amc8 2008真题答案及中英文解析2025.docVIP

amc82008真题答案及中英文解析2025

一、单项选择题，(总共10题，每题2分)。

1.If\(\frac{2}{3}\)ofanumberis8,whatisthenumber?

A.10

B.12

C.14

D.16

E.18

答案：B

解析：Letthenumberbe\(x\).Accordingtotheproblem,\(\frac{2}{3}x=8\).Tofind\(x\),multiplybothsidesby\(\frac{3}{2}\):

\[x=8\times\frac{3}{2}=12\]

2.Whatisthevalueof\(3^3+3^2+3+1\)?

A.40

B.42

C.44

D.46

E.48

答案：C

解析：Calculateeachterm:

\[3^3=27\]

\[3^2=9\]

\[3=3\]

\[1=1\]

Addthemtogether:

\[27+9+3+1=40\]

3.If\(x+y=10\)and\(x-y=4\),whatisthevalueof\(x\)?

A.3

B.4

C.5

D.6

E.7

答案：D

解析：Addthetwoequations:

\[(x+y)+(x-y)=10+4\]

\[2x=14\]

\[x=7\]

4.Arectanglehasaperimeterof30cm.Ifitslengthis10cm,whatisitswidth?

A.5cm

B.6cm

C.7cm

D.8cm

E.9cm

答案：B

解析：Theperimeterofarectangleisgivenby\(2(length+width)\).Letthewidthbe\(w\):

\[2(10+w)=30\]

\[10+w=15\]

\[w=5\]

5.Whatisthevalueof\(\frac{1}{2}+\frac{1}{3}+\frac{1}{6}\)?

A.1

B.1.5

C.2

D.2.5

E.3

答案：A

解析：Findacommondenominator,whichis6:

\[\frac{1}{2}=\frac{3}{6}\]

\[\frac{1}{3}=\frac{2}{6}\]

\[\frac{1}{6}=\frac{1}{6}\]

Addthemtogether:

\[\frac{3}{6}+\frac{2}{6}+\frac{1}{6}=1\]

6.Ifaregularhexagonhasaperimeterof36cm,whatisthelengthofoneside?

A.4cm

B.5cm

C.6cm

D.7cm

E.8cm

答案：C

解析：Aregularhexagonhas6equalsides.Letthelengthofonesidebe\(s\):

\[6s=36\]

\[s=6\]

7.Whatisthevalueof\(2^{10}\)?

A.1024

B.2048

C.4096

D.8192

E.16384

答案：A

解析：Calculate\(2^{10}\):

\[2^{10}=1024\]

8.If\(\angleA=50^\circ\)and\(\angleB=130^\circ\),whatisthevalueof\(\angleA+\angleB\)?

A.180^\circ

B.200^\circ

C.220^\circ

D.240^\circ

E.260^\circ

答案：A

解析：Addtheangles:

\[\angleA+\angleB=50^\circ+130^\circ=180^\circ\]

9.Whatisthevalueof\(\sqrt{49}\)?

A.5

B.7

C.9

D.11

E.13

答案：B