A, multiple-choice questions (this big topic ***8 small questions, each small question 3 points, * * 24 points. Of the four options given in each small question, just one meets the requirements of the topic. Please fill in the letter code of the correct option in the corresponding position on the answer sheet.
1. equals ()
A.B. C. D。
2. The radii of the circumscribed two circles are 2cm and 3cm respectively, so the center distance between the two circles is ().
A.B. C. D。
3. Rational number, the position on the number axis is as shown in the figure, then the value of ().
A. greater than 0 b less than 0 c less than d greater than.
4. In the following operations, the correct one is ().
A.B. C. D。
A classmate took part in a singing contest, and their preliminaries were different. Now, the top one has been selected to participate in the finals. Xiaohong needs to know this classmate's score () to judge whether she can enter the final.
A. Mode B. Median C. Mean D. Range
Xiaoming climbed a hillside with a slope of 100 degrees, so he stood up.
A.B. C. D。
7. As shown in the figure, △ABC is the left view of a cone, where the lateral area of this cone is ().
A.B. C. D。
8. As shown in the figure, in a rectangle, when the right-angled vertex of a right-angled triangle moves on the edge, the right-angled edge always passes through the point. Let the other right-angled side of the right-angled triangle intersect with points Q,,, and, then the function image between and is roughly ().
Two. Fill in the blanks (this big question * * *, a total of 10, 3 points for each small question, * * * 30 points. There is no need to write the answer process, please fill in the answer directly in the corresponding position on the answer sheet).
9. Factorization:
10. If the solution of the equation is known, the value of is _ _ _ _ _.
1 1. The National Audit Office issued an announcement: As of May 20th, 20 10, the national * * * received billions of donations for earthquake relief in Yushu, which was expressed as _ _ _ _ _ yuan by scientific notation.
12. If, then.
13. As shown in the figure, two squares and regular pentagons on the plane have a common edge, then.
14. In the plane rectangular coordinate system, the coordinates of the endpoint of the line segment are, and the line segment is obtained by translating units to the right and then translating units down, so the coordinates of the corresponding points are _ _ _ _ _ _.
15. There is a point on the line. We do the following: insert a point between every two adjacent points. After this operation, there are _ _ _ _ _ _ _ points on the straight line.
16. As shown in the figure, the side length of a square piece of paper is, and the sum of the perimeters of the four triangles in the figure is _ _ _ _ _.
17. As shown in the figure, in △,, is the center line on the side, and its value is _ _ _ _ _.
18. In the math activity class, the teacher draws a straight line parallel to the ray on the blackboard (as shown in the figure), so that the students can find a little sum on the straight line and the ray, so that the triangle with,, and as the vertex is an isosceles right triangle. Such a triangle can draw at most _ _ _ _.
Three. Solution (this big question * * *, there are 10 small questions, and the score is * * 96. Please answer in the designated area of the answer sheet, and write the necessary text description, proof process or calculus steps when answering).
19. (The full mark of this question is 8) Calculation:
.
20. (The full mark of this question is 8) Solve the equation:
2 1. (The full mark of this question is 8 points) As shown in the figure, the sum of points in the middle is two points on the diagonal, and. Verification:.
22. (The full mark of this question is 8) When a company recruits employees, each applicant should randomly choose one of the questions ",,,and" to answer, and it is stipulated that one of them is qualified. Knowing that a candidate can answer one or two questions, then try to find out the probability that the candidate is qualified.
23. (The full mark of this question is 10) As shown in the figure, it is known that the images of a linear function and an inverse proportional function intersect at two points.
(1) Find the coordinates of two points;
(2) Observing the image, we can know that the range where the linear function value is less than the inverse proportional function value is _ _ _ _ _ _.
(Write the answer directly in the corresponding position on the answer sheet)
24. (The full mark of this question is 10) In order to understand the students' extracurricular activities, a proofreader conducted a sample survey on the distribution of the number of people who participated in the four extracurricular interest groups of painting, calligraphy, dance and musical instrument, and drew the following two incomplete statistical charts according to the collected data. Please answer the following questions according to the information provided in the picture:
(1) How many students did this * * * survey?
(2) To supplement the bar chart and calculate the degree of the central angle of the calligraphy part in the fan chart;
(3) If the school has * * * students to participate in this extracurricular interest group, each teacher can only tutor at most, and it is estimated that at least how many teachers need to be prepared for each interest.
25. (The full mark of this question is 10) As shown in the figure, in the plane rectangular coordinate system, as the origin, the side length of each small square is a unit length. In the first quadrant, the abscissa and ordinate of two points are integral, and.
(1) written coordinates,;
(2) Draw a graph formed by the rotation of a line segment around a point, and find its area (the result is reserved).
26. (The full mark of this question is 10) As shown in the figure, it is the diameter of ⊙O, any point on the extension line, the midpoint of the semicircle, where ⊙O is cut, and CD is connected to AB at point E. 。
Verification: (1) pd = pe;
(2) .
27. (The full mark of this question is 12) A flower farmer cultivates 2 species of flowers and trees and 3 species of flowers and trees, and the cost of * * * is 1700 yuan; To cultivate three kinds of flowers and trees, 1 plant flowers and trees requires 1500 yuan.
(1) Calculate A, B and the cost per plant for planting flowers and trees respectively;
(2) According to the market survey, the price of 1 species of flowers and trees is 760 yuan, and the price of 1 species of flowers and trees is 540 yuan. The flower shop decided to cultivate two kinds of flowers and trees under the premise of not exceeding 30 thousand yuan. If the number of plants cultivated by the second kind of flowers and trees is three times that of the first kind of flowers and trees, there are 10 plants, and the total profit is not less than 2 168.
28. (full mark of this question 12) It is known that a parabola intersects with a point and intersects with a point, and its vertex is.
(1) and write the symmetry axis of parabola;
(2) Connecting line, a straight line passes through this point, and passes through the symmetry axis of parabola at this point. Prove that quadrilateral is isosceles trapezoid;
(3) Is there a point on the q parabola that makes the area of △OBQ equal to the area of the quadrilateral? If it exists, find out the coordinates of the point; If it does not exist, please explain why. Please forgive me (because you can't draw).