SASMO竞赛六年级（小学六年级）样题及答案

新加坡国际奥林匹克数学学术活动 (SINGAPORE & ASIAN SCHOOLS MATH OLYMPIAD)，简称 SASMO，创立于2006年，是新加坡国际数学学术活动中心 SIMCC 主办的其中一项国际数学学术活动。

与传统的奥数比赛相比，SASMO 团队在题目设计中投入了无数的时间和心血，使得参赛者在 SASMO 数学学术活动中可以表现的更加出色——SASMO 学术活动以现实和高标准的方式来拓展学生未被开发的潜力，激发出其内在的数学家思想以及更高阶思维技巧(HOTS)。

今天这篇文章将会对于Grade 6的部分学术活动样题做展示：

1. Find the smallest whole number between 1 and 100 that is divisible by 12 and by 30.

2. Find the value of (1 + 1/2 ) × (1 + 1/3 ) × (1 + 1/4 ) × …× (1 + 1/2014)

3. The diagram shows a quadrant OAB of a circle with centre O and radius 7cm. Given that the perimeter of the rectangle OPQR is 20cm, find the perimeter of the shaded region. (Take π to be 22/7 ）

4. The average mass of a duck and a chicken is 4 kg. The duck is 1.2 kg heavier than the chicken. Find the mass of the duck.

5. A man travelled at 120 km/h for the first half of a 12-km journey. Then he travelled at 60 km/h for the rest of his journey. What is his average speed for the whole journey?

6. Amy buys an item for a 20% discount during a sale, but she still needs to pay a 5% GST (Goods and Services Tax). She is given two options.

Option A: 20% discount first, then add 5% GST

Option B: Add 5% GST first, then 20% discount

Which option is cheaper for Amy? Or does it not matter?

7. How many digits are there before the 50th ‘8’ of the following number? 85855855585555855555…

8. Find the next term of the following sequence: 1, 4, 9, 7, 7, 9, 4, 1, 9, 1，...

9. Given that 5! means 5*4*3*2*1, find the last two digits of 2014!.

10. There were 210 students in the hall. 5/2 of the boys and 3/1 of the girls wore T-shirts. If there were 78 students in the hall who wore T-shirts, how many boys were in the hall?