First, multiple-choice questions (3 points for each small question, 30 points for * * *)
1, if 2y-7x = 0, then x: y equals ().
A.2∶7 B. 4∶7 C. 7∶2 D. 7∶4
2, the following polynomial factorization is ()
a . x2-y b . x2+ 1 c . x2+xy+y2 d . x2-4x+4
3. Simplified result ()
A.x+y B.x- y C.y- x D.- x- y
4. As shown in the figure, the straight line l 1‖l2 cannot be judged as () under the following circumstances.
A.∠ 1 =∠3b .∠2 =∠3c .∠4 =∠5d .∠2+∠4 = 180
5. In order to know about the mid-term math test 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。
6. As shown in the figure, in △ABC, if ∠ AED = ∠ B, DE = 6, AB = 10, AE = 8, the length of BC is ().
A. the seventh century BC.
(Figure 4) (Figure 6)
7, the following proposition, belongs to the false proposition is ()
A. if a-b = 0, then a = b = 0b. If a-b > 0, then a > b.
C. if a-b < 0, a < b d. if a-b ≠ 0, a ≠ b.
8. if the inequality about x is (a+1) x >; The solution set of a+ 1 is x.
A.a & lt0 B.a & lt- 1 c . a >； 1d . a >； - 1
9. In trapezoidal ABCD, ADBC, AC and BD intersect at O, if ADBC= 13, the following conclusion is correct ().
A.S△COD = 9S△AOD B . S△ABC = 9S△ACD C . S△BOC = 9S△AOD D . S△DBC = 9S△AOD
10, a class of students learned that the class won the prize at the award ceremony in the following table:
It is known that 28 students in this class * * * won prizes, of which 13 students only won two prizes, so the student who won the most prizes in this class may get a prize of ().
A.3, B.4, C.5 and D.6
Fill in the blanks (3 points for each small question, 24 points for * * *)
1 1, and the solution set of the inequality group is;
12, if the value of the algebraic expression is equal to zero, then x =
13, decomposition factor: =
14. As shown in the figure, there is a pond between A and B. Choose a point C outside AB to connect AC and BC, and find their midpoints M and N respectively. If Mn = 15m, the distance between a and b is
(drawing 14) (drawing 15) (drawing 17) (drawing 18)
15, as shown in the figure, in □ABCD, e is the midpoint of CD, AE and BD intersect at point O, and S△DOE= 12cm2, then S△AOB is equal to cm2.
16, a math test, the full score is 100. After the exam results came out, Li Hua and Wu Shan at the same table calculated their scores. Li Hua said that the sum of our scores is 160, and Wu Shan said that the difference between our scores is 60. So for the following two propositions: ① their statements are correct, ② at least.
17, as shown in the figure, with the following conclusions: ① < a > < ACD; ②∠b+∠ACB = 180-∠A； ③∠b+∠ACB & lt； 180 ; ④∠HEC & gt； B. Correct (fill in all serial numbers that you think are correct).
18, as shown in the figure, in the figure formed by splicing four squares, with any three of these ten points as vertices, * * * can form _ _ _ _ _ _ _ isosceles right triangles. Would you like to communicate with others about the method of inquiry to reach the above conclusion? If you like, please briefly write down your inquiry process below (if the conclusion is correct and the written process is agile and reasonable, you can add 2 points, But the total score of the whole paper should not exceed 100): _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
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Three. (6 points for each small question, *** 12 points)
19, solving inequalities
20. The values of x= and y= are known.
Four, (6 points for each small question, *** 18 points)
2 1. In order to understand the physical condition of middle school students, the eighth grade students in a middle school were selected for rope skipping test. After sorting out the obtained data, draw the frequency distribution histogram as shown in the figure. It is known that the three groups of frequencies from left to right in the figure are 0. 1, 0.3 and 0.4 respectively, and the first group of frequencies is 5.
(1) The frequency of the fourth group is _ _ _ _ _ _ _ _ _
(2) The students who took part in this test are _ _ _ _ _ _ _ _ _
(3) Which data group has the largest number of people with scores? how much is it?
(4) Students who have scored more than 100 times (including 100 times).
Percentage of people.
22. In the activity of striving for a national sanitary city, a "youth commando" in our city decided to voluntarily remove a pile of garbage weighing100t. After the start of construction, nearby residents took the initiative to participate in voluntary labor, and the speed of garbage removal was doubled compared with the original plan. As a result, the task was completed four hours ahead of schedule. How many tons of garbage did the "Youth Commando" originally plan to transport?
23. A school cafeteria plans to buy 12 dining table and some dining chairs. Now we know from two shopping malls, A and B, that each dining table of the same model is quoted in 200 yuan, and each dining chair is quoted in 50 yuan. China shopping mall said: each dining table is given a dining chair; According to the regulations of Mall B, all dining tables and chairs are sold at a 15% discount on the quoted price. So, under what circumstances is it more favorable to buy in mall A?
V. (This question 10)
24. As shown in the figure, after the rectangular paper ABCD is folded along EF, the point D coincides with the point B, and the point C falls on the position of the point C'. If ∠ 1 = 60, AE = 1.
(1) Number of times to find ∠2 and ∠3;
(2) Find the area s of rectangular paper ABCD.