60 cases (fill in the blanks) were the finale of the senior high school entrance examination 1. Fill in the blanks (***60 small questions) 1. (20 15? Zhuzhou) "Pique Theorem" is a formula used to calculate the polygon area with vertices at the whole point, and the formula expression is S=a+? -1, Kong Ming only remembers that S in the formula represents the area of the polygon, one of A and B represents the number of integral points on the edge of the polygon, and the other represents the number of integral points inside the polygon, but he can't remember whether A or B represents the number of integral points inside the polygon. Please select some special polygons (as shown in figure 1) for verification, and get the formula representing the interior of polygons. Changchun) As shown in the figure, in the plane rectangular coordinate system, point A moves on parabola y = x2-2x+2. If the intersection point A is the AC⊥x axis of point C, AC is the diagonal rectangle ABCD, and BD is connected, the minimum value of diagonal BD is. ? 3.(20 15? As shown in the figure, it is known that the parabola y=ax2+bx+c intersects the X axis at points A and B, and the ordinate of the vertex C is ﹣2. Now, the parabola Y = A1X2+B1X+C1is translated to the right, and the following conclusion is correct. (all written correctly. Yongzhou) Let an be the last digit of a positive integer n4, such as a 1= 1, a2=6, a3= 1, A4 = 6. Then a1+a2+a3+…+a2013+a2065438+. Laboratory in Yiwu), there are three cylindrical containers A, B and C on the horizontal table (the containers are high enough), and the bottom radius ratio is 1: 2: 1. Two identical pipes are connected at a height of 5cm (that is, the bottom of the pipe is 5cm from the bottom of the container). Of the three containers, only A has water, and the water level is 65438+. The imperial edict (1) began to inject water 1 min, and the water level of C rose by cm. (2) After the water injection clock is started, the water level of B is 0.5 cm.6 higher than that of A, (20 15? Suqian) When x=m or x=n(m≠n), the values of algebraic expression x2-2x+3 are equal, and when x=m+n, the values of algebraic expression x2-2x+3 are.

7.(20 15? As shown in the figure, the quadrilateral ABCD is a rectangular piece of paper, with AB = 2. Fold the rectangular piece of paper ABCD in half, so that AD and BC overlap and the crease is EF; Flatten the rectangular paper and fold it at point B, so that point A falls at point N on EF, and the crease BM intersects with EF at point Q; Flatten again, connect BN and MN, extend the intersection BC of MN to point G, and get the following conclusions: ① ∠ ABN = 60; ②AM = 1； ③QN=？ ; ④△BMG