2022年大联盟(Math League)国际夏季六年级数学挑战活动二（含答案）

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1、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: 1b. Nickel: 5c. Dime: 10d. Quarter: 251.(-1)100 =A) -1B) 1C) -100D) 100Answer: B2.(x + 2) +

2、 (2x + 4) + (3x + 6) + (4x + 8) =A) x + 20B) 9x + 20C) 10x + 20D) 20x + 20Answer: C3.(y + 2)(y 2) =A) y2 4B) y2 2y + 4C) y2 + 2y + 4D) y2 + 4 Answer: A154.1 + 2 + 3 + . + 100 =2 + 4 + 6 + . + 200A) 1 200B) 1 100C) 1 2D) 100Answer: C5. (x2)(x3)(x4) =A) x5B) x9C) x24D) x234Answer: B6.x2 10x + 24 = A)

3、(x 12)(x + 2)B) (x 6)(x 4)C) (x + 12)(x 2)D) (x + 6)(x + 4)Answer: B7.If n 0, which inequality is always true?A) n pB) -n pC) 1 1npD) 1 0 does(32 + 42) + (32 + 42) + (32 + 42) + (32 + 42) = n2?Answer: 1049.What is the largest possible area of a rectangle with integer sides and perimeter 22? Answer:

4、3050.The sum of the squares of the lengths of the four legs of two right triangles is 100. If the length of the hypotenuse of one of the triangles is 6, how long is the hypotenuse of the other triangle?Answer:851.The values of x which satisfy both |x 8| 5 are precisely the values of x that satisfy a

5、 x b. What is a + b?Answer: 2252.Disregarding order, we can write 4 as a sum of one or more integers, each a power of 2, in only four ways: 4, 2 + 2, 2 + 1 + 1, and 1 + 1 + 1 + 1. In at most how many different ways can 5 be written as such a sum?Answer: 453.A plane is partitioned into 2 regions by 1

6、 line and into 4 regions by 2 intersecting lines. Into how many disjoint regions do 5 coplanar lines partition the plane, if no 2 of the lines are parallel and no 3 of them are concurrent?Answer: 1654.Two noncongruent circles are externally tangent. Each base of an isosceles trapezoid is a diameter

7、of one of the circles. If the distance between the centers of the circles is8, what is the area of the trapezoid? Answer: 6455.The 4th term of a sequence is 4 and the 6th term is 6. Every term after the 2nd is the sum of the 2 preceding terms. What is the 8th term of this sequence?Answer: 1456.One d

8、iagonal of a square serves as the shorter base of a trapezoid, and a line through one of the vertices of the square contains the other base. The legs of the trapezoid are extensions of two sides of the square. If the area of the square is 2800, what is the area of the trapezoid?Answer: 420057.Figure

9、 below, the blue circle is the incircle of triangle ABC. (The incircle is the circle which lies inside a triangle and touches all sides.) O is the center the incircle. D is the center of the circle which touches AC and the extensions of BA and BC. Is it true that points B, O, and D are always collin

10、ear, i.e., lying on the same straight line, for any triangle ABC?Choices:(a) Yes(b) No Answer: (a)58.For any integer n 1, 1 + 2 + 3 + . . . + (n 1) + n = (n + 2) + . . . + (2n 1) + (2n) =2n2 + nn(n + 1) . Then, n + (n + 1) +2A)23n2 - nB)23n2 + nC)23n2 + 3nD)2Answer: D59.A series of 7 books was published at 9-year intervals. When the 7th book was published, the sum of the publication years was 13 601. In what year was the 4th book published?Answer: 194360.Semicircles drawn on each side of a triangle have areas of 9, 16, and 25. What is the area of the triangle?Answer: 48