(Time: 100 minutes, full mark: 150 minutes)
Note to candidates:
1. This paper contains three major questions, including ***25 questions. When answering questions, candidates must answer in the position specified in the answer sheet according to the requirements of answering questions. Answering questions on draft paper and this paper is invalid.
2. Except for the first and second questions, unless otherwise specified, the main steps of proof or calculation must be written in the corresponding position on the answer sheet.
1. Multiple-choice questions: (There are 6 questions in this big question, with 4 points for each question, out of 24 points).
There is only one correct option for each small question. Fill in the corresponding item number correctly on the answer sheet with 2B pencil]
1. Among the following radicals, the secondary radical of the same kind is (▲).
(1); (b) and: (c) and: (4).
2. Regarding the image of quadratic function, the following judgment is correct (▲).
(a) The image opening is upward; (b) The symmetry axis of the image is a straight line;
(c) the image has the lowest point; (d) The vertex coordinate of the image is (,2).
3. About the equilateral triangle, the following statement is incorrect (▲)
(a) An equilateral triangle is an axisymmetric figure; (b) An equilateral triangle is a figure with central symmetry;
(c) An equilateral triangle is a rotationally symmetric figure; (d) All equilateral triangles are similar.
4. Cut a piece of paper with a circumference of 20cm and an area of 20 into four small triangular pieces of paper with the same shape and size (as shown in figure 1), and the circumference and area of each small triangular piece of paper are respectively (▲).
(1)10cm, 5; 10cm,10cm;
(C)5cm，5； (D)5cm， 10。
5. It is known that there are two unit vectors, vector, so the following conclusion is correct (▲).
(1); (b) and: (c) and: (4).
6. Figure 2 reflects the functional relationship between the distance s (kilometers) from a to b and the time t (minutes) used. It is known that the car stopped to refuel once. According to the image, the following description is incorrect (▲).
(a) It took 10 minutes to refuel;
(b) The vehicle speed has not changed before and after refueling;
(c) The speed of the car after refueling is 90 kilometers per hour;
(d) The distance between Party A and Party B is 60 kilometers.
Two. Fill in the blanks: (This topic is entitled *** 12, with 4 points for each question, out of 48 points)
[Fill in the answer directly in the blank space after the corresponding question number on the answer sheet]
7. Calculation: ▲.
8. Calculation: ▲.
9. Factorization in the real number range: = ▲.
10. The solution of the equation is: ▲.
1 1. Known, and then ▲.
12. If the image of the known function passes through the first, third and fourth quadrants, the value range of is ▲.
13. Translate the parabola to the left by one unit. The expression of the parabola is: ▲.
14. It is known that if any of the six numbers 1, 2, 3, 4, 5 and 6 is taken as the constant term of the equation, then the probability that the equation has real roots is ▲.
15. As shown in Figure 3, in the known trapezoidal ABCD, ABCD, AB=5, CD=3, AD=BC=4, then ▲.
16. As shown in Figure 4, Xiao Fang is 3 meters away from the street lamp, and she finds that her shadow (DE) on the ground is 2 meters long. If the height of the small square is 1.6 meters, then the height (AB) of the street lamp from the ground is ▲ meters.
17. As shown in Figure 5, it is known that AB is ⊙O, and the diameters ⊙O 1 and ⊙O2 are OA, OB, ⊙O3 and ⊙O, respectively.
⊙O 1 and ⊙O2 are tangent, so the ratio of the radii of ⊙O3 and ⊙O is ▲.
18. It is known that A is a point in the plane rectangular coordinate system. First, move point A upward by 3 units to get point B, and then rotate point A clockwise by 90 degrees around point B to get point C. If the symmetrical point of point C about the Y axis is (1, 2), the coordinate of point A is ▲.
Third, answer: (This big question is ***7 questions, out of 78 points)
[Write down the process of answering the following questions on the answer sheet]
19. (The full mark of this question is 10) Calculation:.
20. (The full score of this question is 10, and the full score of each small question is 5 points.)
As shown in fig. 6, a positive proportional function and an inverse proportional function are known.
The intersection of images in the first quadrant is a (2 2,4).
(1) Find the analytic expressions of proportional function and inverse proportional function;
(2) translating a straight line, wherein the translated straight line intersects the X axis at point b,
The intersection with the inverse proportional function image in the first quadrant is C(4, n).
Find the distance between b and c.
2 1. (The full score of this question is 10, (1) is 6, and (2) is 4. )
As shown in figure 7, in △ABC, AB=AC, and point D is on the side of BC, BD=6, and CD=AB.
(1) Find the length of AB;
(2) Find the tangent of.
22. (The full score of this question is 10, with 5 points for each small question)
As shown in fig. 8, it is known that the points and sum on the line segment are both squares, connecting them.
(1) Verification: =;
(2) Let the intersection of sum be p,
Verification:
23. (The full score of this question is 12, and each small question is 4 points. )
In order to understand the students' attention to hot news, during the "two sessions", Xiao Ming made a survey on the number of times the whole class watched the news of the "two sessions" in a week. The statistics of the survey results are shown in Figure 9 (the number of boys who watched the news three times is not marked).
According to the above information, answer the following questions:
(1) The number of girls in this class is▲, and the median number of times girls watch the news of the "two sessions" is▲;
(2) For a certain group, we will give it a week.
Someone who has watched the hot news at least three times.
The percentage of people in their group is called
Group's attention index to hot news.
If the boys in this class are interested in the news of the "two sessions"
The "attention index" is 5% lower than that of girls.
The number of boys in this class;
(3) Further analyze the boys and girls in this class.
Statistical mean (times) median (times) mode (times) variance ...
The boys in this class
3 4 2 ……
The characteristics of the number of times you watch the news of the "two sessions", Xiao Ming
Some statistics of boys are given (such as table 1).
According to the statistical knowledge you have learned, it is appropriate.
Calculate the relevant statistics of girls and compare them.
The number of times boys and girls in the class watched the news of the "two sessions"
The size of the fluctuation.
24. (Full score for this question 12, 4 points for each small question)
As shown in figure 10, it is known that the parabola intersects the negative semi-axis of the shaft at a point, intersects the positive semi-axis of the shaft at a point, and.
( 1);
(2) If the point is on a parabola, the quadrilateral is
Parallelogram, try to find the analytical formula of parabola;
(3) Under the condition of (2), make an angular bisector of ∠OBC,
Intersect with parabola at point p, and find the coordinates of point p.
25. (The full mark of this question is 14, (1) item 4, (2) item 5, (3) item 5).
As shown in the figure 1 1, it is known that the radius length of ⊙O is 1, PQ is the diameter of ⊙O, point M is a point on the extension line of PQ, make a circle with point M as the center, intersect with ⊙O at points A and B, connect PA and extend with ⊙.
(1) If AB happens to be the diameter of ⊙O, let OM=x and AC=y, try to draw a general graph that meets the requirements in Figure 12, and find the resolution function of Y about X;
(2) Join OA, MA and MC. If OA⊥MA and △OMA are similar to △PMC, find the length and radius of OM ⊙ M;
(3) Is there a ⊙M that makes AB and AC just two sides of a regular Pentagon? If it exists, try to find the length of OM and the radius of ⊙M; If it does not exist, please explain why.