1996年美国数学竞赛-AMC_12

USA

AMC12

1996

thelargestdigitthatcanbechangedtomakethe

additioncorrect?

6

8

+

2

9

4

4

5

7

5

1

2

3

6

(A)4(B)5(C)6(D)7(E)8

EachdayWaltergets$3fordoinghischoresor$10days

ofdoinghischoresdaily,Walterhasreceivedatotalof$anydaysdidWalterdo

themexceptionallywell?

A.3B.4C.5D.6E.7

(3!)!

=

3!

(A)1(B)2(C)6(D)40(E)120

Sixnumbersfromalistofnineintegersare7,8,3,5,gestpossiblevalueofthemedian

ofallninenumbersinthislistis

(A)5(B)(C)7(D)8(E)

Giventhat0

a+db+cb+dc+da+b

B.C.D.E.A.

c+db+ca+da+ca+b

Iff(x)=x

(x+1)

(x+2)

(x+3)

thenf(0)+f(−1)+f(−2)+f(−3)=

A.−8/9B.0C.8/9D.1E.10/9

Afathertakeshistwinsandayoungerchildouttodinneronthetwins’taurant

charges$4.95forthefatherand$0.45foreachyearofachild’sage,whereageisdefinedasthe

illis$9.45,whichofthefollowingcouldbetheageofthe

youngestchild?

A.1B.2C.3D.4E.5

5

2

hatPA=3,PB=4,and

AB=5,what?

√

isPD

√√

A.5B.34C.41D.213E.8

(A)−log

2

5(B)log

5

2(C)log

10

5(D)log

2

5(E)

If3=k·2

r

and15=k·4

r

,thenr=

ThisfilewasdownloadedfromtheAoPS−MathLinksMathOlympiadResourcesPage

/Page1/

USA

AMC12

1996

Howmanylinesegmentshaveboththeirendpointslocatedattheverticesofagivencube?

(A)12(B)15(C)24(D)28(E)56

Givenacircleofraidus2,therearemanylinesegmentsoflength2thataretangenttothecircle

eareaoftheregionconsistingofallsuchlinesegments.

ππ

(A)(B)4−π(C)(D)π(E)2π

42

Afunction