COMO-马来西亚数学邀请赛

MALAYSIA MATHEMATICS INVITATIONAL

学生资料

英文姓名

Name

班级

Class

学校名称

School Name

2017

小学六年级 STANDARD 6

1 小时

INSTRUCTIONS AND INFORMATION

1. Do not open the booklet until told to do so by your teacher.

未获监考老师许可之前不可翻开此比赛试卷。

2. This question paper consists of 30 questions.

本试卷共有 30题。

3. Diagrams are NOT drawn to scale. They are intended only as aids.

题目所提供之图形只是示意图，不一定精准。

4. Neither mathematical tables nor calculators may be used.

不准使用数学表或计算器。

5. Write your answers in the answer boxes on the separate answer sheet provided.

答案请另填写在所提供的作答卷的指定位置上。

6. Working may be shown in the space below each question.

算式可写在试卷的任何空格里。

7. Marks are awarded for correct answers only.

只有正确的答案才能得分。

8. The MiMAS reserves the right to re-examine students before deciding whether to grant

official status to their score.

为确保竞赛之公平及公正，MiMAS主办单位保留要求考生重测之权利。

6 6

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1 - 10 题，每题 3 分。

1. 1~15 中的质数共有□个，合数共有○个，则 □ x ○ = ?

From 1 ~ 15, there are □ prime number and ○ composite number.

The value of □ x ○ = ?

(A) 56 (B) 49 (C) 54 (D) 48

2. 已知 81

3÷ 3

1

3= □ ÷ 10 = ○，则 □－○＝？

Given that 81

3÷ 3

1

3= □ ÷ 10 = ○, then □－○＝？

(A) 215

3 (B) 26

5

2 (C) 22

2

1 (D) 27

2

1

3. 一束花有 6 朵玫瑰和 9 朵郁金香，请问郁金香和玫瑰数量比的比值为多少？

A bunch of flower has 6 roses and 9 tulips. What is the ratio of number of tulips to number of roses?

(A) 2

1 (B)

3

2 (C) 1

2

1 (D) 1

3

2

4. 下面各组数中，两个数互质的共有几组？

How many groups of two numbers below are co-prime each other?

(I) 18，35 (II) 28，49 (III) 38，95

(IV) 52，117 (V) 63，119 (VI) 102，133

(A) 2 组

2 groups

(B) 3 组

3 groups

(C) 4 组

4 groups

(D) 5 组

5 groups

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5. 如果 4÷3＝□……0.01，3.2÷○＝9……0.05，则 □＋○＝？

If 4÷3＝□……0.01，3.2÷○＝9……0.05 then □＋○＝？

(A) 1.65 (B) 1.68 (C) 1.71 (D) 1.74

6. 下面哪一个比的最简整数比和其他不同？

Which of the following has different ratio?

(A) 1

7：

1

8 (B) 40：35 (C) 2

2

3：2

1

3 (D) 2

4

5：3.2

7. 已知□、○、△是三个连续正整数，且□×○×△= 720，则□ + ○ + △ =?

Given that □、○、△ are three continuous integer and □×○×△= 720.

Find □ + ○ + △ =？

(A) 24 (B) 30 (C) 27 (D) 33

8. 右图为弟弟的模型火车轨道示意图，两圆的直径分别

为 3.5 公尺和 7.5 公尺，火车在轨道上从 A→B→C→A→

D→E→F→A 绕行 1 次。请问这列火车大约走了几公

尺？(圆周率以 3.14 计算，并将结果四舍五入取到整

数位)

Right figure is the train track of Brother’s model train.

The Diameter of two circles are 3.5 m and 7.5 m

respectively. The train circled track once according A→

B→C→A→D→E→F→A. How long does these train travel

in m?(PI = 3.14, and round the result into integer)?

(A) 36 公尺

36 m

(B) 35 公尺

35 m

(C) 34 公尺

34 m

(D) 33 公尺

33 m

A

B

C

D

E

F

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9. 半泽骑脚踏车上学，当其中一个轮胎向前滚动 20 圈时，脚踏车向前移动了 37.68

公尺，请问这个轮胎的直径为多少公分? (圆周率以 3.14 计算)

Ben rides a bike to school, when one of the tires rolls forward by 20 turns, the bike move forward 37.68 m. What is the value of diameter of these tire in cm? (PI = 3.14)

(A) 30 公分

30 cm

(B) 40 公分

40 cm

(C) 50 公分

50 cm

(D) 60 公分

60 cm

10. 关于直径 7 公分的圆和半径 7 公分的圆，下列叙述何者正确？

Which of the following statement is true about the circle with 7 cm diameter and circle with 7 cm radius?

(A) 前者为后者的 2 倍放大图

The previous ones is 2 times enlarge view of the later ones

(B) 前者为后者的 4 倍放大图

The previous ones is 4 times enlarge view of the later ones

(C) 前者为后者的 1

2 倍缩图

The previous ones is 1

2 times enlarge view of the later ones

(D) 前者为后者的 1

4 倍缩图

The previous ones is 1

4 times enlarge view of the later ones

11 - 20 题，每题 4 分。

11. 将右边的比例尺用比值表示，则下列何者正确？

Which of the following is correct according the scale ratio on the right figure?

(A) 1

40 (B)

1

80 (C)

1

4000 (D)

1

8000

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12. 在地图上，将甲、乙、丙三个乡镇连接起来，恰好围成一个三角形；已知地图上

的比例尺为 1:75000，图上甲、乙两乡镇相距 5 公分，乙、丙两乡镇相距 9 公分，

请问甲、丙两乡镇的实际距离不可能为下列何者？

On the map, connected Town A, Town B and Town C, it formed a triangle. Given that the scale ratio of map is 1:75000. On the map, the distance between Town A and Town B is 5 cm, Town B and Town C is 9 cm. Which of the following is NOT the real distance between Town A and Town C?

(A) 3 公里

3 km

(B) 5 公里

5 km

(C) 7 公里

7 km

(D) 10 公里

10 km

13. 下面哪一个图形的面积最大？

Which of the following shape has biggest area?

(A) 底 8 公分、高 8 公分的平行四边形

A parallelogram with 8 cm base and 8 cm height

(B) 直径 10 公分的圆

A circle with 10 cm diameter

(C) 圆心角 60 度、半径 12 公分的扇形

A sector with 60 degree central angle, 12 cm radius

(D) 周长 34 公分的正方形

A square with 34 cm perimeter

14. 右图中，阴影部分和白色部分的面积相差多少平方公分？

(圆周率以 3.14 计算，并将结果四舍五入取到整数字)

What is the difference of the area between the shaded area and white area in cm2 on the right figure? (PI = 3.14, round the result into integer)

(A) 924

924 (B) 923

923 (C) 831

831 (D) 830 平方公分

830 cm2

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15. 336 和 560 这两个整数可以同时被一个二位数整除，请问符合条件的所有二位数之

和为多少？

336 and 560 are divisible by a 2-digit number without remainder. What is the sum of these 2-digit numbers which has this property?

(A) 98 (B) 100 (C) 112 (D) 114

16. 一杯可乐的容量为 0.55 公升，同乐会原先准备了 29 杯的可乐，后来发现忘了将 4

位老师计算在内，于是重新装杯，如果每人一杯，且分到的可乐容量要一样多，则

每人大约可以分到多少公升的可乐。(用四舍五入法取到小数第二位)

One cup of coca-cola is 0.55 liter, one association has prepare 29 cups of coca-cola. Later they found out that forget to include 4 teachers, then they reloading each cup. If everyone get a cup with same capacity. How many liters of coca-cola everyone get. (Round the result into second decimal place)

(A) 0.48公升

0.48 l

(B) 0.46公升

0.46 l

(C) 0.49公升

0.49 l

(D) 0.47公升

0.47 l

17. 有一块扇形披萨，半径为 16 公分，周长约为 69.68 公分，请问这块披萨的面积约

为多少平方公分? (圆周率以 3.14 计算，并将结果四舍五入取到整数字)

A piece of pizza in sector shape, 16 cm radius, has 69.68 cm of perimeter. What is the value of area of these pizza in cm2? (PI=3.14, round the result into integer)

(A) 299

299

(B) 300

300

(C) 301

301

(D) 302 平方公分

302 cm2

18. 直树 5 分钟可以打 175 个字，打一篇 574 个字的文章，需要多久的时间？

Aeron types 175 words in 5 minutes. How long he need to finish a 574 words article?

(A) 16 分钟 36 秒

16 min 36 s

(B) 16 分钟 48 秒

16 min 48 s

(C) 16 分钟 12 秒

16 min 12 s

(D) 16 分钟 24 秒

16 min 24 s

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19. 橘线公交车每 18 分钟开出一班，红线公交车每 24 分钟开出一班，在上午 6 时 20

分，两线公交车同时开出，则下一次两线公交车同时开出是上午□时○分；

请问□×○=?

Orange line bus leave station every 18 minutes, red line bus leave station every 24 minutes. At 6:20 am, both line buses leave station at the same time, then next

time both line bus leave station together is □:○ am。 What is □×○＝？

(A) 182 (B) 224 (C) 294 (D) 352

20. 有141

4 公斤的燕麦，每

7

8 公斤装成一袋，最多可以装成 □ 袋，还剩下 ○公斤？

请问□×○＝?

We have 141

4 kg of oat, every

7

8 kg pack into a pack, up to □ packs, leaves ○

kg of oat. What is □×○＝?

(A) 4 (B) 2 (C) 12 (D) 6

21 - 30 题，每题 5 分。

21. 计算： 8.69－57

1×0.56＋4

16

5÷3.45＝？

Compute : 8.69－57

1×0.56＋4

16

5÷3.45＝？

22. 西瓜 15 公斤的批发价格为 268 元，尚青超级市场买进西瓜若干公斤，一共为 4556

元，请问尚青超级市场买进多少公斤的西瓜？

The wholesale price of 15 kg watermelon is $268, A supermarket buy some watermelon in total of $4556. How many kg of watermelon does A supermarket buy?

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23. 用一些长 15 公分、宽 12 公分的相同长方形纸片，拼成一个正方形，所拼出来最小

的正方形面积为多少平方公分？

Make a square by using some rectangles, which has length of 15 cm and width of 12 cm. What is the smallest area of the square can be make, in cm2?

24. 一包软糖卖 40 元，成本为 13.5 元，请问至少要卖几包才能赚到 1600 元？

The sale price of a pack of candy is $40, it cost $13.5. How many pack of candy have been sale to get $1600 profit?

25. 如右图，四边形 ABCD 为一个平行四边形，

请算出阴影部分的面积为多少? (圆周率以

3.14 计算)

On right figure, ABCD is a parallelogram. What is the area of the shaded region? (PI=3.14)

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26. 将4

13化为小数，从小数点后第一个数字算起，连续 2013 个数字的和为多少？

Convert 4

13 into decimal. What is the sum of the first 2013 numbers after the

decimal point？

27. 台湾与日本有一个小时的时差，当台湾下午 2:00 时，日本是下午 3:00；台湾的张

小姐与日本的半泽先生各有一只不准确的表，张小姐的表每天快 64 秒钟，半泽先

生的表每天慢 80 秒钟，现将二人的表拨成当地的正确时间，则几天后二人的表会

指着相同的时间？

Time difference between Taiwan and Japan is 1 hour, which means It is 2 p.m. in Taiwan, 3 pm in Japan. Ms. Chong in Taiwan and Mr. Ban in Japan both have an inaccurate watch. The watch of Ms. Chong fasts 64 seconds per day. The watch of Mr. Ban slows 80 seconds per day. Now, both of them allocated the watch into the local correct time. How many days later both watch will have the same time?

28. 两个合数的乘积为 11774，且它们的最大公因子为 29，则这两个数的和为多少？

The product of the two composite numbers is 11774 and the HCF is 29. What is the sum of these two numbers?

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29. 若 4𝑎𝑏9̅̅ ̅̅ ̅̅ ̅ 可以写成 P×P，其中 P 为一个正整数，则 𝑎 + 𝑏 =?

If 4𝑎𝑏9̅̅ ̅̅ ̅̅ ̅ can be write in P×P， P is a positive integer, then 𝑎 + 𝑏 =?

30. 从 3976 到 7893 的整数中，十位数字与个位数字相同的数共有多少个？

How many numbers, which the digit in the tens place are same with the digit in the ones place, in between 3076 to 7893?

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