小升初英语奥数题

可乐卷 Coke Paper1 小升初英文奥数题 1 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 你知道吗 在十进制数字系统中十个不同的数字 用从 0 到 9 就可以写出所有的数字了 在二进制数字系统 中使用了二个不同的数字 0 和 1 请问在八进制数字系统中 下列的哪一个数字是不存在的 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 一个规则的 20 多边形总共可以画出多少条对角线 3 If a and b are integers 10 3 1 150 7 3 and then 379 6 is equal to 如果 a 和 b 都是整数 那么 379 6 是等于多少 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 假设二个数字的比值是 2 3 当每个数字加上 4 以后 比值就变成了 5 7 那么这二个数字之和是多少 5 The greatest number of Mondays which can occur in 45 consecutive days is 在日历中 续 45 天中最多可以出现多少个星期一 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 索尔在玩一个电子游戏 击中一次得 4 分 打偏则扣 6 分 20 个回合后他的得分是 30 分 那么他打偏了多 少次 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 有 A B C 三个女孩进行 100 米赛跑 当 A 到达终点时 B 落后 A 10 米 当 B 到达终点时 C 落后 B 20 米 那么当 A 到达终点时 C 落后 A 多少米 假设所有的人都是匀速的 8 The areas of the faces of a rectangular box are 84 cm2 70 cm2and 30 cm2 The volume of the box in cm3 is 一个长方形盒子的表面积依次为 84cm2 70 cm2 30 cm2 那么这个盒子的体积是多少 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 你有三个重物 1kg 3kg 9kg 还有一个等臂天平 那么你可以用这三个重物称多少个不同物体 记得这 些重物可以放在天平的任意一边 可乐卷 Coke Paper2 小升初英文奥数题 2 1 An ant covers adistance of 90 metrers in 3 hours The average speed of the ant in decimetres per minute is 一只小蚂蚁用了 3 个小时爬行了 90 米 那么它的平均速度是每分钟多少分米 2 The Ancient Romans used the follwing different numerals in their number system as follows 1 C 100 V 500 10 M 1000 etc L 50 They used these numerals to make up numbers as follows 1 2 3 4 5 6 7 8 9 10 So for example XCIX is 99 What is the value of XLVI 古罗马人用下面的符号来计数 比如 XCIX 是 99 XLVI 等于多少 3 In a certain town some people were affected bya flu epidemic In the first month 20 of the population contracted the ful whilst 80 were healthy In the following month 20 of the sick people recovred and the 20 of the healthy people contracted the disease What fraction of the population is healthy at the end of the healthy month 在某个小镇里一些人感染了流行性感冒 在第一个月里有 20 的分感染了 但 80 的人是健康的 在接下来一个 月里 有 20 的病人恢复了健康 但是 20 的健康的人也感染了 那么现在总共健康的人数的百分比是多少 4 Mpho Barry Sipho Erica and Fatima are sitting on a park bench Mpho is not sitting on the far right Barry is not sitting on the far left Sipho is not sitting at either end Erica si sitting to the right of Barry but not necessarily next to him Fatima is not sitting next to Sipho Sipho is not sitting next to Barry Who is sitting at the far right Mpho Barry Sipho Erica 和 Fatima 坐在公园的长椅上 Mpho 坐在不远的右边 Barry 坐在不远的左边 Sipho 不 坐在长椅的任何一头 Eric 坐在 Barry 的右边 但是并不需要挨着他 Fatima 也不挨着 Sipho Sipho 也不挨着 Barry 那么谁坐在最右边 5 Of the 28 T shirts in a drawer six are red five are blue and the rest arewhite If Bob selects T shirhs at random whilst packing for a holiday what is the least number he must remove from the drawer to be sure that he has three T shirts of the same colour 抽屉里有 28 件 T 恤衫 6 个红色的 5 个蓝色的 剩下的都是白色的 如果他随意取出 T 恤衫去度假 要确保他 有 3 件是同一颜色的 请问他从抽屉中拿出的 T 恤衫的最少数量是多少件 6 In an alien language jalez borg farn means good maths skills Nurf klar borg means maths in harmony and darko klar farn means good in gold What is harmony gold in this language 在外星人语言中 jalez borg farn 意思是 good maths skills 7 Five children Amelia Bongani Charles Devine and Edwina were in the classroom when one of them broke a window The teacher asked each of them to make a statement about the event knowing that three of them always lie and two always tell the truth Their statements were as follows Amelia Charles did not break it nor did Devine Bongani I didn t break it nor did Devine Charles I didn t break it but Edwina did Devine Amelia or Edwina broke it Edwina Charles broke it Who broke the window 五个熊孩子 Amelia Bongani Charles Devine and Edwina 在教室里玩疯了 突然有一个打破了窗户 老师先让每 个人坦白一下事件 其实老师心里知道有三个孩子总是撒谎 二个爱讲实话 下面是他们的辩词 Amelia 不是 Charles 干的 也不是 Devine 干的 Bongani 我没有打破窗户 Devine 也没有 Charles 我没有 是 Edwina 干 得 Devine 是 Amelia 或者 Edwina 干得 Edwina 是 Charles 干得 那么到底是谁打破了窗户 8 Did you know A palindrome is a number which reads the same forards as backwards e g 35453 Next year 2002 is an example of a palindromic number What is the difference between 2002 and the number of the previous palindromic year 你知道吗 回文数字是一种顺读和倒读都一样的数 比如 35453 2002 年就是一个这样的例子 那么 2002 和它 前一个回文数字年的差别是多少 可乐卷 Coke Paper3 小升初英文奥数题 3 1 In 2004 16 June falls on a Wednesday On what day of the week will 16 June fall in2010 在 2004 年 六月 16 号是星期三 那么在 2010 年六月 16 是星期几呢 2 If half of a number is 30 then three quarters of that number is 如果一个数的一半是 30 那么这个数的四分之三是多少 3 The sum of the digits of the following product 999 555 is 999 555 的积的数位上的数字之和是多少 4 Three positive integers have a sum of 28 The greatest possible product that these integers can have is 三个正整数之和是 28 那么这三个正整数之积最大可能是多少 5 In what follows and are different numbers When 503 is divided by the remainder is 20 When 503 is divided by the remainder is 20 When 493 is divided by x the remainder is 有如下几个例子 和 都代表不同的数字 除以 503 的余数是 20 除以 503 的余数也是 20 那么 493 除以 之积的余数是多少 6 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 sex The worst player and the best player are of the same age Who cannot be the worst player s 一位女士 她的弟弟 她的儿子 她的女儿 都打排球 妈妈和她的弟弟是双胞胎 她自己的女儿和儿子也 是双胞胎 最差的球员的双胞胎之一和最好的球员性别是相反的 最差的球员和最好的年龄是一样的 那么谁不 可能是最差的 A brother only B daughter only C son and daughter only D lady and daughter only E lady only 7 If you continue the given number pattern in what row and in what position in that row will the number 320 be 如果你继续把下面这组数字模式写下去 那么在多少排 在这一排的什么位置将会是数字 320 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 10 Two ants start at point A and walk at the same pace One ant walks around a 3 cm by 3 cm square whilst the other walks around a 6cm by 3 cm rectangle What is the minimun distance in centimetres any one must cover before they meet again 二只可怜的小蚂蚁都以同样的速度从 A 点出发 其中一只爬行了 3cm 3cm 的正方形 另一只爬行了 6cm 3cm 的 长方形 那么如果二只蚂蚁再次相遇 每只必须爬行的最小距离的多少 可乐卷 Coke Paper4 参考答案 1 1 A 考察我们学过的简单的进制问题 显然 8 进制中没有 8 出现 2 170 找规律 公式为 n n 3 2 3 1 定义新运算 就是求 379 6 的余数 4 40 16 和 24 5 7 6 5 7 28 米 根据距离比求出速度比 三者的速度比为 1 9 10 18 25 8 420 分解质因数 9 13 种 2 1 单位换算 注意单词 90 10 3 60 2 46 3 68 4 Erica 5 7 抽屉原则 6 nurf darko 注意一一对应 borg maths farn good jalez skills klar in nurf harmony darko gold 7 Charles 8 1001 3 1 Wednesday 2 45 3 27 求数位上上的数字之和 4 28 9 9 10 因此答案为 810 5 503 20 483 483 3 7 23 21 23 因此 x 483 因此此题余数是 10 6 D 7 25 20 10 108 可乐卷 Coke Paper5 一 填空题 每题 5 分 共 25 分 1 1 2 3 3 4 5 5 6 7 7 8 9 9 10 11 2 思思和学学在探讨年龄问题 学学说 当你像我这么大时 我已经 35 岁了 思思说 当你像我这么大时 我才 5 岁 则思思 岁 3 10 个人站一排照相 其中三个人是甲乙丙 则甲不在乙丙之间的拍照方式有 种 4 依次从 1 开始写自然数 一直写到 2009 则这个多位数 12345678910111213 20082009 除以 9 的余数 是 5 车过河交渡费 3 元 马过河交渡费 2 元 人过河交渡费 1 元 某天过河的车和马的数目之比为 2 9 马和 人的数目之比为 3 7 共收渡费 315 元 求这天过河的车 马和人的数目各是多少 二 填空题 每题 7 分 共 35 分 1 在长方形 ABCD 内部有一点 O 形成等腰 ABO 的面积为 16 等腰 DOC 的面积占长方形面积的 18 那么阴影 AOC 的面积是多少 2 已知 ABC 中 AB AC 16 ABC 面积是 64 P 是 BC