2021美国数学大联盟Math League夏季数学挑战活动5年级真题及答案.pdf

202 1 美国"大联盟"(Math League)国际夏季数学挑战活动 202 1 Math League International Summer Challenge Grade 5, Individual Questions Question 1: Sarah is using popsicle sticks to build some grids for her city planning project. She needs 4 popsicle sticks to make a 1 by 1 grid, and 12 sticks to make a 2 by 2 grid as shown below. How many sticks does she need to make a 10 by 20 grid? Question 2: The sides of the large rectangle are 20 m and 16 m, figure below, not drawn to scale. All six shaded rectangles are identical. What is the total area of all the shaded regions, in square meters? 1 Question 3: If two sides of a square field were increased by five feet, as seen in the diagram below, not drawn to scale, the area of the field would increase by 245 square feet. Find the area of the original square. Question 4: During practice, Dana’s six arrows land on the target shown. Each arrow is inside one of the regions of the target. Which of the following total scores is possible: 44, 31, 26, 16? (If an arrow lands inside the smallest circle in the center, the score Dana gets is 7. If an arrow lands inside the second circle, but not inside the smallest circle, the score Dana gets is 5. If an arrow lands inside the largest circle, but not inside the second circle or the smallest circle, the score Dana gets is 3. Assume no arrow lands on the boundary of any of the three circles.) (a) 44 (b) 31 (c) 26 (d) 16 Question 5: There are 1000 people in a room. Each pair either shakes hands or does not. 2 (1) Is it always true that some two people shook the same number of hands? (Please enter 1 if your answer is Yes, and 0 if your answer is No.) (2) Is it always true that some three people shook the same number of hands? (Please enter 1 if your answer is Yes, a