SASMO競賽六年級（小學六年級）樣題及答案

新加坡國際奧林匹克數學學術活動?(SINGAPORE & ASIAN SCHOOLS MATH OLYMPIAD)，簡稱?SASMO，創(chuàng)立于2006年，是新加坡國際數學學術活動中心 SIMCC 主辦的其中一項國際數學學術活動。

與傳統的奧數比賽相比，SASMO 團隊在題目設計中投入了無數的時間和心血，使得參賽者在 SASMO 數學學術活動中可以表現的更加出色——SASMO 學術活動以現實和高標準的方式來拓展學生未被開發(fā)的潛力，激發(fā)出其內在的數學家思想以及更高階思維技巧(HOTS)。

今天這篇文章將會對于Grade 6的部分學術活動樣題做展示：

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?