2022年大联盟(Math League)国际夏季六年级数学挑战活动二

Speed Questions (Grade 6) 2022 Math League International Summer Challenge (Unofficial version, for reference only) Note: Listed below are the four types of coins currently being minted in United States. a. Penny: 1 b. Nickel: 5 c. Dime: 10 d. Quarter: 25 1. (-1)100 = A) -1 B) 1 C) -100 D) 100 Answer: B 2. (x + 2) + (2x + 4) + (3x + 6) + (4x + 8) = A) x + 20 B) 9x + 20 C) 10x + 20 D) 20x + 20 Answer: C 3. (y + 2)(y – 2) = A) y2 – 4 B) y2 – 2y + 4 C) y2 + 2y + 4 D) y2 + 4 Answer: A ( 10 ) 学科网(北京)股份有限公司 4. 1 2 3 ... 100 2 4 6 ... 200 A) 1 200 B) 1 100 C) 1 2 D) 100 Answer: C 5. (x2)(x3)(x4) = A) x5 B) x9 C) x24 D) x234 Answer: B 6. x2 – 10x + 24 = A) (x – 12)(x + 2) B) (x – 6)(x – 4) C) (x + 12)(x – 2) D) (x + 6)(x + 4) Answer: B 7. If n < 0 and p > 0, which inequality is always true? A) n > p B) -n > p C) 1 1 n p D) 1 1 n p Answer: D 8. I am thinking of a number. When I subtract 2 from the number, then take 300% of the result, the number I get is my original number. What is my original number? A) 0 B) 2 C) 3 D) 6 Answer: C 9. x(x(x(x + 1) + 1) + 1) + 1 = A) 4x + 4 B) x4 + 2x3 + 3x2 + 2x + 1 C) x4 + 4 D) x4 + x3 + x2 + x + 1 Answer: D 10. How many solutions does the equation |x + 2| = 2x have? A) 0 B) 1 C) 2 D) 3 Answer: B 11. How many different numbers satisfy the equation (x – 2)2(x – 1)3(x + 1)4(x + 2)5 = 0? A) 4 B) 5 C) 14 D) 120 Answer: A 12. Triangles ABC and DCB are both isosceles right triangles, as shown. If AC = 12, what is the area of triangle BCE? Answer: 18 13. In a certain circle, the length of a radius is equal to the reciprocal of the length of a diameter. What is the area of this circle? A) 1 2 B) C) 2 D) 2 Answer: A 14. The sum of 20 positive numbers is what percent of the average of these same 20 numbers? Note: This is the way to enter your answer. If, for example, your answer is 5%, please enter 5. Answer: 2000 15. What are the three ordered pairs of non-negative integers (a, b) for which ( a b ) a b ? Note: This is the way to enter your answer. If