First, multiple-choice questions (3 points for each small question, *** 18 points)
There are four answers to each question below, and only one is correct. Fill in the brackets after the question with the code letters of the correct answer.
The reciprocal of 1 Yes ()
A.B. C. D。
2. As shown in the figure, move the equilateral △ABC with a side length of 2 units to the right along BC by 1 unit to get △DEF, and the perimeter of the quadrilateral ABFD is ().
a6b . 8
c 10d 12
In order to let residents have more places for leisure and entertainment, * * * has built several new squares. When paving the floor, the masters are going to choose the same regular polygon floor tile. Regular polygon floor tiles in the following shapes, of which () can't be inlaid in plane.
A. regular triangle B. square C. regular pentagon D. regular hexagon
4. In the plane rectangular coordinate system, the position of the point is in ().
A. first quadrant B. second quadrant C. third quadrant D. fourth quadrant
5. In a set of data 3, 4, 4, 6, 8, the following statement is true ()
A. the average is less than the median B. Average equals median.
C. the average is greater than the median D. Average equals mode.
6. It is estimated that the operation result should be in ().
A.6 to 7, B.7 to 8, C.8 to 9, D.9 to 10.
Fill in the blanks (3 points for each small question, 27 points for * * *)
7. To be meaningful in the real number range, the following conditions should be met.
8. A polygon is a polygon if the sum of its internal angles is equal to.
9. With the elevation, the oxygen content in the air is directly proportional to the atmospheric pressure. If yes, please write the functional relationship with.
10. As shown in the figure, the real number corresponding to each point on the number axis is,
Then the distance between them is. (expressed by inclusion)
1 1. A rhombus with a side length of 5cm and a diagonal length of 6cm, then the length of the other diagonal is.
12. Write a letter satisfying 14.
13. As shown in the figure, there is a cylinder with a height of 20cm and a bottom radius of 7 cm. There is a bracket at the bottom of the cylinder. It wants to eat flies at the point opposite to the top and bottom, and the shortest path it needs to crawl is cm (the result is expressed by the formula with the sum of the roots).
14. The straight line passes through a point and a point on the positive semi-axis of the shaft. If the area (as the coordinate origin) is 2, the value of is.
15. If the sum of the upper and lower bottoms of the isosceles trapezoid is 4, and the acute angles of the two diagonals are 0, the area of the isosceles trapezoid is 0 (as a result, the root sign form is retained).
Iii. Answering questions (8 small questions in this big question, ***75 points)
Scoring reviewer
16.(8 points) (1) Calculation:.
(2) Solve the equation:
Scoring reviewer
17.(9 points) As shown in the figure, each small square in the grid paper is a square with a side length of 1 unit. After the plane rectangular coordinate system is established, the vertices are all on the grid points, and the coordinates of the points are.
(1) translate at most 5 units to get the corresponding and drawn graph, and write the coordinates of the point;
② Take the origin as the center of symmetry, then draw the symmetry relative to the origin and write the coordinates of this point.
18.(9 points) This year, a fruit plantation harvested two kinds of litchi, Feizixiao and seedless No.1, and all of them were sold in RMB. It is understood that the price of Litchi is RMB per kilogram, and the price of Litchi No.1 without seeds is RMB per kilogram. How many kilograms did this plantation harvest this year?
L9。 (9 points) As shown in the figure, it is known that the circumference of an isosceles triangle is 16, and the height on the base is 4. Find the length of each side of this triangle.
20.(9 points) As shown in the figure: in the plane rectangular coordinate system, there are three points: A (0, 1), B (0), C (1, 0).
(1) If one point and three points form a parallelogram, please write down the coordinates of all qualified points;
(2) Choose a point that meets the requirements in (1) and find the analytical formula of the straight line.
2 1.( 10) In order to investigate the residents' water consumption, the math activity group in a middle school randomly selected the monthly water consumption of 30 households from a certain district 1500 households. The results are shown in the following table:
Monthly water consumption (ton) 3 4 5 7 8 9 10
Number of families 4 3 5 1 1 4 2 1
(1) Find the average, mode and median of the monthly water consumption of these 30 households;
(2) According to the above data, try to estimate the monthly water consumption of the community;
(3) Due to the lack of water resources in China, many cities often use the method of charging by stages to guide people to save water, that is, the basic monthly water consumption of each family is (tons), and the monthly water consumption of each family does not exceed (tons) at the original price, and the part that exceeds (tons) is charged twice. Which of the above questions is more reasonable as the average, mode and median monthly basic water consumption? Briefly explain why.
22.( 10) Recreation Company has the same type of machine platforms and platforms in two places, and now it will be transported to Platform A and Platform B. The expenses for transporting from two places to two places are as follows:
Party A (RMB/set) and Party B (RMB/set)
land
(1) If it is transported from the ground to Platform A, find the functional relationship between the total cost (yuan) and (platform) required to complete the above transportation;
(2) Please design an optimal transportation scheme for the amusement company to minimize the total cost and explain the reasons.
Scoring reviewer
23.( 1 1 point) As shown in the figure, BD is an angular bisector, which intersects with BC at point E, DK=BC, and connects BK and CK to obtain a quadrilateral DCKB. Please judge what kind of quadrangle DCKB is and explain the reasons.
Reference answers and grading standards of mathematics test questions
First, multiple-choice questions (3 points for each small question, * *18 points) BBBC BBCC
Fill in the blanks (3 points for each small question, 27 points for * * *)
7., 8.6, 9., 10., 1 1.8cm， 12。 The answer is not unique, such as 13. , 14.2, 12.
Third, answer questions.
16.( 1) solution: 12 (4 points)
(2) Solution: Yes. (2 points)
Replace (1),
The solution of the original equation is. (4 points)
17. Answer: 65438+ 6 points, 0 point for each painting;
(1) get 1 minute;
② Get 2 points (out of 9).
18. Solution: Set this plantation to harvest kilograms of "Feizixiao" litchi and "No.1 seedless litchi" this year. Get 1 point according to the meaning of the question.
5 points
9 points for solving this equation group.
A: This year, "Feizixiao" and "Seedless No.1" litchi harvested 2,000 Jin and 1.200 Jin respectively, with a score of 10.
19 solution: let BD=x, then ab = 8-X.
From Pythagorean Theorem, we can get AB2=BD2+AD2, that is, (8-x)2=x2+42.
So x=3, so AB=AC=5, BC=6.
20. Solution: (1) The coordinates of qualified points are respectively
,, .3 points
(2) (1) When selecting a point, let the analytical formula of a straight line be,
Get 8 points from the meaning of the question
The analytical formula of a straight line is .9 points.
② When a point is selected, a solution similar to ① can be obtained as follows
The analytical formula of a straight line is .9 points.
(3) When selecting points, use a method similar to (1) to solve the problem, and the analytical formula of the straight line can be obtained as .9 points.
Note: In the question (1), you will get 1 for each correct answer.
2 1. Solution: (1), the mode is 7, and the median is 0.
(2) (ton)
The monthly water consumption of this community is about 9300 tons.
(3) It is reasonable to take the median or mode as the basic monthly water consumption, because it can not only meet the monthly water consumption of most families, but also guide families with water consumption higher than 7 tons to save water.
22. Solution: (1);
(2) From (1): total freight.
Once again,
With the increase of, it also increases when, (yuan).
The company needs at least 14800 yuan freight to complete the above transportation plan. The best scheme is: 3 units will be transferred from the ground to the first place, 14 units will be transferred to the second place, and 15 units will be transferred from the ground to the first place.
23. Solution:
If BD is a public side, then. Therefore ∠KBD=∠CDB. (5 points).
(i) When BA≠BC, the quadrangle DCKB is an isosceles trapezoid for the following reasons:
By dividing ∠ABC by BA≠BC and BD, we know that BD is not perpendicular to AC, so ∠KBD+∠CDB = 2∠CDB≦.
Therefore, DC and Bk are not parallel. The quadrangle DCKB is an isosceles trapezoid. (8 points)
(ii) When BA=BC, the quadrangle DCKB is a rectangle.