1、Did you know? In the decimal number system (base 10) ten different digits, 0 to 9, are used to write all the numbers. In the binary number system (base 2) two different digits are used, i.e. 0 and 1.

　　Which one of the following numbers is not a valid number in the

　　octal number system (base 8)?

　　A) 128 B) 127 C) 126 D) 125 E) 124

　　2、The number of diagonals that can be drawn in a regular polygon with

　　twenty sides (icosagon) is_____.

　　3、If a and b are integers, 10?3=1,152?7=3, and then 379?6 is equal to_____.

　　4、Two numbers are in the ratio 2 : 3. When 4 is added to each number the ratio changes to 5 : 7.The sum of the two original numbers is____.

　　5、The greatest number of Mondays which can occur in 45 consecutive

　　days is____

　　6、Saul plays a video game in which he scores 4 for a hit and lost 6 for a miss. After 20 rounds his score is 30. The number of times he has missed is____.

　　7、Three girls A, B and C run in a 100 m race. When A finishes, B is 10 m

　　behind A and when B finishes C is 20 m behind B. How far in metres was C from A when A finished?(Let’s assume all the athletes run at a constant speed)

　　8、The areas of the faces of a rectangulabox are 84 cm2 , 70 cm2and 30 cm2.The volume of the box in cm3 is____.

　　9、You have 3 weights: 1 kg, 3 kg and 9 kg as well as an equal arm balance, as shown. How many different weight objects can you weigh with these three?

　　[Remember the weights may be placed on either side]

　　參考答案：

　　1、A 考察我們學過的簡單的進制問題，顯然8進制中沒有8出現

　　2、170 找規律，公式為n×(n-3)÷2

　　3、1 定義新運算，就是求379÷6的余數。

　　4、40，16和24

　　5、7

　　6、5

　　7、28米，根據距離比求出速度比，三者的速度比為1：9/10：18/25

　　8、420 分解質因數

　　9、13種