(Full score 120, time 120 minutes)
First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)
The value of 1. Yes ()
a . 3 B- 3 c . eq \ f( 1.3)d .-eq
\f( 1，3)
2. The following operation is correct ()
a . a3 a2 = a5 b .(a2)3 = a5 c . a3+a3 = a6 d .(a+b)2 = a2+B2
3. The front view of the following geometric figures is both a central symmetrical figure and an axisymmetric figure ()
A B C D
4. As shown in the figure, if ∨,,, is known, the degree is ().
(Figure 2)
B.32.5 C.35 D. 37.5
5. As shown in the figure, if a square is placed in a plane rectangular coordinate system, it is the origin and its coordinate is (1,), then the coordinate of this point is ().
(Figure 5)
A.(-， 1) B.(- 1，)c .(， 1) D.(-，- 1)
6. The solution set of inequality group is correctly expressed as () on the number axis.
A
B
C
D
7. In order to actively respond to Nanchong's call to create a "national health city", a school 1
500 students participated in the health knowledge contest, and their scores were recorded as A, B, C, D, etc. The scores of some students were randomly selected for statistics, and the following two incomplete statistical charts were drawn. According to the chart information, calculate the students' scores.
The following statement is incorrect ()
A. the sample size is 200 b. the central angle of the sector is 15.
C. the percentage of c in the sample is 10%. D. it is estimated that there are about 900 students with a grade in the whole school.
8. As shown in the figure, when △AB=AC, AB=AC, D is a point above BC, CD = AD, AB = BD, then the degree of ∠B is ().
A.30 B.36 C.40 D.45
(Figure 8)
9. As shown in the figure, in the rectangular ABCD, AB = 5 and AD = 12. If the rectangular ABCD rotates twice in a straight line as shown in the figure, the path length of point B during the two rotations is (
)
(Figure 9)
Asian Development Bank.
10. Quadratic function = (≠ 0) The image is as shown in the figure, and the following conclusions are drawn: ① > 0; ②=0; ③ When ≠1,>; ④>0; ⑤ If =, and ≦, = 2. The correct one is ().
A.①②③B。 ②④c。 ②⑤d。 ②③⑤
(DrawingNo. 10)
II. Fill in the blanks (6 small questions in this big question, 3 points for each small question, *** 18 points)
1 1. The solution of the fractional equation is _ _ _ _ _ _ _.
12. Factorization _ _ _ _ _ _ _ _.
13. A set of data is 1, 2, 3, 4, 5 in descending order. If the median of this set of data is 3, the variance of this set of data is _ _ _ _ _ _ _.
14. As shown in the figure, if the centers of two circles are the same, and the chord AB of the big circle is tangent to the small circle, and AB = 8, the area of the shaded part in the figure is _ _ _ _ _ _ _ _ _. (The result remains π).
O
B
A
(DrawingNo. 14)
15. Number of columns ..., where _ _ _ _ _ _ _.
Third, answer the question (this big question * * 9 small questions, ***72 points)
16. As shown in the figure, there is a rectangular piece of paper ABCD with AB=8 and AD= 17. Fold this rectangular piece of paper so that the vertex A falls on the A' on the BC side, and the straight line where the crease is located passes through both the AB side and the AD side (including the end).
Point), let BA'=x, then the value range of x is.
17.(6 points) Calculation:
18.(8 points) As shown in the figure, AD and BC intersect at O, OA=OC, ∠OBD=∠ODB.
A
B
O
C
D
(18 map)
Proof: AB=CD.
19.(8 points) When studying the Solution of Binary Linear Equation, the math teacher Zhang designed a math activity. There are a and B.
Two groups of cards, 3 cards in each group, with 0, 2 and 3 written on the cards in Group A respectively; Group B cards are written as -5,-1 and 1 respectively. Every card is the same except the numbers written on the front. A is randomly selected from group a.
Take one as X, and B randomly selects one from Group B as Y. 。
(1) If the number extracted by A is 2 and the number extracted by B is-1, they are exactly the solution of AX-Y = 5, find the value of A;
(2) Find the probability that the number randomly selected by A and B is exactly the solution of equation AX-Y = 5. (Please use the tree diagram or list method to solve. )
20.(8 points) It is known that the univariate quadratic equation x2-2eq about x \ r (,2) x+m = 0 has two unequal real roots.
The maximum integer value of (1) real number m;
(2) Under (1), the real root of the equation is x 1, x2, and the value of the algebraic expression X 12+X22-X 1x2 is found.
2 1.(8 points) As shown in the figure, the image of linear function y 1=kx+b and inverse proportional function y2= EQ.
The image of \F(m, x) intersects with points A (2, 5) and B, and intersects with Y axis at point C (0, 7). /preview/SD9-QNO-648。