6年級英語奧數題目(一)

　　4、The sum of the digits of the following product 999×555

　　5、Three positive integers have a sum of 28. The greatest possible product that these integers can have is_____.

　　6、Jack was trying to tessellate regular pentagons. He managed the following figure. The size of angle .a. is______.

　　7、If the area of the shaded region of the regular hexagon in the diagram below is 36 cm2, the area of the whole hexagon in cm2 is_____.

　　8、In what follows, □ and Δ are different numbers.

　　When 503 is divided by □ the remainder is 20.

　　When 503 is divided by Δ the remainder is 20.

　　When 493 is divided by □ x Δ the remainder is_____.

　　9、A lady, her brother, her son and her daughter (all related by birth) played volleyball. The worst player's twin (who is one of the four players) and the best player are of opposite.

　　The worst player and the best player are of the same age.

　　Who cannot be the worst player(s)?

　　A) brother only B) daughter only

　　C) son and daughter only

　　D) lady and daughter only

　　E) lady only

　　10、If you continue the given number pattern, in what row and in what position in that row will the number 320 be?

　　1 -------------- row 1

　　2 3 -------------- row 2

　　4 5 6 -------------- row 3

　　7 8 9 10 -------------- row 4

　　The answers are given in the order of row; position.

　　6年級英語奧數題目(二)

　　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, 10Ä3=1,152Ä7=3, and then 379Ä6 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]

　　6年級英語奧數題目答案

　　(一)

　　1、Wednesday

　　2、12

　　3、45

　　4、27(求數位上上的數字之和)

　　5、28=9+9+10，因此答案為810

　　6、36度

　　7、108

　　8、503-20=483 483=3×7×23=21×23，因此□ x Δ=483，因此此題余數是10

　　9、D

　　10、25，20

　　(二)

　　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