2012-2013 second semester ninth grade mathematics first training exam paper

Multiple choice questions (10 questions, 3 points each, 30 points in total)

1. The square root of the

A.3 B.±3 C. D.±

2. The partial image of the quadratic function y -x2+2x+k is shown in the figure, then the unary quadratic equation for x -x2+2x+k 0 is one solution and the other solution ( ).

A.1B.-1C.-2D.0. D．

5. Among the following figures, which are both axisymmetric and centrally symmetrical, are ()

A. Right triangle B. Isosceles trapezoidal C. Parallelogram D. Rhomboid

The solution set of the inequality group is

A．．． D．

． A．．．． As shown in the figure, in the midpoint of AB, BD, CD, AC in the middle, E, F, G, H respectively, to make a diamond, there should also be a ()

D CD BDB D BC

A company undertook the task of making 600 road traffic guidance signs for the Shanghai World Expo, and the original plan was to make one per day, but the actual average of 10 more per day than the original plan was made, so the task was completed 5 days ahead of schedule. According to the question, the following equation is correct

A． ． D. In the following four function graphs, when x > 0, y increases with the increase of x is ()

___________

12. To make the equation meaningful, the value range of a is .

13. As shown in the figure, △ABC is an equilateral triangle with a side length of 6cm, which is parallel to BC

The rectangle is truncated into thirds, then the area of the quadrilateral EFGH in the figure is .

14. Enclosing a semicircle with an area of 32π into the side of a cone, then the radius of the bottom surface of this cone is Fractional equation 16.Fig. (1) is the pattern of a tile, with which the ground is laid with this tile, and Fig. (2) is paved with an approximate square of 2×2, in which there are 5 complete diamonds; If the approximate square pattern (3) is paved into 3×3, there are 13 complete diamonds; In this way, it can be laid into an approximate square pattern of n×n. When a total of 181 complete diamonds are obtained, the value of n is .

3. Answer questions (there are small questions in this major question)

18. As shown in the figure, ABC is connected to O, ADBC is to D, and AE is the diameter of O. If AB 6, AC 8, AE 11, find the length of AD.

19. On holidays, Xiaoqiang flies a kite in the square. As shown in the figure, in order to calculate the height of the kite from the ground, he measured the elevation angle of the kite to be 60 °, and the length of the kite line BC is known to be 10 meters, and the height of Xiao Qiang AB is 1.55 meters≈≈.

Four. Answer questions (there are 3 sub-questions in this major question, each sub-question is 8 points, a total of 24 points)

20. On November 26, 2011, after 15 hours of negotiations, the NBA finally announced that an agreement had been reached, ending the long shutdown that lasted 149 days. To this end, a middle school basketball team carried out a special survey of your favorite NBA team among the students of the school", and the results of the voting were "Heat", "Lakers", "Rockets", and "Magic" four teams, and according to the survey results, the bar chart and fan chart as shown in the figure were drawn, please answer the following questions based on the information given in the figure.

Question 23 (A) Question 23 (B)

(1) The students surveyed have a total ____________; Among the respondents, the "Rocket" team was selected ____________.

(2) What is the central angle of the fan that the "Lakers" team is opposing?

(3) In the survey results of the "Heat" team, there are 5 ninth-grade students, including 3 men and 2 women, among these 5 people, you plan to randomly select 2 for interviews, please use the tree map method or the list method to find out the probability that the two selected students happen to be male students.

21 As shown in the figure, in the planar Cartesian coordinate system xOy, it is known that the image of the primary function y kx+b passes through the point A(1,0) and intersects the image of the inverse proportional function (x>0) at the point B(2,1).(1) Find the value of m and the analytic formula of the primary function;(2) Combine the image and write directly: when x>0, the solution set of the inequality kx+b>.

As shown in the figure, it is known that △ABC is an isosceles right triangle, BAC 90°, and point D is the midpoint of BC. Make a square DEFG, so that the points A and C are on DG and DE respectively, and connect AE and BG.

(1) Try to guess the quantitative relationship between BG and AE in the line segment, please write the conclusion you got directly;

(2) After rotating the square DEFG around point D at a certain angle in the counterclockwise direction (the rotation angle is greater than 0°, less than or equal to 360°), as shown in the figure, does the conclusion in (1) still hold? If so, prove it; If not, please state the reasons;

(n is a positive integer) (in order of the number of times a). For example, the three numbers 1,2,1 in the third row of a triangle correspond exactly to the coefficients in the expansion; The four numbers 1, 3, 3, and 1 in the fourth row correspond to the coefficients in the expansion, and so on.

(1) According to the above law, m.

(2) According to the above rules, write the expansion formula.

(3) Using the above rules to calculate:

24. In isosceles trapezoidal ABCD, AB∥CD, AD BC 4, CD 6, AB 10. Point P moves from point B to point A at a constant velocity of 2 units/second. The crossing point P is the perpendicular PE of the straight line BC, E is the perpendicular foot, and the straight line PE divides the trapezoidal ABCD into two parts.

（1）∠A °；

(2) Fold the lower left part upwards with PE as the symmetrical axis. If the area of the two parts coincides is S, try to find the functional relationship between S and the motion time t.

(3) Under the condition of (2), if the corresponding point of point B is B′, is there a triangle with points D, P, B′ as vertices as a right triangle in the whole motion? If so, write it directly