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First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)

1.(3 points) As shown in the figure, the numbers represented by points A and B on the number axis are opposite, so the number represented by point B is ().

A.-6 B. 6 C. 0 D. Not sure

2.(3 points) As shown in the figure, after the shadow triangle in the square ABCD rotates 90 clockwise around the point A, the figure obtained is ().

A.B. C. D。

3.(3 points) A six-member activity group made a survey to find out the ages of its members. Statistical age is as follows (unit: years old): 12, 13, 14, 15, 15.

A. 12， 14 B. 12， 15 C. 15， 14 D. 15， 13

4.(3 points) The following operation is correct ()

A.= B.2×= C.=a D.|a|=a(a≥0)

5.(3 points) The unary quadratic equation x2+8x+q=0 about x has two unequal real roots, so the range of q is ().

a . q < 16 b . q > 16 c . q≤4d . q≥4

6.(3 points) As shown in the figure, ⊙O is the inscribed circle of △ABC, then point O is △ABC's ().

A. The intersection of perpendicular bisector of three sides B. The intersection of three angular bisectors

C. Intersection point of three midlines D. Intersection point of three heights

7.(3 points) Calculate (a2b)3? The result of is ()

A.a5b5 B.a4b5 C.ab5 D.a5b6

8.(3 points) As shown in the figure, what are E and F respectively? Points on the sides of AD and BC of ABCD, EF=6, ∠ dEF = 60. Fold the quadrilateral efCD along EF to get EFC'D'. If ED' passes through BC at G point, the circumference of △GEF is ().

A.6 B. 12 C. 18 D.24

9.(3 points) As shown in the figure, in ⊙O, AB is the diameter, CD is the chord, AB⊥CD, the vertical foot is E, and the connecting line is CO, AD, ∠ Bad = 20, so the following statement is correct ().

A.AD = 20b B . CE = EO c .∠OCE = 40d .∠BOC = 2∠BAD

10.(3 points) a≠0, the approximate images of functions y= and Y =-AX2+A in the same rectangular coordinate system may be ().

A.B. C. D。

Fill in the blanks (this topic is entitled ***6 small questions, 3 points for each small question, *** 18 points)

1 1.(3 points) As shown in the figure, if AD∨BC, ∠ A = 1 10, then ∠ B =.

12.(3 points) Decomposition factor: xy2-9x =.

13.(3 points) When x=, the quadratic function y = x2-2x+6 has a minimum value.

14.(3 points) As shown in the figure, in Rt△ABC, ∠ c = 90, BC= 15, tanA=, then AB =.

15.(3 points) As shown in the figure, the side development of the cone is a sector with a central angle of120. If the radius of the bottom circle of the cone is, then the generatrix L of the cone is =.

16.(3 points) As shown in the figure, O is the origin in the plane rectangular coordinate system. The coordinates of vertices A and C of ABCD are (8,0) and (3,4) respectively. Points D and E divide the line segment OB into three equal parts, and the extended CD and CE meet OA and AB at points F and G respectively to connect FG. Then draw the following conclusions:

①F is the midpoint of OA; ②△OFD is similar to△△ beg; ③ quadrilateral area DEGF is; ④OD=

The correct conclusion is (fill in the serial numbers of all correct conclusions).

Third, answer the question (this big question is ***9 small questions, *** 102 points)

17.(9 points) Solve the equation.

18.(9 points) As shown in the figure, points E and F are on AB, AD=BC, ∠A=∠B, AE = BF. Verification: △ ADF △ BCE.

19.( 10) In order to know the time for students to fill in their volunteers in one semester, a survey was conducted among 50 students in the class. According to the time t (unit: hours) for filling in their volunteers, the students were divided into A (0≤t≤2), B (2 < t ≤ 4) and C (4).

Such as a picture, an incomplete bar chart. According to the above information, answer the following questions:

(1) There are students in Class E, and the bar graph is completed;

(2) The number of students in category D accounts for% of the total number of people surveyed;

(3) Choose two students from this class whose volunteer time is 0≤t≤4, and find the solution set of two students whose volunteer time is 2.

23.( 12 points) It is known that the parabola y 1=﹣x2+mx+n, the straight line y2=kx+b, and the symmetry axis y 1 intersects with Y2 at point A (﹣ 1 5), point A.

(1) Find the analytical formula of y 1;

(2) If y2 increases with the increase of X, and both y 1 and y2 pass through the same point on the X axis, find the analytical expression of y2.

24.( 14 points) As shown in the figure, the diagonal AC and BD of rectangular ABCD intersect at point O, and the symmetrical figure of △COD about CD is △ ced.

(1) verification: the quadrangle OCED is a diamond;

(2) Connect AE, if AB=6cm, BC = cm.

① Find the value of sin∠EAD;

(2) If the point P is a moving point on the AE line (not coincident with the point A), connect the OP, and the moving point Q starts from the point O, moves to the point P along the OP line at the speed of 1cm/s, then moves to the point A along the PA line at the speed of 1.5cm/s, and stops moving when it reaches the point A..

25.( 14 points) As shown in the figure, AB is the diameter ⊙O, =, AB=2, connecting AC.

(1) Verification: ∠ cab = 45;

(2) If the straight line L is tangent to ⊙O and C is the tangent point, take a point D on the straight line L so that BD=AB, and the straight line where BD is located intersects with the straight line where AC is located at point E to connect AD.

① Try to explore the quantitative relationship between AE and AD to prove your conclusion;

② Is it a fixed value? If yes, request the fixed value; If not, please explain why.