1, decomposition factor: 3a3-12a = _ _ _ _ _ _ _ _ _.
2. The four line segments A, B, C and D are in direct proportion, where a=3cm, d=4cm, c=6cm and B = _ _ _ _ _ _ _ cm.
3. The solution set of inequality group is _ _ _ _ _ _ _ _;
4. If the score is zero, then x = _ _ _ _ _ _ _ _ _
5, is completely flat, then the value of m is _ _ _ _ _ _ _.
6. The condition of the proposition "Equal angle is antipodal angle" is "If the two angles are equal", and the conclusion is _ _ _ _ _ _.
7. At the same time, the height of the object is proportional to the length of the shadow. If the shadow length of a measuring pole with a height of 1.5m is 2.5m, then the height of a flagpole with a shadow length of 30m is _ _ _ _ _ _ _ _ _ _ _ m. ..
8. The distance between the two places is 350km. On the map of 1: 1000000, the distance _ _ _ _ _ _ _ _ cm.
9. It is known that point C is the golden section of line segment AB, and if AC >: BC and AB=2, then AC = _ _ _ _ _ _ _
10, a school organized students to conduct social surveys and compared the survey reports of students. A score greater than or equal to 80 is considered excellent, and the score is an integer. Now sort out the scores of 60 student survey reports in a certain grade and draw the histogram of frequency distribution in groups (Figure 2). It is known that the four groups of frequencies from left to right are 0.05, 0. 15 and 0.35, respectively.
1 1. It is known that the fractional equation about x has an increasing root, k = _ _ _ _ _ _ _ _ _ _ _ _
12, as shown in the figure, AB‖CD, EG⊥AB, and the vertical foot is g. If ∠ 1 = 50, then ∠ E = _ _ _ _ _ _ _
13, as shown in the figure. This is a schematic diagram of the shadow (circle) formed on the ground after the light from the light bulb (regarded as a point) directly above the round table illuminates the desktop. It is known that the diameter of the desktop is 1.2m, and the desktop is off the ground1m. If the light bulb is 3m away from the ground, the area of the shadow on the ground is _ _ _ _ _ _.
2. Multiple choice questions: (3 points for each question, ***2 1 point)
14, if 3y-7x = 0, then x: y equals ().
a、3∶7 B、4∶7 C、7∶3 D、7∶4
15 and 248- 1 can be divisible by some two numbers between 60 and 70, so these two numbers are:
a、6 1，63 B、63，65 C。 65，67 D。 67,69 ( )
16, the following statement is true ()
A, similar graphics must be similar graphics, similar graphics must be similar graphics;
B, the similarity graph must be a similarity graph, and the similarity ratio is equal to the similarity ratio;
C, using potential transformation can only enlarge the graph, but can't reduce the graph;
D, using potential transformation can only reduce the graphics, not expand the graphics.
17, Zhao Qiang borrowed a ***280-page book, which he had to finish within a two-week loan period. When he was in the middle of reading, he found that he had to read 2 1 page every day on average during the borrowing period. When he reads the first half, how many pages does he read on average every day? If you read X pages a day in the first half, the correct one in the following equation is ().
A B、c d。
18, the following figures must be similar ()
A two rectangles b two isosceles trapezoid.
C has an inner angle corresponding to two equal diamonds, and D corresponds to two quadrilaterals with proportional sides.
19. In order to know about the mid-term math examination of 800 students in Grade 8 in our school, 200 students' math scores were selected for statistics. Make the following judgments: ① The survey method is sampling survey; ②800 students as a whole; ③ Each student's math score is individual; ④200 students are the overall sample; ⑤ The sample size is 200 students. The correct judgment is ().
1。
20. As shown in Figure 4, there are three black spots A, B and C and two Bai Zi P and Q on the chessboard. To make △ABC∽△RPQ, the position where the third Bai Zi R should be placed can be ().
A，A B，B C，C D，D
3. Calculation questions: (4 points for each small question, *** 20 points)
2 1. Solve inequalities and express the solution set on the number axis.
22. simplification 23. Decomposition factor: (a-b) +8(b-a)+ 16.
24. Solve the fractional equation: x 2+x (x+ 1) = 7 (x+ 1).
Answer the following questions (25,26, 6 points for each question, 5 points for 27 questions,)
25. As shown in the trapezoidal ABCD, AD ‖ BC, ∠ A = 90, BD ⊥ DC, ask (6 points).
(1) Are△ Abd and△ △DCB similar? Please explain the reason. (2) If AD = 3 and BC = 5, can we find the length of BD?
26. A section of the banks of a river is parallel. There is a tree every 5 meters on this side of the river and a telephone pole every 50 meters on the other side of the river. Looking at another bank 25 meters away from this bank, we can see that two telephone poles adjacent to another bank are just covered by two trees of this bank, and there are three trees between them. Please ask the width of this river.
27. As shown in the figure, there are two stone steps, A and B, and the number is the height of each step (in centimeters). Use the statistical knowledge you have learned to answer the following questions: (1) Which way is more comfortable to walk?
(2) Design a comfortable stone step road and briefly explain the reasons.
28. The examination results of students A and B this semester 1 1 are as follows:
a 98 100 100 90 96 9 1 89 99 100 100 93
B 98 99 96 94 95 92 98 96 99 97
(1)(3 points) What is their average score and variance? (2) (2 points) What are the characteristics of their achievements?
(3)(2 points) Now one of the two people should take part in the competition. The results of previous competitions show that it is possible to enter the finals only if the score is above 98. Who do you think should take part in this competition? Why?
29. It is known that in trapezoidal ABCD, AD‖BC, AD < BC, and AD = 5, AB = DC = 2. (10).
(1) As shown in the figure, p is a point on AD, which satisfies ∠ BPC = ∠ a. 。
1 verification; △ABP∽△DPC ② Find the length of AP.
(2) If point P moves on the edge of AD (point P does not coincide with point A and point D), PE intersects with a straight line BC at point E and a straight line DC at point Q, and satisfies ∠ BPE = ∠ A, then when CE = 1, find the length of AP (write a short problem solving process).
30. Fill in the basis of reasoning. (***6 points) (1) Known: AB‖CD, AD‖BC. Proof: ∠ b = ∠ d.
Proof: ∫AB‖CD, AD‖BC (known)
∴∠a+∠b= 180,∠a+∠d= 180()
∴∠B=∠D()
(2) known DF‖AC, ∠ A = ∠ F. Proof: AE‖BF.
Proof: ∫DF‖AC (known)
∴∠FBC=∠()
∠∠A =∠F (known)
∴∠A=∠FBC()
∴AE‖FB(