2010代数部分1-1.doc

2010 AMC8竞赛培训-代数部分（第一讲）数的运算1. (1996AJHSME-4) (A) (B) (C) (D) (E) Key: B2. （2007GAUSS8-18）The number n is doubled and then has y added to it. The result is then divided by 2 and has the original number n subtracted from it. The final result is(A) n(B) y(C) n + y(D) (E) Key: E3. （2007AMC8-10）For any positive integer n, define n to be the sum of the positive factors of n. For example, 6 = 1 + 2 + 3 + 6 = 12.Find (11) .(A) 13(B) 20(C) 24(D) 28(E) 30Key: D4. （2007AMC8-15）Let a, b and c be numbers with 0 a b c. Which of the following is impossible?(A) a+c b(B) ab c(C) a + b c(D) ac b(E) = aKey: A5. （2003AMC8-7）Blake and Jenny each took four 100-point tests. Blake averaged 78 on the four tests. Jenny scored 10 points higher than Blake on the first test, 10 points lower than him on the second test, and 20 points higher on both the third and fourth tests. What is the difference between Jennys average and Blakes average on these four tests?(A) 10(B) 15(C) 20(D) 25(E) 40Key: A整数的性质6. (2003AMC8-19) How many integers between 1000 and 2000 have all three of the numbers 15, 20 and 25 as factors?(A) 4(B) 5(C) 6(D) 8(E) 15Key: C7. (2007GAUSS8-15)Sally picks four consecutive positive integers. She divides each integer by four, and then adds the remainders together. The sum of the remainders is ?(A) 6(B) 1(C) 2(D) 3(E) 4Key: A8. （2004AMC8-19）A whole number larger than 2 leaves a remainder of 2 when divided by each of the numbers 3, 4, 5 and 6. The smallest such number lies between which two numbers?(A)40 and 49(B)60 and 79(C)100and129(D)210and249(E)320and 369Key: B9. (2007AMC8-18) The product of the two 99-digit numbers 303,030,303,030,303 and 505,050,505, . . . ,050,505 has thousands digit A and units digit B. What is the sum ofA and B?(A) 3(B) 5(C) 6(D) 8(E) 10Key: D10. （2002GAUSS8-20）The units digit (that is, the last digit) of is?(A) 7(B) 1(C) 3(D) 9(E) 5Key: D11. （2008GAUSS8-24）The sum of all of the digits of the integers from 98 to 101 is 9 + 8 + 9 + 9 + 1 + 0 + 0 + 1 + 0 + 1 = 38. The sum of all of the digits of the integers from 1 to 2008 is(A) 30 054(B) 27 018(C) 28 036(D) 30 036(E) 28 054Key: E12. （2003GAUSS8-23）In her backyard garden, Gabriella has 12 tomato plants in a row. As she walks along the row, she notices that each plant in the row has one more tomato than the plant before. If she counts 186 tomatoes in total, how many tomatoes are there on the last plant in the row?(A) 15(B) 16(C) 20(D) 21(E) 22Key: D13. （2005AMC8-12）Big Al, the ape, ate 100 bananas from May 1 through May 5. Each day he ate six more bananas than on the previous day. How many bananas did Big Al eat on May 5?(A) 20(B) 22(C) 30(D) 32(E) 34Key: D14. （2005AMC8-8）Suppose m and n are positive odd integers. Which of the following must also be an odd integer?(A) m + 3n(B) 3m - n(C) 3m2 + 3n2(D) (nm + 3)2(E) 3mnKey: E15. (2008GAUSS8-17) The decimal expansion of is the repeating decimal . What digit occurs in the 2008th place after the decimal point?(A) 8(B) 6(C) 5(D) 4(E) 3 Key: A16. （2002GAUSS8-15）A perfect number is an integer that is equal to the sum of all of its positive divisors, except itself. For example, 28 is a perfect number because 28=1+2+4+7+14. Which of the following is a perfect number?(A) 10(B) 13(C) 6(D) 8(E) 9Key: C17. （2008AMC8-5）Barney Schwinn notices that the odometer on his bicycle reads 1441, a palindrome, because it reads the same forward and backward. After riding 4 more hours that day and 6 the next, he notices that the odometer shows another palindrome, 1661. What was his average speed in miles per hour?(A) 15(B) 16(C) 18(D) 20(E)22Key: E应用题（一）18. (2008AMC8-20) The students in Mr. Neatkins class took a penmanship test. Two-thirds of the boys and of the girls passed the test, and an equal number of boys and gils passed the test. What is the minimum possible number of students in the class?(A) 12(B)17(C) 24(D) 27(E) 36Key: B19. （2002AMC8-17）In a mathematics contest with ten problems, a student gains 5 points for a correct answer and loses 2 points for an incorrect answer. If Olivia answered every problem and her score was 29, how many correct answers did she have?(A) 5(B) 6(C) 7(D) 8(E) 9Key: C20. （2006AMC8-23）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 ?(A) 0(B) 1(C) 2(D) 3(E) 5Key: AVocabularyadd加addition增加adjacent邻近的，相邻的approximate近似，大概average平均blank space空白cents美分clockwise顺时针方向的coin硬币combine结合，合并composite number合数consecutive连续的count计数counterclockwise逆时针方向的decimal十进制的，小数的decimal expansion十进制展开decrease减少determine确定diagram图表difference差digit数字，位dime10分美金discount打折扣divide除divisible可分开的,可除尽的divisor因子，除数equal等于even偶数的exactly恰好，准确factor因数feet英尺（单位、复数）fraction分数gain获得， 收益height高度horizontal row水平行increase增加integer整数in pairs一对儿loss损失maximum最大mean平均数, 平均值median中位数minimum最小minus减multiple倍数multiply乘nickel5分美金odd奇数的od