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淮安某重点中学小升初自主招生数学试卷

淮安某重点中学小升初自主招生数学试卷
淮安某重点中学小升初自主招生数学试卷

淮 安 小 升 初 自 主 招 生

数 学 试 题2008

1. 小说《达·芬奇密码》中的一个故事里出现了一串神秘排列的数:1,1,2,3,5,8,…,则这列数的第8个数是 (C)

A.17

B.19

C.21

D.34

2. 我国古代的“河图”是由3×3的方格构成,每个方格内均有数目不同的点图,每一行、每一列以及每一条对角线上的三个点图的点数之和均相等.

如图给出了“河图”的部分点图,

请你推算出P 处所对应的点图. 有以下4个点图可供选择 ① ② ③ ④

其中,正确的是 (C)

A.①

B.②

C.③

D.④

3. 用M,N,P,Q 各代表四种简单几何图形(线段、等边三角形、正方形、圆)中的一种. 图1—图4是由M ,N ,P ,Q 中的两种图形组合而成的(组合用“&”表示).

那么,表示P&Q 的有以下4个组合图形可供选择

① ② ③ ④

其中,正确的是 (B )

A.①

B.②

C.③

D.④

4. A 和B 都是自然数,而且A ÷B=5,则A 和B 的最大公约数是 (D)

A.1

B.5

C.A

D.B

5. 现有甲、乙、丙、丁、戊五个同学,他们分别来自a 小学、b 小学、c 小学.已知:

(1)每所学校至少有他们中的一名学生;(2)在b 小学联欢会上,甲、乙、戊作为被邀请的客人演奏了小提琴;(3)乙过去曾在c 小学学习,后来转学了,现在同丁在同一个

M&P N&P N&Q M&Q 图1 图2 图3 图

4

根据以上叙述可以断定甲所在的学校为 (C)

A. a 小学

B.b 小学

C. c 小学

D.不确定

6. 图1是三个直立于水平面上的形状完全相同的几何体(下底面为圆面,单位:cm ). 将它们拼成如图2的新几何体,则该新几何体的体积用π表示, 应为 (B)

A.64πcm 3

B.60πcm 3

C.56πcm 3

D.40πcm 3

7. 如图是测量一颗玻璃球体积的过程:

(1)将300cm 3的水倒进一个容量为500cm 3

的杯子中;

(2)将四颗相同的玻璃球放入水中,结果水没有满;

(3)再加一颗同样的玻璃球放入水中,结果水满溢出.

根据以上过程,推测这样一颗玻璃球的体积在 (C)

A.20cm 3以上,30cm 3以下

B.30cm 3以上,40cm 3以下

C.40cm 3以上,50cm 3以下

D.50cm 3以上,60cm 3以下

8. 如图,按英文字母表A 、B 、C 、D 、E 、F 、G 、H

案中,字母“O ”出现的个数为 (B) A.27 B.29 C.31 D.33

9. 下面有4个图形

① ② ③ ④

其中, 不能折成正方体的是 (B)

A.①

B.②

C.③

D.④

图2 图1

10. 如图所示, 四个小长方形的面积分别是9、6、8、S 平方厘米,则S 为 (A)

A.12

B.11

C.10

D.9

11. 电影门票30元一张,降价后观众增加1倍,收入增加13

,则一张门票降价 (D) A.25元 B.20元 C.15元 D.10元

12. 如图,一个正方形, 边长增加5米, 面积增加125米2, 则原来这个正方形的边长为 (A)

A.10米

B.20米

C.50米

D.100米

13. 用6个长、宽、高分别为3、2、1厘米的长方体拼成一个大长方体,则大长方体的表面积最小为 (C )

A.80平方厘米

B. 72平方厘米

C.66平方厘米

D.56平方厘米

14. 大于27而小于57

的分数有 (D) A.2个 B.5个 C.8个 D.无数个

15. 一列火车以同一速度驶过两个隧道,第一隧道长420米, 用了27秒,第二隧道长480米,用了30秒, 则这列火车的长度是 (D)

A.20米

B.54米

C.60米

D.120米

16. 小明在计算除法时,把被除数472错看成427,结果商比原来小5,但余数恰好相同,则该题的余数是 (D)

A.9

B.7

C.5

D.4

9

S 6

85米5米

17.如图,一个大长方形恰好分成6个小正方形,其中最小的正方形面积是1平方厘米,则这个大长方形的面积为(B) A.154平方厘米 B.143平方厘米

C.132平方厘米

D.120平方厘米

18.两支粗细、长短都不同的蜡烛,长的能点燃7小时, 短的能点燃10小时. 同时点燃4小时后,两支蜡烛的长度相同. 那么,原来短蜡烛的长度与长蜡烛的长度的比为(D) A.7:10 B.3:5 C.4:7 D.5:7

19.一辆接送学生的汽车,离开车库时,车上只有一个司机和一个学生,后来共有3个车站有学生上车,一路上没有学生下车.在第一个车站以后的每一个车站,上车的学生数是在前一站上车的学生数的两倍. 当汽车到达学校的时候,车上的学生人数只可能是(B)

A.48

B.43

C.35

D.32

20.将2008减去它的1

2

,再减去余下的

1

3

,再减去余下的

1

4

,……依此类推,直至最后减去余

下的

1

2008

,最后的结果是(C)

A. 2007

2008

B.

2006

2007

C. 1

D.

2009

2008

F E D

C

B

A

21.如图,沿着边长为90米的正方形,按A→B→C→D→A……方向,甲从A以63米/分的速度,乙从B以72米/分的速度同时行走,当乙第一次追上甲时是在正方形的某个顶点处,则这个顶点是 (B) A.顶点A B.顶点B

C.顶点C

D.顶点D

22. 将整数1,2,3,…,按如图所示的方式排列. 这样,第1次转弯的是2,第2次转弯的是3,第3次转弯的是5,第4次转弯的是7,…。则第16次转弯的是(C)

A.71

B.72

C.73

D.74

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