Math test questions
(Examination time 120 minutes, full mark 120 minutes)
Fill it out carefully first, I believe you have filled it in correctly! (3 points for each space, ***33 points)
1. Calculation:; ; .
2. Decomposition factor:; Simplify:
Calculation:.
3. If the point is in the first quadrant, the value range of is; If a straight line passes through this point, then; The symmetry axis of parabola is a straight line.
4. It is known that the diameter of the cone bottom is 4 cm and the length of its generatrix is 3 cm.
Then its lateral area is.
As shown in the figure, sum is an equilateral triangle with a side length of 2. If these points are on the same line and connected, the length is.
Second, choose carefully, I believe you can choose correctly! One and only one of the four answers A, B, C and D is correct. Please put the only correct answer serial number in the question in parentheses after the question. If you leave it blank, fill it wrong or fill it too much, you won't get a score. The full mark of this question is 12).
6. To know the service life of a batch of TV sets, 30 TV sets were randomly selected for experiments. In this question, 30 is ().
A. Individual B. Population C. Sample size D. A sample of the population
7. The calculation result is ()
A.B. C. D。
8. Known inverse proportional function, the following conclusion is incorrect ().
A. the image must pass through point B. It decreases with the increase of.
C. the image is in the first and third quadrants. D. if so, then
9. As shown in the figure, the four geometric bodies are cuboid, cylinder, sphere and triangular prism, and one view of three of these four geometric bodies is the same geometric figure, so the other geometric body is ().
A. cuboid B. cylinder C. sphere D. triangular prism
Third, multiple-choice questions, I believe you have chosen! (**3 small questions, 3 points for each small question, 9 points for each small question, at least two answers for each small question are correct, 3 points for all answers, 0 points for incomplete answers and 0 points for all answers).
10. The following statement is true ()
A. is an irrational number
B. The range of independent variables of this function is
The cube root of c is
D If the points are symmetrical, the value of is 5.
1 1. The following proposition is correct and affirmative ()
A. the variance of a set of data is
B. To know the performance of a batch of new missiles, adopt the method of sampling survey.
C. buy a welfare lottery to win the prize. This is a random event.
D if two cards are randomly selected from three cards with three numbers written on them, the probability that the product of two numbers on the cards is positive is
12. As shown in the figure, it is known that in a trapezoid,, intersects at one point, and the following statement is true ().
A. the trapezoid is an axisymmetric figure B.
C. A trapezoid is a figure with central symmetry.
Fourth, be patient and try to see if I can do it! (**8 questions, out of 66 points)
13. (The full mark of this question is 6) Solve the inequality group.
14. (The full mark of this question is 7) As shown in the figure, a point is any point on the side of a square, and the extension line passing through this point is at this point.
15. (The full mark of this question is 7) On May 3, 20081day, the Olympic torch relay was held in Wuhan, Hubei Province. The Youth League Committee of Hongcheng Middle School in our city held a knowledge contest of "Welcome the Olympics, Cheer for the Olympics" in 8 classes of Grade 7. The class with the highest score is the winning class. The results are as follows:
Class seven (1) Seven (2) Seven (3) Seven (4) Seven (5) Seven (6) Seven (7) Seven (8)
Score 90 90 80 80 90 80 100 90
Number of students 46 46 48 47 49 45 50 50
(1) Please write down the average, mode and median scores of each class and team directly;
(2) The school decided to send five students randomly from the winning class to Wuhan for free to watch the Olympic flame. Xiaoying is a student in Class 7, so what is the probability that she will be sent to Wuhan for free to watch the Olympic flame?
16. (The full mark of this question is 8) It is known, as shown in the figure, in the middle, the intersection with the diameter is a point, and the intersection is a point.
Proof: the tangent of yes.
17. (The full mark of this question is 8) The picture shows the arc door of "Ming and Qing Film and Television City". Ms. Huang Hong went to the film and television city to play and wanted to know the relevant data of this door. So she learned from the scenic spot manager that the circle where the arc door is located is tangent to the horizontal ground, cm, cm, and perpendicular to the horizontal ground. Please help Ms. Huang Hong to calculate the highest point of this arc door according to the above data.
18. (The full mark of this question is 8) A certain city has a piece of land of *** 100 mu, and a real estate agent bought this land at the price of 800,000 mu, and plans to build a "harmonious garden" residential community. It is planned to build eight residential areas (districts, districts and districts) in this residential area, each of which will build a 24-story building. Each district will build a building with 18 floors; A 16-storey building will be built in each district. In order to meet the different housing needs of citizens, the developer is going to build both communities into high-grade buildings, with 800 yuan on each floor, and initially calculate the cost of 800 yuan/; District, District, District three residential areas will be built into mid-range housing, each floor of 800 yuan, preliminary accounting cost 700 yuan/; District, district, district will be built affordable housing, each floor of 750 yuan, preliminary accounting cost 600 yuan/.
Other idle land in the whole community is used for building roads, greening, gardens, sports fields and residents' living shops. These expenses, together with property management fees and installation of floor elevators, will cost 99 million yuan.
After the construction is completed, the developer plans to set the average price of high-end, mid-range and affordable housing at 3,000 yuan/,
The prices are 2600 yuan/and 2 100 yuan/respectively. If all the houses are sold out, please help me calculate the estimated profit of the real estate developer.
19. (Full mark for this question is 8) After the Wenchuan earthquake in Sichuan, a factory workshop in our city received an urgent task to produce a batch of tents, which must be completed within 12 days (inclusive). It is known that the cost of each tent is 800 yuan, and the workshop can produce 20 tents every day. In order to speed up the progress, the workshop adopts workers to work overtime day and night in batches, and the machines are running at full capacity. Production efficiency has improved. In this way, 22 tents were produced on the first day, and then 2 tents were produced every day. Due to machine wear and other reasons, when the number of tents produced every day reaches 30, the average cost of each tent produced that day will increase by 20 yuan for every additional 1 tent. Let the time to produce these tents be days, and the tents produced every day are the top.
(1) Write the functional relationship between and directly, and write the range of independent variables.
(2) If the order price of these tents is 1.200 yuan per tent, the workshop decides to donate all the profits on the day when the highest profits are obtained to the disaster area. Suppose the daily profit of the workshop is RMB, try to find out the functional relationship between RMB and RMB, and find out how much money the workshop donated to the disaster area.
20. (The full mark of this question is 14) As shown in the figure, in a right-angled trapezoid, a plane rectangular coordinate system is established with the origin, the three-point coordinates are respectively, the point is the midpoint of the line segment, and the moving point starts from the point and moves along the polyline at a speed of 1 unit per second, and the moving time is seconds.
(1) Find the analytical formula of the straight line;
(2) If the moving point moves on the line segment, what is the value, and the area of the quadrilateral is the trapezoid area?
(3) When the moving point starts from the point and moves along the broken line, the area is set to, please write the functional relationship of sum directly and point out the value range of the independent variable;
(4) When the moving point moves on the line segment, can you find a point on the line segment to make the quadrilateral rectangular? Request the coordinates of the moving point at this time; If not, please explain why.