I. Fill in the blanks (10× 3' = 30 points)

1. If the image of the inverse proportional function passes (1, -2), the analytical formula of the inverse proportional function is _ _ _ _ _ _ _ _ _ _ _ _.

2. If the value of the score is 0, then x = _ _ _ _ _ _ _ _ _ _ _ _

3. If yes, then _ _ _ _ _ _ _ _ _ _.

4. Simplification: _ _ _ _ _ _ _ _ _ _.

5. As shown in figure 1, if AB//CD in quadrilateral ABCD is added with AD//BC, then quadrilateral ABCD is a parallelogram. Now please add a suitable condition: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Figure 1 Figure 2

6. As shown in Figure 2, it is a movable diamond-shaped clothes rack with a side length of 10cm. If the nail spacing on the wall is AB = BC = 10 cm, then ∠1= _ _ _ _ _ _.

7. As shown in Figure 3, in the square ABCD, AB= 1, and point P is a point on the diagonal AC. If AP and PC are diagonal squares, then the sum of the perimeters of the two small squares is _ _ _ _ _ _ _ _.

Figure 3 Figure 4

8. As shown in Figure 4, if ABCD, AD//CD, diagonal AC⊥BD, and AC = 5cm, BD = 12cm, the sum of the lengths of the two bottoms of the trapezoid is equal _ _ _ _ _ _ _ _ _ _ _ cm.

9. If the straight line Y=2X- 1 intersects the X axis at point A and the Y axis at point B, the length of AB is _ _ _ _ _ _ _ _.

As shown in Figure 5, p is the point of the inverse proportion function image in the first quadrant, and the area of the rectangle PEOF is 3, then the inverse proportion function expression is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

Y

P

E

O F X

Figure 5

10, the straight line y = 2x-4 intersects the X axis at point A and the Y axis at point B, so the length of AB is

Second, the multiple-choice question (this big question ***8 small questions, each small question 3 points, ***24 points. The first question has only one correct option. Fill in the code of the correct option in the brackets after the question. )

1 1, the score is meaningful, so the value range of x is ()

a、X & gt3 B、X & lt3 C、X≠3 D、X≠-3

12, the weather forecast says that the highest temperature in Yichun today is 34℃ and the lowest temperature is 20℃, so the temperature range in Yichun today is ().

a、54℃ B、 14℃ C 、- 14℃ D 、-62℃

13, among the following four functions, when x >; 0, y increases with the increase of x is ()

a、Y= B、Y=- C、Y=-x D、Y=-2x- 1

Although 14 and 10 students bought shoes in the following sizes: 20, 20, 2 1, 22, 22, 22, 23, 24. (unit: Cm), shoe store owners are most concerned about () in this set of data.

A, mean b, median c, mode d, variance

15 As shown in Figure 6, the images of the proportional function y = x and the inverse proportional function y = intersect at point A and point C, the AB┴X axis is at point B, and the CD┴X axis is at point D. The area of this quadrilateral ABCD is ().

A、 1 B、2 C、D、A D

A

D

C B figure 6 B E C figure 7

16, as shown in fig. 7, in the isosceles trapezoid ABCD, AD//BC, AE//DC, ∠ B = 60, BC = 3, and the circumference of δδABE is 6, then the circumference of the isosceles trapezoid ABCD is ().

a、8 B、 10 C、 12 D、 16

17. Fold a rectangular piece of paper ABCD as shown in Figure 8, so that the vertex C falls on C', where AB = 4. If ∠ c' ED = 30, the length of the crease ED is ().

A c

A, B, C, D and 8th.

B

Council of Europe

18 as shown in fig. 9, in the same rectangular coordinate system, the image positions of the proportional function y= kx+3 and the inverse function y= may be ().

yoyoyo

x x

x

A B C D

Three. (This big title is ***3 small questions, 19, 4 points on the 20th, 5 points on the 2nd1,* *13).

19, simplified:

20, solve the equation:

2 1, simplify first, and then choose an x value that you like and make the original formula meaningful to substitute for evaluation.

Four. (There are ***3 small questions in this big question, each with 6 points, *** 18 points)

22. Lao Li, a large vegetable farmer in Yifeng County, has a square vegetable field. He is going to leave two straight paths in the middle of the vegetable field and divide the vegetable field into four pieces with equal area for special planting. Please add two intersecting lines in the figure below to help Lao Li design three different segmentation schemes and briefly explain the drawing method.

Method one, method two and method three.

23. As shown in figure 10, it is known that in ABCD, E is the midpoint of AD, and the extension line of CE intersects the extension line of BA at point F ... Prove that A is the midpoint of BF.

C D

E

B F

A

As shown in figure 10.

24. Teacher Zhang will choose one of the two students with excellent math scores in the class to participate in the "National Junior Middle School Mathematics League". To this end, he tutored two students and took 10 times during the tutoring period. The test results are as follows:

The first time 1 time 2 3 4 5 6 7 8 9 10

A 68 80 78 79 78 84 8 1 83 77 92

B 86 80 75 83 79 80 85 80 77 75

Answer the following questions with the data in the table: (1) Fill in the blanks and complete the table below:

Average score median model

One 80 79.5

B 80 80

(2) Teacher Zhang got the variance of A from the examination report form, with S A 2 = 33.2. Please calculate the variance of B 10 test scores.

(3) According to the above information, please use the statistical knowledge you have learned to help Mr. Zhang select the candidates to participate in the "National Mathematics League" and briefly explain the reasons.

Verb (abbreviation of verb) (this big topic has two small topics, 7 points in question 25, 8 points in question 26, *** 15 points).

25. as shown in figure 1 1, the image of the linear function y=kx+b and the image of the inverse proportional function y= intersect at point a and point b. ..

(1) Using the conditions in the graph, the analytic expression of the inverse proportional function and the value of n are obtained.

y

A(-2， 1)

x

B( 1，n)

Figure 1 1

(2) Find the analytical formula of linear function.

(3) Write the value range of x that makes the value of linear function greater than the value of inverse proportional function according to the image.

26. As shown in figure 12, the edge CD of rhombic ABCD is on the edge CE of rhombic ECGF, and D is the midpoint of CE. Connect BE, DF

(1) Observe and guess the relationship between be and DF, and prove your conclusion.

(2) Are the rotations of two triangles coincident? If yes, please explain the rotation process; If not, please explain why.