2024年MK袋鼠数学竞赛 等级F 高二高三年级真题（扫描版，含答案）

MATH KANGAROO 2024 (CHINA)-LEVEL F 3 points 1.A pattern is made of equal pentagons.Which of the tiles below,when placed in the central hole,will form a self-intersecting loop 右侧图形由相同的五边形瓷砖组成。请问将下列哪块瓷砖放入图 形的中心处可以形成一条自相交叉的环线？ (C) D E 2.Which of these integers is two less than a multiple of ten.two more than a square.and two times a prime 请问下列哪一个整数比10的倍数少2，比一个平方数多2，并且是一个质数的两倍？ (A)78 (B)58 (C)38 (D)18 (E)6 3.A young kangaroo cut a pizza into six equal slices.After eating one slice.he arranged the remaining slices with equal gaps between slices.What size is the angle of each gap 一只小袋鼠将披萨分为6等份。小袋鼠吃了一份之后，将剩余的披萨 披萨之间的夹角相等。请问相邻披萨之间的夹角为多少度？ (A)5 (B)8 (C)9° (D)10° (E)12° 4.Juuso has an unusual habit of drawing the xy-plane with the positive coordinate axes pointing left and down.What would the graph of the equation y =z+1 look like in a coordinate system drawn by Juuso Juso画xy平面直角坐标系时，习惯将向左和向下的方向定为坐标轴的正方向。请问下列哪一项 是方程y=x+1在Juuso画的xy平面直角坐标系上的图像？ 5.Kaito has manipulated a die.The probabilities of rolling a2.3.4or 5 are still each,but the 1 probability of rolling a 6 is twice the probability of rolling a 1.What is the probability of rolling a 6 Kato操控一枚骰子，使得点数2、3、4、5中各个点数朝上的概率始终为后但是点数6朝上的 概率是点数1朝上的概率的两倍。请问点数6朝上的概率是多少？ ( B) 1 (C)36 (D) (E)8 6.Which of the expressions below has the same value as 1615+1615+1615+1615 请问下列哪个表达式与1615+1615+1615+1615的值相等？ (A)1619 (B)431 (C)460 (D)1660 (E)4122 7.Beaver wishes to color the squares and triangles of the following figure so that no two neighbouring figures,even those sharing a single vertex.are the same color. Beaver想为下图中的正方形和三角形上色，使得任意两个相邻图形不同色，包括共用一个顶点的 两个图形也不同色。 What is the least number of colors needed 请问Beaver至少需要几种颜色？ (A)3 (B)4 (C)5 (D)6 (E)7 8.There are 6 glasses on a table with their open ends up.In any one move,we turn over exactly 4 of them.What is the least number of moves required to have all glasses upside down 桌上有6个开口朝上的玻璃杯。每一轮只翻转4个玻璃杯，请问至少需要几轮才能使得所有玻璃 杯开口朝下？ (A)2 (B)3 (C)4 (D)5 (E)6 9.A student started with the number 1 and multiplied it by either 6 or 10.He then multiplied the result by either 6 or 10,and continued this procedure many times.Which of the following cannot be one of the numbers he obtained 一名学生从数字1开始，将其乘6或10，然后再将得到的结果乘6或10，以此类推，多次重 复该过程。请问这名学生无法得到下列哪一个数字？ (A)2100320580 (B)290320580 (C)290320570 (D)2110380530(E)250550 0 ... ...