1996小学数学奥林匹克试题
预赛(A)卷
 

1.计算:=_________。

2.下面五个图形中,有一个不是正方形的展开图:

          
  (1)    (2)    (3)     (4)   (5)
  那么“不是的”图形编号是__________。

3. 将60分成10个质数之和,要求最大的质数尽可能小,那么其中最大的质数是________。

4. 减去一个分数,加上同一个分数,两次计算结果相等,那么这个相等的结果是_____。

5.右面残缺算式中已知三个“4”,那么补全后它的乘积是__________。

6.有A 、B两个整数,A的各位数字之和为35,B的各位数字之和为26,两数相加时进位三次,那么A+B的各位数字之和是__________。

7.苹果和梨各有若干只,如果5只苹果和3只梨装一袋,还多4只苹果,梨恰好装完;如果7只苹果和3只梨装一袋,苹果恰好装完,梨还多12只,那么苹果和梨共有__________只。

8.甲班51人,乙班49人,某次考试两个班全体同学的平均成绩是81分,乙班的平均成绩比甲班的平均成绩高7分,那么乙班的平均成绩是__________分。

9.在大于1000的整数中,找出所有被34除后商与余数相等的数,那么这些数的和是__________。

10.高中学生的人数是初中学生人数的,高中毕业生的人数是初中毕业生人数的,高、初中毕业生毕业后,高、初中留下的人数都是520人,那么高、初中毕业生共有_____人。

11.如左图,一个长方形的纸盒内,放着九个正方形的纸片,其中正方形A和B的边长分别为4和7,那么长方形(纸盒)的面积是__________。

12.甲和乙两地相距100千米,张先骑摩托车从甲出发,1小时后李驾驶汽车从甲出发,两人同时到达乙地。摩托车开始速度是50千米/小时,中途减速为40 千米/小时。汽车速度是80千米/小时。汽车曾经在途中停驶10分钟,那么张驾驶的摩托车减速时在他出发后的__________小时。

预赛(B)卷

1.同预赛(A)卷第1题。

2.将50拆分成10个质数之和,要求其中最大的质数尽可能大,那么这个最大的质数是__________。

3.同预赛(A)卷第2题。

4.同预赛(A)卷第4题。

5.规定:(3)=2×3×4,(4)=3×4×5,(5)=4×5×6,…,(10)=9×10×11,…如果,那么方框代表的数是__________。

6.同预赛(A)卷第5题。

7.有A、B两个整数,A的各位数字之和为17,B的各位数字之和为11,两数相加时进位两次,那么A+B的各位数字之和是__________。

8.原有男、女同学325人,新学年男生增加25人,女生减少5%,总人数增加16人,那么现有男同学__________人。

9.苹果362个,梨234个,等分给若干位小朋友,最后多了5个苹果和3个梨,每人分到的苹果和梨的总数不超过30个,那么小朋友有__________人。

10.如图,长方形面积为35平方厘米,左边直角三角形的面积为5平方厘米,右上角直角三角形面积为7平方厘米,那么中间三角形(阴影部分)面积是__________平方厘米。

11.同预赛(A)卷第10题。

12.张、李两人骑自行车同时从甲地出发,向同一方向行进。张的速度比李的速度每小时快4千米,张比李早20分钟通过途中乙地。当李到达乙地时,张又前进了8千米,那么甲、乙两地距离是__________千米。

预赛(民族)卷

1.同预赛(A)卷第1题。

2.1996不同的质数有几个,它们的和是__________。

3.右面乘法算式缺了一些数字,补全后它的乘积是__________。

4. 规定:(3)=2×3×4,(4)=3×4×5,(5)=4×5×6,…,(10)=9×10×11,…。如果,那么方框内应是__________。

5.同预赛(A)卷第4题。

6.两个整数,它们的积能被和整除,就称为一对"好数",例如70与30,那么在1、2、…、16 这十六个整数中,有好数__________对。

7.有A、B两个整数,A的各位数字之和是8,B的各位数字之和为7,两数相加时进位一次,那么A+B的各位数字之和是__________。

8.同预赛(A)卷第8题。

9.有四个不同整数,它们的平均数是14,三个大数的平均数是5,三个小数的平均数是。如果第二大的数是奇数,那么它是__________。

10.如右图,左面是一个等腰直角三角形(正方形的一半),右面是一个梯形,它们恰好拼成一个长方形。如果梯形的上底长是下底长的,那么三角形面积是梯形面积的__________%(百分数)。

11.同预赛(A)卷第7题。

12.同预赛(A)卷第12题。

决赛(A)卷

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