2006 AMC 8 真题与答案及免费中文视频详解(翰林独家)


2006 AMC 8 Problems & Solutions

2006 AMC 8 真题与答案及中文视频详解(翰林独家)

Problem 1

Mindy made three purchases for 68168bcc4d01aa7aec743b633742b464519a242ae0b506b83b576af8cf6e642d947fd2dfe10c66b3, and 2a8a525881ca3fd279d0e34b225d62495687339a. What was her total, to the nearest dollar?





Problem 2

On the AMC 8 contest Billy answers 13 questions correctly, answers 7 questions incorrectly and doesn't answer the last 5. What is his score?



Problem 3

Elisa swims laps in the pool. When she first started, she completed 10 laps in 25 minutes. Now she can finish 12 laps in 24 minutes. By how many minutes has she improved her lap time?



Problem 4

Initially, a spinner points west. Chenille moves it clockwise b6c1f128b6984cebccb828f839748e2c894485dc revolutions and then counterclockwise bd187a7fe0e2167ff693aab9c1a76cc2d7d4f44c revolutions. In what direction does the spinner point after the two moves?




Problem 5

Points 299ddf7c0f03ea46bf09f81f93adeea0756aa15c and 9ffb448918db29f2a72f8f87f421b3b3cad18f95 are midpoints of the sides of the larger square. If the larger square has area 60, what is the area of the smaller square?




Problem 6

The letter T is formed by placing two 3c357e004b6a219b581c96a89fe448077ca1cdb2 inch rectangles next to each other, as shown. What is the perimeter of the T, in inches?




Problem 9

What is the product of c6afca46c66b0378b58e9c3ea02cb9be64dfd394 ?



Problem 10

Jorge's teacher asks him to plot all the ordered pairs 5ba43dbafbe2a629e4d0301a47c5c7cd4cb45901 of positive integers for which 9ee4b825a2e36ae093ed7be5e4851ef453b34914 is the width and 9b25f8e64b484493fda944d25cad453423041fe6 is the length of a rectangle with area 12. What should his graph look like?







Problem 11

How many two-digit numbers have digits whose sum is a perfect square?



Problem 12

Antonette gets aa4c1a3a8cac685385a2cb0b9459671466814a21 on a 10-problem test, 87cc18e719d1a8e2cf150e5e347aa7958f8035d3 on a 20-problem test and 16f96f13ccefc8551b345cf2752f88a2c1e37f13 on a 30-problem test. If the three tests are combined into one 60-problem test, which percent is closest to her overall score?



Problem 13

Cassie leaves Escanaba at 8:30 AM heading for Marquette on her bike. She bikes at a uniform rate of 12 miles per hour. Brian leaves Marquette at 9:00 AM heading for Escanaba on his bike. He bikes at a uniform rate of 16 miles per hour. They both bike on the same 62-mile route between Escanaba and Marquette. At what time in the morning do they meet?



Problem 14

Problems 14, 15 and 16 involve Mrs. Reed's English assignment.

A Novel Assignment

The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds.

If Bob and Chandra both read the whole book, Bob will spend how many more seconds reading than Chandra?


Problem 15

Problems 14, 15 and 16 involve Mrs. Reed's English assignment.

A Novel Assignment

The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds.

Chandra and Bob, who each have a copy of the book, decide that they can save time by "team reading" the novel. In this scheme, Chandra will read from page 1 to a certain page and Bob will read from the next page through page 760, finishing the book. When they are through they will tell each other about the part they read. What is the last page that Chandra should read so that she and Bob spend the same amount of time reading the novel?


Problem 16

Problems 14, 15 and 16 involve Mrs. Reed's English assignment.

A Novel Assignment

The students in Mrs. Reed's English class are reading the same 760-page novel. Three friends, Alice, Bob and Chandra, are in the class. Alice reads a page in 20 seconds, Bob reads a page in 45 seconds and Chandra reads a page in 30 seconds.

Before Chandra and Bob start reading, Alice says she would like to team read with them. If they divide the book into three sections so that each reads for the same length of time, how many seconds will each have to read?


Problem 17

Jeff rotates spinners 4b4cade9ca8a2c8311fafcf040bc5b15ca507f529866e3a998d628ba0941eb4fea0666ac391d149a and eff43e84f8a3bcf7b6965f0a3248bc4d3a9d0cd4 and adds the resulting numbers. What is the probability that his sum is an odd number?



Problem 18

A cube with 3-inch edges is made using 27 cubes with 1-inch edges. Nineteen of the smaller cubes are white and eight are black. If the eight black cubes are placed at the corners of the larger cube, what fraction of the surface area of the larger cube is white?


Problem 19

Triangle e2a559986ed5a0ffc5654bd367c29dfc92913c36 is an isosceles triangle with 7a466c16eabfd85eaa3c5c5e1ed6cab3a27d200c. Point 9ffb448918db29f2a72f8f87f421b3b3cad18f95 is the midpoint of both e33fe7d65facd8868f58b6e94ddc7f153a5a3f9f and 5e8bc36793a7c64d05fff20d519f0f72d9256fab, and 95eaca439ccbf2863a43b05f4de566ccdabdc392 is 11 units long. Triangle a6adfd3ad27a2dddeb0af7131d73c33c86991e93is congruent to triangle b3d74045abcfa098fd661ad0693fc7461570ad63. What is the length of 4373e7b4be983c0315e82e1fda1df66ed34dd7fb?



Problem 20

A singles tournament had six players. Each player played every other player only once, with no ties. If Helen won 4 games, Ines won 3 games, Janet won 2 games, Kendra won 2 games and Lara won 2 games, how many games did Monica (the sixth player) win?


Problem 21

An aquarium has a rectangular base that measures e59e2c6e83eb78cca610a5fd4070ae01c8d4ae60 cm by 78792fe4680a164f537ea72a4f900e4471433c3b cm and has a height of 906734e2f1010e9a171ffee8050cbc0649cea37c cm. The aquarium is filled with water to a depth of 78916550838bd31d66e4cdefbc366edb11fd00bd cm. A rock with volume 65358636f817cd1d7b37222ba577ed6261c8a1cf is then placed in the aquarium and completely submerged. By how many centimeters does the water level rise?



Problem 22

Three different one-digit positive integers are placed in the bottom row of cells. Numbers in adjacent cells are added and the sum is placed in the cell above them. In the second row, continue the same process to obtain a number in the top cell. What is the difference between the largest and smallest numbers possible in the top cell?



Problem 23

A box contains gold coins. If the coins are equally divided among six people, four coins are left over. If the coins are equally divided among five people, three coins are left over. If the box holds the smallest number of coins that meets these two conditions, how many coins are left when equally divided among seven people?



Problem 24

In the multiplication problem below 019e9892786e493964e145e7c5cf7b700314e53bff5fb3d775862e2123b007eb4373ff6cc1a34d4ec3355896da590fc491a10150a50416687626d7cc9ffb448918db29f2a72f8f87f421b3b3cad18f95 and are different digits. What is b831312585cb4ab6697896f86b72accbddbc4b45?




Problem 25

Barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. The sums of the two numbers on each of the three cards are equal. The three numbers on the hidden sides are prime numbers. What is the average of the hidden prime numbers?