2023年新加坡六年级国际数学竞赛试题

1.[问答题]The large square below is made up of4 identical right-angled triangles and 1 small square.The length of the large square is 20 cm.If the sum of the length of two small sides of the right-angle triangle is 28 cm,find the area (in cm2)of the small square. 下面的大正方形是由4个相同的直角三角形和一个小正方形组成的。大正方形的边长是20 厘米。如果直角三角形的两条直角边的长度之和为28厘米，求小正方形的面积（单位： 平方厘米)。 2.[]David uses the digits 1,2,3,5,7 and 8 to form a four-digit multiple of 12.If he does not use any of the digits more than once,what is the greatest four- digit multiple of 12 David can form? 大卫用数字1、2、3、5、7和8组成四位数的12的倍数。如果他使用任何一个数字都不超 过一次，那么大卫能组成的12的倍数中，最大的四位数是多少？ 3.[In the following cryptarithm,all the different letters stand for different digits.If D is an odd digit,what is the value of the sum S+A+S+M+O? 在下面的密码图中，所有不同的字母代表不同的数字。如果D是一个奇数，那么S,A, S,M,O之和是多少？ 2023 +A WA R D SA SMO 4.[问答题How many squares are there in the figure below? 下图中共有多少个正方形？ 5.[问答题How many3-digit numbers are divisible by6and9? 有多少个三位数能被6和9整除？ 6.问答题] Peter had 525 more nails than screws.He used an equal amount of screws and nails to construct a wooden cupboard.If he is left with of the number of screws and of the number of nails,how many nails did Peter have at first? 彼得的钉子比螺丝多525颗。他用等量的螺丝和钉子来建造一个木柜。如果他剩下的 螺丝和的钉子，那么彼得一开始有多少钉子？ 7.[]What is the largest 4-digit multiple of 36 that has no odd digits? 36的倍数中，最大的不含奇数数字的4位数是什么？ 8.[问答题How many times do the hour and minute hands form90°from12pm to 11 pm? 从下午12点到晚上11点，时针和分针会形成多少次90°的角？ 9.[In triangle ABC below,point D is the midpoint of side AC and point E is on side AB such that EC is perpendicular to DB and ZECA=ZECB. If the area of the shaded region is 125 cm2,find the area (in cm2)of triangle ABC. 在下面的三角形ABC中，点D是边AC的中点，点E在边AB上，使EC垂直于DB并且 ∠ECA=∠ECB。如果阴影区域的面积是125平方厘米，求三角形ABC的面积（单 位：平方厘米)。 D 10.[The sum of a 4-digit number and all of its digits is 2023.What is the average of all such 4-digit numbers? 一个4位数与其各位数字的总和是2023。所有这样的4位数的平均数是多少？ 11.[单选题] What isof 20%ofof 480? 480的的20%的是多少？ A.18 B.36 C.54 D.360 E.None of the abovel以上都不是 12.[Figure 1 has 4 unshaded squares.Figure 2 has 16 unshaded squares. If the pattern goes on,how many unshaded squares are there in the 24th figure? 图1有4个无阴影的方格。图2有16个无阴影的方格。如果这个模式继续下去，第24个图 中有多少个无阴影的方格？ Figure 1 Figure 2 Figure 3 A.2116 B.2304 C.2401 D.2500 E.None of the abovel以上都不是 13.[单选题]Tom spent75%of his allowance in January.In February,his allowance was reduced by 20%but he still spent the same amount.What fraction of his total allowance in January and February did he save? 汤姆在一月份花掉了他75%的零用钱。2月份，他的零用钱减少了20%，但他还是花了同 样的钱。他在1月和2月存下了多少零用钱？ 6 c 4 E.None of the abovel以上都不是 14.[单选题 is rotated to 被旋转至 A rotated to 就像 被旋转至 15.[单选题]Find the value of the following. 找出下面式子的结果。 2023×2023-2020×2026 A.1 B.4 C.8 D.9 E.None of the above以上都不是 I6.[单选题]What is the next number in the sequence below? 下面数列的下一个数是什么？ 1,2,6,15,31,56, A.88 B.90 C.92 D.97 E.None of the abovel以上都不是 17.[]What is the missing digit in the 5-digit perfect square below? 下面的5位完全平方数中缺少的数字是什么？ 6 9 A.4 B.5 C.6 D.9 E.None of the above以上都不是 18.[单选题Find the missing number in the pattern below. 按照规律，找出下面图案中缺少的数。 12 3 8 2 7 5 1 2 5 1215 810 1611 46 A.207 B.205 C.157 D.77 E.None of the above以上都不是 19.[单选题How many seconds are there in1.8 hours and8.8 minutes? 1.8小时又8.8分钟是多少秒？ A.7007 B.7008 C.536 D.528 E.None of the abovel以上都不是 20.[Find the largest value of A if the 5-digit number 845A1 is divisible by 9. 如果5位数845A1能被9整除，请找出A的最大值。 A.0 B.2 C.7 D.8 E.None of the abovel以上都不是 21.[The floor of a rectangular room is covered with square tiles.The room is 351 cm long and 195 cm wide.If a square tile is 13 cm long,how many tiles touch the walls of the room? 一个长方形房间的地板上铺着方形瓷砖。房间长351厘米，宽195厘米。如果一块方砖边 长为13厘米，那么有多少块方砖接触到房间的墙壁？ A.80 B.82 C.84 D.1088 E.None of the above以上都不是 22.[单选题The sum of7 consecutive numbers is equal to2023.What is the largest odd number among these consecutive numbers? 7个连续的数之和等于2023。在这些连续的数中，最大的一个奇数是什么？ A.292 B.289 C.287 D.291 E.None of the abovel以上都不是 23.[单选题]Given that 已知下列式子 5 1 7=A+ 1 B+- C+D What is the value of A+B+C+D? A+B+C+D的和为多少 A.13 B.10 C.11 D.12 E.None of the abovel以上都不是 24.[On Monday,Derrick bought 268 stickers.On Tuesday,he bought 261 stickers.Every following day,he bought 7 stickers less than the previous day.On which day of the week did Derrick buy 51 stickers? 周一，德里克买了268张贴纸。星期二，他买了261张贴纸。接下来的每一天，他都比前 一天少买了7张贴纸。德里克在一周的哪一天买了51张贴纸？ A.Wednesday星期三 B.Thursday星期四 C.Saturday星期六 D.Monday星期- E.None of the above以上都不是 25.[单选题]Which of the numbers below is the average of the other four numbers? 下面哪个数是其他四个数的平均值？ A.52 B.50 C.54 D.61 E.53