2000年AMC 8 真题：
Problem 1
Aunt Anna is 
years old. Caitlin is 
years younger than Brianna, and Brianna is half as old as Aunt Anna. How old is Caitlin?
Problem 2
Which of these numbers is less than its reciprocal?
Problem 3
How many whole numbers lie in the interval between 
and 
Problem 4
In 
only 
of the working adults in Carlin City worked at home. By 
the "at-home" work force increased to 
. In 
there were approximately 
working at home, and in 
there were 
. The graph that best illustrates this is
![[asy] unitsize(18); draw((0,4)--(0,0)--(7,0)); draw((0,1)--(.2,1)); draw((0,2)--(.2,2)); draw((0,3)--(.2,3)); draw((2,0)--(2,.2)); draw((4,0)--(4,.2)); draw((6,0)--(6,.2)); for (int a = 1; a < 4; ++a) { for (int b = 1; b < 4; ++b) { draw((2*a,b-.1)--(2*a,b+.1)); draw((2*a-.1,b)--(2*a+.1,b)); } } label("1960",(0,0),S); label("1970",(2,0),S); label("1980",(4,0),S); label("1990",(6,0),S); label("10",(0,1),W); label("20",(0,2),W); label("30",(0,3),W); label("$\%$",(0,4),N); draw((12,4)--(12,0)--(19,0)); draw((12,1)--(12.2,1)); draw((12,2)--(12.2,2)); draw((12,3)--(12.2,3)); draw((14,0)--(14,.2)); draw((16,0)--(16,.2)); draw((18,0)--(18,.2)); for (int a = 1; a < 4; ++a) { for (int b = 1; b < 4; ++b) { draw((2*a+12,b-.1)--(2*a+12,b+.1)); draw((2*a+11.9,b)--(2*a+12.1,b)); } } label("1960",(12,0),S); label("1970",(14,0),S); label("1980",(16,0),S); label("1990",(18,0),S); label("10",(12,1),W); label("20",(12,2),W); label("30",(12,3),W); label("$\%$",(12,4),N); draw((0,12)--(0,8)--(7,8)); draw((0,9)--(.2,9)); draw((0,10)--(.2,10)); draw((0,11)--(.2,11)); draw((2,8)--(2,8.2)); draw((4,8)--(4,8.2)); draw((6,8)--(6,8.2)); for (int a = 1; a < 4; ++a) { for (int b = 1; b < 4; ++b) { draw((2*a,b+7.9)--(2*a,b+8.1)); draw((2*a-.1,b+8)--(2*a+.1,b+8)); } } label("1960",(0,8),S); label("1970",(2,8),S); label("1980",(4,8),S); label("1990",(6,8),S); label("10",(0,9),W); label("20",(0,10),W); label("30",(0,11),W); label("$\%$",(0,12),N); draw((12,12)--(12,8)--(19,8)); draw((12,9)--(12.2,9)); draw((12,10)--(12.2,10)); draw((12,11)--(12.2,11)); draw((14,8)--(14,8.2)); draw((16,8)--(16,8.2)); draw((18,8)--(18,8.2)); for (int a = 1; a < 4; ++a) { for (int b = 1; b < 4; ++b) { draw((2*a+12,b+7.9)--(2*a+12,b+8.1)); draw((2*a+11.9,b+8)--(2*a+12.1,b+8)); } } label("1960",(12,8),S); label("1970",(14,8),S); label("1980",(16,8),S); label("1990",(18,8),S); label("10",(12,9),W); label("20",(12,10),W); label("30",(12,11),W); label("$\%$",(12,12),N); draw((24,12)--(24,8)--(31,8)); draw((24,9)--(24.2,9)); draw((24,10)--(24.2,10)); draw((24,11)--(24.2,11)); draw((26,8)--(26,8.2)); draw((28,8)--(28,8.2)); draw((30,8)--(30,8.2)); for (int a = 1; a < 4; ++a) { for (int b = 1; b < 4; ++b) { draw((2*a+24,b+7.9)--(2*a+24,b+8.1)); draw((2*a+23.9,b+8)--(2*a+24.1,b+8)); } } label("1960",(24,8),S); label("1970",(26,8),S); label("1980",(28,8),S); label("1990",(30,8),S); label("10",(24,9),W); label("20",(24,10),W); label("30",(24,11),W); label("$\%$",(24,12),N); draw((0,9)--(2,9.25)--(4,10)--(6,11)); draw((12,8.5)--(14,9)--(16,10)--(18,10.5)); draw((24,8.5)--(26,8.8)--(28,10.5)--(30,11)); draw((0,0.5)--(2,1)--(4,2.8)--(6,3)); draw((12,0.5)--(14,.8)--(16,1.5)--(18,3)); label("(A)",(-1,12),W); label("(B)",(11,12),W); label("(C)",(23,12),W); label("(D)",(-1,4),W); label("(E)",(11,4),W); [/asy]](https://latex.artofproblemsolving.com/6/5/6/656eabcc57c768cb1f63e28160766b9874093f65.png)
Problem 5
Each principal of Lincoln High School serves exactly one 
-year term. What is the maximum number of principals this school could have during an 8-year period?
Problem 6
Figure 
is a square. Inside this square three smaller squares are drawn with the side lengths as labeled. The area of the shaded 
-shaped region is
![[asy] pair A,B,C,D; A = (5,5); B = (5,0); C = (0,0); D = (0,5); fill((0,0)--(0,4)--(1,4)--(1,1)--(4,1)--(4,0)--cycle,gray); draw(A--B--C--D--cycle); draw((4,0)--(4,4)--(0,4)); draw((1,5)--(1,1)--(5,1)); label("$A$",A,NE); label("$B$",B,SE); label("$C$",C,SW); label("$D$",D,NW); label("$1$",(1,4.5),E); label("$1$",(0.5,5),N); label("$3$",(1,2.5),E); label("$3$",(2.5,1),N); label("$1$",(4,0.5),E); label("$1$",(4.5,1),N); [/asy]](https://latex.artofproblemsolving.com/7/c/6/7c6ea431a00e38c9ba0b8513fa0b9a39252cfcef.png)
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dimples on a golf ball. If it takes him 
seconds to paint one dimple, how many minutes will he need to do his job?
![[asy] draw((0,0)--(-5,12)--(7,17)--(12,5)--(17,5)--(17,0)--(12,0)--(12,-12)--(0,-12)--(0,0)--(12,5)--(12,0)--cycle,linewidth(1)); label("$25$",(14.5,1),N); label("$144$",(6,-7.5),N); label("$169$",(3.5,7),N); [/asy]](https://latex.artofproblemsolving.com/3/7/2/372ee1f13836b7ad774c0aa23e598d4f8b07cbb6.png)
-centimeter length represents 
kilometers. How many kilometers does a 
-centimeter length represent?
?
people. If they shared, how many meals should they have ordered to have just enough food for the 
shots, she has made 
of her shots. After she takes 
. How many of the last 
each. Pay-A-Lot had a 20%-off sale the following day. How much could Karl have saved on the purchase by waiting a day?
of square ![[asy]defaultpen(linewidth(1)); for ( int x = 0; x < 5; ++x ) { draw((0,x)--(4,x)); draw((x,0)--(x,4)); } fill((1,0)--(2,0)--(2,1)--(1,1)--cycle); fill((0,3)--(1,3)--(1,4)--(0,4)--cycle); fill((2,3)--(4,3)--(4,4)--(2,4)--cycle); fill((3,1)--(4,1)--(4,2)--(3,2)--cycle); label("$A$", (0, 4), NW); label("$B$", (4, 4), NE); label("$C$", (4, 0), SE); label("$D$", (0, 0), SW);[/asy]](https://latex.artofproblemsolving.com/8/6/2/8629b93782f55e1fd2fa0292ae5ad9c3587cc003.png)
is a digit. For how many values of 
?
students were surveyed about their pasta preferences. The choices were lasagna, manicotti, ravioli and spaghetti. The results of the survey are displayed in the bar graph. What is the ratio of the number of students who preferred spaghetti to the number of students who preferred manicotti?
?
mountain bike. For his birthday, his grandparents send him 
, his aunt sends him 
and his cousin gives him 
. He earns 
per week for his paper route. He will use all of his birthday money and all of the money he earns from his paper route. In how many weeks will he be able to buy the mountain bike?
represents the ten digits 
, in order. What 4-digit number is represented by the code word 
?
, what day of the week is February 1?
, the inner equilateral triangle has area 
, and the three trapezoids are congruent. What is the area of one of the trapezoids?![[asy] size((70)); draw((0,0)--(7.5,13)--(15,0)--(0,0)); draw((1.88,3.25)--(9.45,3.25)); draw((11.2,0)--(7.5,6.5)); draw((9.4,9.7)--(5.6,3.25)); [/asy]](https://latex.artofproblemsolving.com/e/3/4/e34c3dede3f2bef33570072537b95ad87b3894f5.png)
, a palindrome, because it reads the same forward and backward. After riding 
more hours that day and 
the next, he notices that the odometer shows another palindrome, 
. What was his average speed in miles per hour?
![[asy] size((70)); draw((10,0)--(0,10)--(-10,0)--(0,-10)--(10,0)); draw((-2.5,-7.5)--(7.5,2.5)); draw((-5,-5)--(5,5)); draw((-7.5,-2.5)--(2.5,7.5)); draw((-7.5,2.5)--(2.5,-7.5)); draw((-5,5)--(5,-5)); draw((-2.5,7.5)--(7.5,-2.5)); fill((-10,0)--(-7.5,2.5)--(-5,0)--(-7.5,-2.5)--cycle, gray); fill((-5,0)--(0,5)--(5,0)--(0,-5)--cycle, gray); fill((5,0)--(7.5,2.5)--(10,0)--(7.5,-2.5)--cycle, gray); [/asy]](https://latex.artofproblemsolving.com/3/c/4/3c4476181cee26306aeb555b3e4b864d592dca35.png)
, 
, and 
. What was her total, to the nearest dollar?
revolutions and then counterclockwise 
revolutions. In what direction does the spinner point after the two moves?![[asy]size(96); draw(circle((0,0),1),linewidth(1)); draw((0,0.75)--(0,1.25),linewidth(1)); draw((0,-0.75)--(0,-1.25),linewidth(1)); draw((0.75,0)--(1.25,0),linewidth(1)); draw((-0.75,0)--(-1.25,0),linewidth(1)); label("$N$",(0,1.25), N); label("$W$",(-1.25,0), W); label("$E$",(1.25,0), E); label("$S$",(0,-1.25), S); draw((0,0)--(-0.5,0),EndArrow);[/asy]](https://latex.artofproblemsolving.com/3/9/f/39f6c3905c23037677847312e6fe6254d0dd9923.png)
and 
are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square?![[asy]size(100); draw((0,0)--(2,0)--(2,2)--(0,2)--cycle,linewidth(1)); draw((0,1)--(1,2)--(2,1)--(1,0)--cycle); label("$A$", (1,2), N); label("$B$", (2,1), E); label("$C$", (1,0), S); label("$D$", (0,1), W);[/asy]](https://latex.artofproblemsolving.com/e/7/8/e7899c538a174faf9963a60d09886b7fb12ae942.png)
. Then she switched the digits of the result, obtaining a number between 
and 
, inclusive. What was Mary's number?
-meter track at her school. For each lap, she ran the first 
meters at an average speed of 
, 
, and 
satisfy the inequalities 
, 
, and 
. Which of the following numbers is necessarily positive?
. What is the value of 
?
pieces of each kind, she now has three times as many blueberry jelly beans as cherry jelly beans. How many blueberry jelly beans did she originally have?
by 
blocks that can fit in a 
by 
