Mathematics Test
School: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Instructions for candidates 1. This test paper is ***6 pages, with * * big questions and 25 small questions, with full marks of 120. The examination time is 120 minutes.
2. Fill in the school name, name and admission ticket number accurately on the test paper and answer sheet.
3. The answers to the test questions are all filled in or written on the answer sheet, and the answers on the test paper are invalid.
4. On the answer sheet, multiple-choice questions and drawing questions are answered with 2B pencil, and other questions are answered with black pen.
After the exam, return this paper, answer sheet and draft paper together.
First, multiple-choice questions (32 points for this question, 4 points for each small question)
There are four options for each of the following questions, and only one of them meets the meaning of the question.
The absolute value of 1 be
A.B. C. D。
2. According to the data of the sixth national census in China, the total population living in cities and towns reached 665,575,306. The scientific notation of 665,565,306 (with three significant figures reserved) is about
A.B. C. D。
3. In the picture below, which one is centrosymmetric and which one is axisymmetric?
A. equilateral triangle b parallelogram c trapezoid d rectangle
4. As shown in the figure, in the trapezoid, the diagonal line intersects with the point. If is, the value of is.
A.B.
C.D.
The highest temperature in some districts and counties of Beijing in June this year is as follows:
County Daxing Tongzhou Pinggu Shunyi Beirou Mentougou Yanqing Changping Miyun Fangshan
Maximum temperature (℃) 32 32 30 32 30 32 30 32
Then the modes and median values of daily temperature in these 10 districts and counties are respectively
A.32，32b . 32，30c . 30，32d . 32，3 1
6. There are two white balls, five red balls and eight yellow balls in an opaque box. There is no difference between these balls except color. Now, the probability of touching the red ball is
A.B. C. D。
7. The vertex coordinates of parabola are
A.B. C. D。
8. As shown in the figure,,, is a moving point on the edge (not coincident with the point,), and the perpendicular intersecting with the point intersects with the point. If,, then the following image can express the functional relationship with.
II. Fill in the blanks (the score for this question is *** 16, with 4 points for each small question)
9. If the value of the score is 0, the value of is equal to _ _ _ _ _ _ _.
10. Decomposition factor: _ _ _ _ _ _.
1 1. If the figure on the right is a surface expansion of a geometric figure, then this geometric figure is _ _ _ _ _ _ _.
12. In the right table, we record the numbers in the first column of this row as (where all
Is a positive integer not greater than 5), and each number in the table is specified as follows:
When,; When, for example, when,
According to this regulation, _ _ _ _ _; on the table
Of the 25 numbers, * * * has _ _ _ _1; The calculated value is
__________.
Iii. Answer the question (30 points for this question, 5 points for each small question)
13. Calculation:
14. Solve inequality:.
15. Given, find algebraic expression.
The value.
16. As shown in the figure, the points,,, are on the same straight line.
.
Prove:
17. As shown in the figure, in the plane rectangular coordinate system, the intersection of the image of the intersection function and the image of the inverse proportional function is.
(1) Find the analytical formula of inverse proportional function;
(2) If it is a point on the coordinate axis, and it is satisfied, write the coordinates of the point directly.
18. Solving equations or the application of equations:
After the opening of Jingtong Bus Rapid Transit, in response to the call of the municipal government for "green travel", Xiao Wang, who lives in Tongzhou New Town, took a bus to work instead of a car. It is understood that Xiao Wang's home is away from his work place 18km, and his average hourly travel distance by bus is more than twice that of self-driving car, 9 km more. It takes time for him to go to work by bus from home. How many kilometers per hour does Xiao Wang drive to work?
Iv. Answer questions (20 points for this question, 5 points for each small question)
19. As shown in the figure, in,, is the midpoint of,. If,, find the perimeter of the quadrilateral.
20. As shown in the figure, the points with middle diameters of, and are respectively on the extension lines of, and.
(1) Verification: A straight line is a tangent;
(2) If, the length of summation.
2 1. The following are some statistical charts drawn according to the relevant data in the Statistical Bulletin of Beijing National Economic and Social Development.
Please answer the following questions based on the above information:
⑴ What is the number of private cars in Beijing in 2008 (Result: three significant figures are reserved)?
(2) completing the bar graph;
(3) The increase in the number of cars not only causes traffic congestion, but also increases carbon emissions. In order to understand the situation of automobile carbon emissions, Xiaoming learned through the internet that automobile carbon emissions are related to automobile emissions. For example, if a car with a displacement of 1000 km drives for one year, its carbon emission is about tons. So he investigated 1500 private cars in his community. The number of vehicles with different displacement is shown in the following table. According to Xiao Ming's statistical data, please estimate the total carbon emission of this kind of private car with a displacement of only 0 in Beijing in 20 10 (assuming that each car travels in a balanced way 10000 km).
Statistics on the Number of Private Cars with Different Displacement in Xiaoming Community
The displacement (l) is less than
Bigger than ...
Quantity (vehicle) 29 75 3 1 15
22. Read the following materials:
Xiao Wei encountered such a problem: as shown in figure 1, in a trapezoid, the diagonal line intersects the point. If the area of a trapezoid is 1, try to find the area of a triangle with a side length of.
Xiao Wei thought this way: To solve this problem, first try to move these scattered line segments, construct a triangle, and then calculate its area. He tried the methods of folding, rotating and translating, and found that this problem can be solved by translating. His method is that the extension line of the intersection of parallel lines extends to point, and a triangular triangle is obtained (as shown in Figure 2).
Please answer: The area in Figure 2 is equal to _ _ _ _ _.
Refer to Xiao Wei's thinking method to solve the following problems:
As shown in Figure 3, the three center lines of are,,, respectively.
(1) Draw and mark a triangle with a side length of (keep drawing lines) in Figure 3;
(2) If the area of is 1, the area of a triangle with three sides of length, and is equal to _ _ _ _ _.
Five, answer (this question ***22 points, 23 questions 7 points, 24 questions 7 points, 25 questions 8 points)
23. In the plane rectangular coordinate system, the image of quadratic function intersects with the axis, two points (the point is on the left of the point), and the axis intersects with the point.
(1) Find the coordinates of this point;
2 when, the value of;
⑶ A linear function is known, and this point is a moving point on the axis. Under the condition of (3), the image of a linear function is too much, and the image of a quadratic function is too much. If only the point is above the point, find the analytical expression of this linear function.
24. In a parallelogram, the bisector intersects with the point and intersects with the point.
(1) The diagram proves that1;
(2) If it is the midpoint (as shown in Figure 2), directly write the degree;
(3) If,, and are respectively connected with (as shown in Figure 3), find the degree.
25. As shown in the figure, in the plane rectangular coordinate system, we call a graph composed of two rays and a semicircle with a diameter of. It is known that the intersection of,, and semicircles with the axis is on the reverse extension line of the ray.
(1) Find the distance between two rays and a straight line;
(2) When the image and graph of the function have only one common point, write the range of values;
When the image and graph of a linear function have exactly two common points, the value range written;
⑶ It is known that all points of a parallelogram (four vertices,,, arranged clockwise) are on the graph, not all on two rays. Find the range of abscissas of these points.