Name score

(Full score 150, time 90)

1. Multiple choice questions (3 points for each small question, 30 points for * * *)

1. In △ABC, AB=AC, BC=5cm, which is the perpendicular bisector of another waist AC at AB and D, connecting BD. If the circumference of △BCD is 17cm, the waist circumference of △ABC is ().

a . 5cm b . 7cm c . 1 1cm d . 12cm

2. It is known that when Rt△ABC, ∠ C = 90, AD is divided by ∠BAC and passes through BC to D. If BC=32 and BD: DC = 9: 7, the distance from D to AB is ().

12 14 c 16d 16

3. Freshmen in a school are in military training. If you form a phalanx, there will be six more students.

If each row is reduced by 4 people and the number of rows is increased by 6 rows, then 2 people are less, and the total number of students is ().

AD 256-260

4. As shown in the figure, in the parallelogram ABCD, EF intersects with the diagonal intersection o,

If AD=6cm, AB=5cm, OE=2cm, then the circumference of the trapezoidal ABEF is ().

a . 13㎝b . 14㎝c . 15㎝d . 16㎝

5. It is known that point P(m, n) is on the image of inverse proportional function, so there is another point () on this image.

A.(-m，n) B.(m，-n)c .(m，-n) (0，0)

6. If A is the root of quadratic equation and -A is the root of equation, then the value of A is ().

A.0 B.3 C.0 or 3d.cannot be determined.

7. The following four pictures are the tree shadows at four different times on the same day. Their time sequence from morning till night is as follows.

a . 1234 b . 43 12 c . 342 1d . 423 1

8. The bisector of the inner corner of a rectangle divides one side of the rectangle into 3㎝ and 5㎝, so the perimeter of the rectangle is ().

A. 16cm B.22cm C.22cm or 26cm d.30cm

9. Throw four coins up, and the probability of two heads up and two heads down after landing is ()

A.B. C. D。

10. One intersection of inverse proportional function and direct proportional function is (2,3), and the other intersection is ().

A.(3，2) B. (-2，3) C. (-2，-3) D. (-3，-2)

2. Fill in the blanks (3 points for each small question, 30 points for * * *)

1. It is known that O is the intersection of two sides AB of △ABC and the perpendicular line of AC, and ∠ BOC = 50, then ∠A=.

2. If two cards are randomly selected from 52 playing cards (except the king of size), the probability of reaching the same suit is.

There are six black balls and several white balls in a pocket. Don't pour your balls. ) Take a ball out of your pocket at random, write down its color, put it back in your pocket, and repeat the above process. If * * * touches the black ball 200 times, including 60 times, please estimate that there is probably a white ball in your pocket.

4. If one root of the equation about x is,

Then its other root is.

5. If the two roots of the equation about x are flat.

If the square is m and the sum of two roots is n, then algebra

The value of the formula is.

6. It is known that y is inversely proportional to x+ 1, when

When x=2, y =12; When x=-3, the value of y is.

7. As shown in the figure, P is one side of the square ABCD.

The midpoint of AD, BM⊥PC is at point M, then the length of BM is.

8. It takes 10 days for Party A to complete a project alone.

B it takes 15 days to complete it alone. Now two people cooperate, and the manufacturer needs * * * after the completion.

Paid to 450 yuan, if distributed according to the completed workload,

A is worthy of yuan.

9. As shown in the figure, in △ABC, D and E are the midpoint of AB and AC respectively.

Connect DE,

BE, DC and BE, CD intersect at point O, if, then

.

10. The quadrilateral formed by connecting the midpoints of each side of the quadrilateral is a diamond.

Then the characteristics of the original quadrangle are.

Three. Solution and proof (***90 points)

1.( 10 minute) As shown in the figure, it is known that O is the intersection of diagonal AC and BD of parallelogram ABCD, and the bisectors of AF ∠BAC, DE⊥AF, AC, AF and AB intersect at G, H and E respectively.

Verification: OG=

2.( 10/0) Xiaoming has his back to Liang Xiao, so that Liang Xiao can follow the following four steps:

Step 1: stack not less than two cards in left, middle and right stacks, and the number of cards in each stack is equal;

Step 2: Take out two pieces from the left pile and put them in the middle pile;

Step 3: Take one from the right pile and put it in the middle pile.

Step 4: If there are several cards in the left pile, take some cards from the middle pile and put them in the left pile.

At this time, Xiao accurately said the number of existing sheets in the middle sheet piling. What do you think is the current number of sheets in Zhongdui?

3. As shown in the figure, find the area of this trapezoid in the known trapezoid ABCD, AD‖BC, AD=2, BC=4, diagonal AC=5, BD=3.

4.( 15 point) As shown in the figure, it is known that the image of the inverse proportional function and the image of the linear function intersect at point A (-2,3) and point B (3 3,m).

(1) Find the expression of linear function;

(2) According to the image, it is pointed out that the value of linear function is greater than the value x range of inverse proportional function.

5.(20) As shown in the figure, in a square ABCD with a side length of 4, E is the midpoint of DC, F is on BC, CF= 1, and a square is made at △AEF, so that the other two vertices on AF are on EF and AE respectively.

(1) Please write three right-angled triangles with the ratio of two right-angled sides equal to 1: 2 (without additional letters and auxiliary lines);

(2) Find the length of AF and the side length of the square;

(3) Under the condition of (2), take out △AEF, as shown in the figure, fold △E and △F into squares along straight lines respectively, and find the area of the small square in the quadrilateral that is not covered by two folded triangles.

6.(20 minutes) As shown in the figure, the side lengths of square ABCD and square EFGH are sum, diagonal BD and FH are on a straight line, the point is the center of two squares, and the length of the line segment is called the center distance of two squares. When the center moves in a straight line, the square EFGH also translates, and the shape and size of the square EFGH remain unchanged when moving.

(1) calculation:; .

(2) When the center line is translated to two squares with only one common point, the center distance =.

(3) With the center of the circle moving in a straight line, what happened to the common points of two squares? And find out the value or range of the corresponding center distance (no need to write out the calculation process)