SAT MATh 1 & 2 SubjecT TeST2

–6

–6 1

1

10y

K

H

G

x

6

4. Theverticesof�GHKabovehavecoordinatesG(–3,4),H(1,–3),

andK(2,7).Theequationofthealtitudeto____

HKis

(A)10x+y=–26 (B)10x+y=7 (C)10x+y=27

(D)x+10y=37 (E)x+10y=72

5. Whenthefigureaboveisspunarounditsverticalaxis,thetotalsur-

faceareaofthesolidformedwillbe

(A)144π (B)108π (C)72π (D)36π (E)9π+12

6. Iff(x)=4x2−1andg(x)=8x+7,g f(2)=

(A)15 (B)23 (C)127 (D)345 (E)2115

7. Ifpandqarepositiveintegerswithpq=36,then qp

cannotbe

(A)14

(B)49

(C)1 (D)2 (E)9

SAT MATheMATIcS LeVeL 2 PRAcTIce TeST 3

8.

2 13 4

21

3 12

x

x

+−

−−

=

(A)23

2−xx

(B)2382

−−

xx

(C)2 83 12

xx−

−

(D)2 73 12

xx−

− (E)

2 53 14

xx−

−

9. If 1251 625

a a abab43 3 102

2

=-

+

` ^j h andifaandbdonotequal0,ba =

(A)421

(B)2 (C)7621

(D)4 (E)763

10. In isosceles �KHJ, ___

HJ = 8, NL HJ⊥ , and MP HJ⊥ . If K is

10cmfrombaseHJandKL=.4KH,theareaof�LNHis

(A)4 (B)4.8 (C)6 (D)7.2 (E)16

SAT MATh 1 & 2 SubjecT TeST4

11. Theequationoftheperpendicularbisectorofthesegmentjoining

A(–9,2)toB(3,–4)is

(A)y−1=–1___2(x−3) (B)y+1=–1___

2(x+3)

(C)y+1=2(x+3) (D)y+3=2(x+1) (E)y−1=2(x−3)

12. TangentTBandsecantTCA aredrawntocircleO.DiameterABis

drawn.IfTC=6andCA=10,thenCB=

(A)2 6 (B)4 6 (C)2 15 (D)10 (E)2 33

13. Letp@q= q ppq

-.(5@3)−(3@5)=

(A)–184 (B)–59 (C)0 (D)59 (E)184

SAT MATheMATIcS LeVeL 2 PRAcTIce TeST 5

14. Gradesforthetestonproofsdidnotgoaswellastheteacherhad

hoped.Themeangradewas68,themediangradewas64,andthestan-

darddeviationwas12.Theteachercurvesthescorebyraisingeachscore

byatotalof7points.Whichofthefollowingstatementsistrue?

I.Thenewmeanis75.

II.Thenewmedianis71.

III.Thenewstandarddeviationis7.

(A)Ionly (B)IIIonly (C)IandIIonly

(D)I,II,andIII (E)Noneofthestatementsaretrue

15. Asetoftrianglesisformedbyjoiningthemidpointsofthelarger

triangles.Iftheareaof�ABCis128,thentheareaof�DEF,thesmall-

esttriangleformed,is

(A)18

(B)14

(C)12

(D)1 (E)4

SAT MATh 1 & 2 SubjecT TeST6

16. Thegraphofy=f(x)isshownabove.Whichisthegraphofg(x)=

2f(x−2)+1?

(A)

(B)

(C)

(D)

(E)

SAT MATheMATIcS LeVeL 2 PRAcTIce TeST 7

17. Thenumberofbacteria,measuredinthousands,inacultureis

modeledbytheequation ( )2.31

3.21

380175

t

t

eb t

e=

+,where t isthenumberof

dayssincetheculturewasformed.Accordingtothismodel,theculture

cansupportamaximumpopulationof

(A)2.17 (B)205 (C)380 (D)760 (E)∞

18. Aspherewithdiameter50cmintersectsaplane14cmfromthe

centerofthesphere.Whatisthenumberofsquarecentimetersinthe

areaofthecircleformed?

(A)49π (B)196π (C)429π (D)576π (E)2304π

19. Giveng(x)=9213

+−

xx

,g(g(x))=

(A)7649

+−xx

(B) 7 1224 79

xx−

+ (C) 10

21 80xx−

+

(D) 7 624 79

xx+

+ (E)

2

2

9 6 14 36 81

x xx x

− +

+ +

20. Theareaof�QED=750.QE=48andQD=52.Tothenearest

degree,whatisthemeasureofthelargestpossibleangleof�QED?

(A)76 (B)77 (C)78 (D)143 (E)145

21. Givenlog3(a)=candlog3(b)=2c,a=

(A)3c (B)c +3 (C)b2 (D) b (E)2b

SAT MATh 1 & 2 SubjecT TeST8

22. InisoscelestrapezoidWTYH, || ||WH XZ TY ,m∠TWH=120,and

m∠HWE=30.XZpassesthroughpointE,theintersectionofthediago-

nals.IfWH=30,determinetheratioofXZ:TY.

(A)1:2 (B)2:3 (C)3:4 (D)4:5 (E)5:6

23. Thelengthsofthesidesofatriangleare25,29,and34.Tothenear-

esttenthofadegree,themeasureofthelargestangleis

(A)77.6° (B)77.7° (C)87.6° (D)87.7° (E)102.3°

24. Oneoftherootsofaquadraticequationthathasintegralcoeffi-

cientsis i823

54+

−.Whichofthefollowingdescribesthequadratic

equation?

(A)800x2+1280x+737=0 (B)800x2−1280x+737=0

(C)800x2+1280x+287=0 (D)800x2−1280x+287=0

(E)800x2+1280x−287=0

25. Theparametricequationsx=cos(2t)+1andy=3sin(t)+2cor-

respondtoasubsetofthegraph

(A)( ) ( ) 1

92

11 22

=−

+− yx

(B)( ) ( ) 1

92

11 22

=−

−− yx

(C) ( )22922 −=− yx (D) ( )22

922 −−=− yx

(E) ( )2322 −−=− yx

SAT MATheMATIcS LeVeL 2 PRAcTIce TeST 9

26. A county commissioner will randomly select 5 people to form a

non-partisan committee to look into the issue of county services. If

thereare8Democratsand6Republicanstochoosefrom,whatisthe

probabilitythattheDemocratswillhavethemoremembersthanthe

Republicansonthiscommittee?

(A)6862002

(B)13162002

(C)18762002

(D)268824024

(E)2133624024

27. Giventhevectorsu=[–5,4]andv=[3,–1],|2u−3v|=

(A)[–19,11] (B) 502 (C)[19,11]

(D)2 41 3 10− (E)2 65

28. �ABChasverticesA(–11,4),B(–3,8),andC(3,–10).Thecoordi-

natesofthecenterofthecirclecircumscribedabout�ABCare

(A)(–2,–3) (B)(–3,–2) (C)(3,2)

(D)(2,3) (E)(–1,–1)

29. Eachsideofthebaseofasquarepyramidisreducedby20%.By

whatpercentmusttheheightbeincreasedsothatthevolumeofthenew

pyramidisthesameasthevolumeoftheoriginalpyramid?

(A)20 (B)40 (C)46.875 (D)56.25 (E)71.875

30.

1920cis

182

5cis9

=

(A) i232 +− (B) i232 −− (C) i232 +

(D) 322 i+− (E) 322 i

SAT MATh 1 & 2 SubjecT TeST10

31. Givenlogb(a)=xandlogb(c)=y, ( )3 452log cba

=

(A)2

4

35

x

y+ (B)xy

645+

(C)203

yx

(D)2x+4y (E)20

23

yx +

32. Theasymptotesofahyperbolahaveequationsy−1= 43 (x+3).

If a focusof thehyperbolahascoordinates (7,1), theequationof the

hyperbolais

(A)2 2( 3) ( 1)

116 9

x y+ −− = (B)

2 2( 1) ( 3)1

9 16y x− +

− =

(C)2 2( 3) ( 1)

164 36

x y+ −− = (D)

2 2( 1) ( 3)1

36 64y x− +

− =

(E)2 2( 3) ( 1)

14 3

x y+ −− =

33. Aninvertedcone(vertexisdown)withheight12inchesandbase

ofradius8inchesisbeingfilledwithwater.Whatistheheightofthe

waterwhentheconeishalffilled?

(A)6 (B)6 43 (C)8 63 (D)9 43 (E)9 63

34. Solvesin(t)=cos(2t)for–4π≤ t ≤–2π.

(A) 5, ,

6 6 2 (B)

5, ,

3 3 2

(C)23 19 5

, ,6 6 2

(D)23 19 5

, ,3 3 2

(E)11 7 5

, ,3 3 2

SAT MATheMATIcS LeVeL 2 PRAcTIce TeST 11

35. |2x−3||x−1|<2when

(A)15

<x <5 (B)15

<x <2and2<x <5 (C)x <15

orx >5

(D)x <5 (E)x >15

36. 12 32 1 28 1

k k

kk

0 0

=- -3 3

= =

c `m j/ /

(A)–5 (B)5 (C)24 (D)27 (E)30

37. If x y z3 4 2 3- + =

x y z2 8 1 8- =- -

x y z4 6 3 1- - =

thenzyx +−

1 =

(A)225

(B)3031

(C)3130

(D)192

(E)252

38. Which of the following statements is true about the function

3 3( ) 3 2cos

5 10f x x ?

I.Thegraphhasanamplitudeof2.

II.Thegraphisshiftedtotheright2.

III.Thefunctionsatisfiestheequation f f25

631=c cm m.

(A)Ionly (B)IIonly (C)IIIonly

(D)IandIIonly (E)IandIIIonly

SAT MATh 1 & 2 SubjecT TeST12

39. Allofthefollowingsolvetheequationz5=32iEXCEPT

(A)2cis(π __2) (B)2cis(9π ___

10) (C)2cis(11π ____

10)

(D)2cis(13π ____10

) (E)2cis(17π ____10

)

40. Givena1=4,a2=–2,andan=2an–2−3an–1,whatisthesmallest

valueofnforwhich|an|>1,000,000?

(A)11 (B)12 (C)13 (D)14 (E)15

41. Whichofthefollowingstatements is trueaboutthegraphofthe

function2

(2 3)( 2)(2 1)( )

4 9x x x

f xx

− + −=

−?

I.f(x)=94

hastwosolutions.

II.f(x)=76

hastwosolutions.

III.Therangeofthefunctionisthesetofrealnumbers.

(A)IIIonly (B)IandIIonly (C)IIandIIIonly

(D)IandIIIonly (E)I,II,andIII

42. Giveng(x)=9log8(x−3)−5,g –1(13)=

(A)313

(B)6 (C)61 (D)67 (E)259

43. Isosceles�QRShasdimensionsQR=QS=60andRS=30.The

centroidof�QRS is locatedatpointT.What is thedistance from

TtoQR?

(A)2 15 (B)5215 (C)3 15

(D)7215 (E)5 15

SAT MATheMATIcS LeVeL 2 PRAcTIce TeST 13

44. Diagonals AC and BD of quadrilateral ABCD are perpendicular.

AD=DC=8,AC=BC=6,m∠ADC=60°.TheareaofABCDis

(A)4 5 +8 3 (B)16 3 (C)32 3

(D)8 5 +16 3 (E)48

45. cos csc x25

41 +- cc mm=

(A)2 8 16

4x x

x+ −

+ (B)

( )

2

2

8 16

4

x x

x

+ −

+ (C)

2 8 344

x xx+ −

+

(D)( )

2

2

8 34

4

x x

x

+ −

+ (E)

( )

2

2

16 8

4

x x

x

− − −

+

46. Which of the following statements is true about the expression

(a+b)n−(a−b)n?

I.Ithas2n termsifniseven.

II.Ithas21+n termsifnisodd.

III.Theexponentonthelasttermisalwaysn.

(A)Ionly (B)IIonly (C)IandIIonly

(D)IandIIIonly (E)IIandIIIonly

47. In�VWX,sin(X)= 178 andcos(W)=–3___

5.Findcos V

2c m=

(A) 8577- (B)

852- (C)

852 (D)

859 (E) 85

77

SAT MATh 1 & 2 SubjecT TeST14

48. The intersection of the hyperbola 19)1(

8)1( 22

=+ yx –– and the

ellipse2 2( 1) ( 1)

132 18

x y+ −+ = is

(A)(3,4),(3,–4),(–5,4),(–5,–4)

(B)(3,2),(3,–2),(–5,2),(–5,–2)

(C)(3,4),(3,–2),(–5,4),(–5,–2)

(D)(–3,4),(–3,–2),(5,4),(5,–2)

(E)(3,–4),(3,2),(–5,–4),(–5,2)

49. Theequation8x6+72x5+bx4+cx3–687x2–2160x–1700=0,as

showninthefigure,hastwocomplexroots.Theproductofthesecom-

plexrootsis

(A)–4 (B)17___2 (C)9 (D)–687_____

2 (E)425____

2

50. If sin(A) = –8___17

, 3π ___2 < A < 2π, and cos(B) 0 = –24____

25, π < B < 3π ___

2,

cos(2A+B)=

(A)5544

7225−

(B)2184

7225−

(C)3696

7225−

(D)21847225

(E)55447225