1. Fill in the blanks: (This big question *** 10 small question. 2 points for each small question. ***20 points. )
1.23×83= .
2. The circumference of an isosceles triangle with 3 as the base and 6 as the waist is.
It is reported that the smallest flowering and fruiting plant in the world is duckweed in Australia. The fruit of this plant is like a tiny fig, with a mass of only 0.00000007 g, which is expressed by scientific notation.
4. "A is nonnegative" can be expressed as inequality.
5. Decomposition factor x2+ 10x+25 =.
6. As shown in the figure, put the right vertex of the triangle on one side of the ruler, ∠ 1 = 30.
∠ 2 = 50, ∠3 = degrees.
7. Convert the binary linear equation 2x+3y-4 = 0 into the form of y=kx+m, then m-k =.
8. A regular polygon with an outer angle equal to its adjacent inner angle is a polygon.
9. If both sides of a triangle are 7, 10, then the range of the third side length A is.
10. As shown in the figure, in △ABC, AB=AC, AD is the bisector of ∠BAC, DE⊥AB, DF⊥AC, and the vertical feet are E and F respectively, then the following conclusions are correct.
①DA divided by ∠ EDF; Equally ∞;
②AE=AF，DE=DF:
③ The distance from the point on AD to point B and point C is equal;
④ There are three pairs of congruent triangles in the picture.
Second, multiple-choice questions: (This big question ***6 small questions. 3 points for each small question, *** 18 points,
1 1. Through translation, the Fuwa Huanhuan in figure 1 can be moved to the figure.
12. According to your judgment, the following events are most likely to happen.
(a) The 1 ball found in the bag containing 1 red ball and 2 yellow balls is only a white ball; (b) Randomly draw 65,438+0 cards from a deck of playing cards with Wang and Xiao removed, and the drawn cards are red; (c) Investigating customers born in leap years in shopping centers; (d) Stand on the flat ground and throw a small stone, and it will fall.
13. Of the following operations, the correct one is ().
(A)(A+B)2 = a2+B2(B)(-x-y)2 = x2+2xy+y2
(C)(x+3)(x-2)= x2-6(D)(-a-b)(a+b)= a2-B2
14. Among the following surveys, the most suitable one is ().
(a) to understand the quality of fruits in large-scale fruit wholesale markets;
(two) the unit shall carry out health examination for employees;
(c) Chinese teachers should check the typos in students' compositions;
(d) Schools should know about the spread of influenza in schools.
15. As shown in the figure, a rectangular ruler is broken and dislocated along a straight line, and points E, D, B and F are on the same straight line.
If ∠ ade = 125, the degree of ∠DBC is ().
(A)55 (B)65 (C)75 (D) 125
16. Xiao Rui and Xiao Zhi are playing marbles. Xiao Rui said to Xiao Zhi, "Give me half of your beads, and I will have 10". Xiao Zhi said, "Give me yours and I will 10". If Xiao Zhi has X marbles, Xiao Rui has X marbles.
(A) (B)
(C) (D)
19. Solve the following inequality about X: (Full score for this question, 4 points for each small question)
( 1) ; (2) 1+3(x- 1)>8-x。
20. (The full mark of this question is 4) Randomly select 1000 sets of commercial houses with different areas recently sold in a city for statistics, and draw a statistical chart as shown in the figure according to the results. Please answer the following questions with the information in the picture:
(1) There are sets of commercial houses with the sales area of110 ~130m2.
And complete the statistical chart on the right;
(2) As can be seen from the figure, the commercial housing that sells the most accounts for about.
% of all commercial housing sales.
2 1. (The full mark of this question is 4) Place a pair of right-angle triangular rulers as shown in the figure. Given AE‖BC, find the degree of ∠AFD.
22. (Full score for this question is 4) As shown in the figure, it is an expanded diagram of a cube, and the face marked with the letter "A" is the front of the cube. If the values of algebraic expressions on two opposite sides of the cube are equal, try to find the values of algebraic expressions.
23. As the picture shows, there is a beautiful and lovely little goldfish in the square.
(1) If the side length of the square is 1, the area of the small fish is.
(2) After the small fish is translated to the left by 10 squares, draw the figure of the small fish (drawing steps and processes are not needed).
24. As shown in the figure, AB and CD are known to intersect at point O, AC ‖/BD, OC=OD, E and F are two points on AB, AE=BF. Try to explain CE = DF.
25. (Full score for this question is 7) In order to attract more student tourists during the summer vacation, a scenic spot has launched a group ticket purchase preferential fare activity, and its ticket prices are as follows:
No more than 30 people, no more than 30 people, but no more than 50 people, no more than 50 people
20 yuan 15 yuan 10 yuan per person.
A total of 60 people from two tour groups A and B of the same travel agency (group A has more people than group B) are going to travel to this scenic spot. If Group A and Group B buy tickets separately, then Group A has to pay 980 yuan.
(1) If two groups buy tickets jointly, how much will they save compared with buying tickets separately?
(2) How many people are there in Group A and Group B?
26. (The full mark of this question is 7) It is known that the line segment AB and CD intersect at point O, connecting AD and CB. We call the figure with the shape of 1 the "8" shape. As shown in Figure 2, the bisector AP of ∠DAB and ∠BCD under the condition of Figure 1
(1) In the figure 1, please directly write the quantitative relationship between ∠A, ∠B, ∠C and ∠D:;
(2) Look carefully, the number of "8" in Figure 2 is:
(3) In Figure 2, if ∠ d = 40 and ∠ b = 30, try to find ∠P times;
(4) If ∠D and ∠B are arbitrary angles in Figure 2, and other conditions remain unchanged, try to write the quantitative relationship between ∠P and ∠D and ∠B (just write the conclusion directly).