1.(3 points) (20 15 spring? Xiangfang District) The general form of the following unary quadratic equation is ()

A.(x﹣ 1)2=0b.3x2﹣4x+ 1=0c.x(x+5)=0d.(x+6)2﹣9=0

2.(3 points) (20 15 spring? At the end of Xiangfang District, the point on the image with the proportional function y=3x is ().

A.( 1,3)b.(﹣ 1,3)c.(3, 1)d.(﹣3, 1)

3.(3 points) (20 15 spring? At the end of Xiangfang District) Among the following axisymmetric figures, the axis of symmetry is the most ()

A.

An equilateral triangle B.

Rectangular C.

Diamond D.

square

4.(3 points) (20 15 spring? At the end of Xiangfang District, the right triangle formed by line segments A, B and C is ().

a=5，b=8，c=7B.a= 1，b=3，c=C.a=3，b=4，c=5D.a=5，b=5，c=6

5.(3 points) (20 15 spring? The linear function y = (m- 1) x+3, y decreases with the increase of x, so the range of m is ().

Morning >1b.m > 0c.m ≥1d.m <1

6.(3 points) (20 15 spring? At the end of the xiangfang district) the following proposition is correct ()

A. A quadrilateral with diagonal lines perpendicular to each other is a diamond.

B. A quadrilateral with three right angles is a rectangle.

A quadrilateral with two equal sides is a parallelogram.

A parallelogram with four equal sides is a square.

7.(3 points) (20 15 spring? As shown in the figure, a telephone pole A with a height of16m is broken, and the top C of the telephone pole falls 8m away from the bottom B of the high telephone pole, so the distance AB from the broken telephone pole A to the ground is ().

A.6m B.7m C.8m D.9m

8.(3 points) (20 14? Tianjin) Organize a volleyball invitational tournament, and each team will have a match. According to the venue, time and other conditions, arrange a 7-day schedule and arrange 4 games every day. If the organizer of the tournament wants to invite X teams to participate, then the relationship that X satisfies is ().

a.x(x+ 1)=28b.x(x﹣ 1)=28c.x(x+ 1)=28d.x(x﹣ 1)=28

9.(3 points) (20 15 spring? The end of Xiangfang District) is folded into a rectangle ABCD as shown in the figure, AE and EF are creases, ∠ BAE = 30, AB=, after folding, point C falls at C' on the AD side and point B falls at B' on the EC' side, then the length of BC is ().

A.B.B2C.2D.3

10.(3 points) (20 15 spring? At the end of Xiangfang District, Party A and Party B set off from the school and went to the Science and Technology Museum along the same road. Party A rides a bike and Party B walks. When Party A picked up the school at the original speed, Party B just arrived at the Science and Technology Museum. The dotted line O→A→B→C and the line segment OD respectively represent the functional relationship between their distance y (m) from the school and time x (min), so the correct number in the following conclusion is ().

(1) The school is 600 meters away from the Science and Technology Museum;

(2) A stays in the Science and Technology Museum for 5 minutes;

(3) The circulating speed of A is120m/min;

(4) A and B are 500 meters away from the school when they meet head-on;

(5) When A arrived at the Science and Technology Museum, B only walked 200 meters.

A.2 B.3 C.4 D.5

Second, fill in the blanks

1 1.(3 points) (20 15? In Chenzhou), the function y=, and the range of the independent variable x is.

12.(3 points) (20 15 spring? If x= 1 is a solution of quadratic equation x2+x+m=0, then the value of m is.

13.(3 points) (20 15 spring? The length of one side of a rectangle is 2 and the length of one diagonal is 4, so the area of this rectangle is.

14.(3 points) (20 15 spring? The end of Xiangfang District, as shown in the figure, is in? In ABCD, AC and BD intersect at O, E is the midpoint of CD, and the perimeter of △BCD connecting OE is 10, then the perimeter of △ODE is.

15.(3 points) (20 15 spring? The quadratic equation x2+4x+ 1+k=0 has two equal real roots, then k=.

16.(3 points) (20 15 spring? At the end of Xiangfang District, there is an image with known linear function y=kx+b, and the solution set of inequality kx+b < 0 is.

17.(3 points) (20 15 spring? At the end of Xiangfang District, a product was originally 100 yuan per piece. Due to two consecutive price reductions, the current price is 8 1 yuan per piece. If the two price reductions are the same, the percentage of each reduction is.

18.(3 points) (20 15 spring? In the rectangular ABCD, AB=4, AD=8, point P is on one side of the rectangle, and PB=PD, then the length of line segment PA is.

19.(3 points) (20 15 spring? As shown in the figure, in the plane rectangular coordinate system, O is the coordinate origin, and the quadrilateral ABCF is a diamond. If the coordinate of point C is (5,4), the analytical formula of straight line AC is.

20.(3 points) (20 15 spring? As shown in the figure, the quadrilateral ABCD is a rectangle, e is a point on the CD, connect AE, take the midpoint G of AE, and the sum of two DGs extends the CB extension line to point F, and connect AF, ∠AFC=3∠EAD. If DG=4, BF= 1, the length of AB is.

Three. Problem solving (2 1 8, 22 questions 6, 23, 24 questions 8, 25, 26, 27 questions 10, * * questions 60).

2 1.(8 points) (20 15 spring? At the end of Xiangfang District, solve the following unary quadratic equation.

( 1)(x﹣5)2=4

(2)x2+3x+ 1=0。

22.(6 points) (20 15 spring? As shown in the figure, in the grid paper with the side length of each small square of 1, there is a line segment AB, and points A and B are on the vertices of the small square.

(1) Draw a right triangle ABC with AB as one side on the square paper of Figure 1. Point C is at the vertex of the small square, and the area of triangle ABC is 5;

(2) Draw a rhombic ABDE with AB as one side on the square paper in Figure 2. Points D and E are on the vertices of the small square, and the area of the rhombic ABDE is 8.

23.(8 points) (20 10? Harbin) On the physical education class, the teacher used ropes to enclose a playground with a circumference of 30m. The closed playground is a rectangular ABCD as shown in the figure. Let the length of side AB be X (unit: meter) and the area of rectangular ABCD be S (unit: square meter).

(1) Find the functional relationship between S and X (it is not required to write the range of the independent variable X);

(2) If the area of rectangular ABCD is 50 square meters and AB < AD, find the length of AB at this time.

24.(8 points) (20 15 spring? Xiangfang district final) as shown in the picture, will it? The side DC of ABCD extends to point E, so that CE=DC, connecting AC and Be.

(1) As shown in figure 1, it is proved that the quadrilateral ABEC is a parallelogram;

(2) Connect AE as shown in Figure 2. If AE⊥BC, please write all isosceles triangles in Figure 2 directly.

25.( 10) (20 15 spring? At the end of Xiangfang District, it is known that the distance between A and B is 6 kilometers. A rides a bike and B rides a motorcycle. They walk from A to B along the same route. The function relation image of the distance between A and B during driving is shown in the figure. According to the image, the following problems are solved:

(1) Find the functional relationship between the distance y (unit: kilometers) and the time x (unit: minutes) (the range of independent variables is not required);

(2) What is the value of x and the distance between them is 1km?

26.( 10) (20 15 spring? As shown in the figure, in the diamond ABCD, e is a point above BC, and f is a point on CD, connecting AE, AF, EF, ∠ AEB = ∠ AEF.

(1) As shown in figure 1, it is proved that AF is equal ∠ EFD;

(2) As shown in Figure 2, if ∠ c = 90, then verify: ef = be+df;

(3) Under the condition of (2), if AB=3BE and AE=2, find the length of AF.

27.( 10) (20 15 spring? As shown in the figure, in the plane rectangular coordinate system, point O is the coordinate origin, the straight line AB: Y = X+B intersects the X axis at point B, the straight line AC: Y =-2x+ 10 intersects the X axis at point C, and the ordinate of point A is 8.

(1) Find the analytical formula of straight line AB;

(2) Starting from B, the moving point P moves along BO to the end point O at a speed of 3 units/second, passing through P is the PE⊥x axis, passing through AB and E is the EF⊥y axis, passing through AC and F, the moving time of the point P is t, and the length of the line segment EF is d. Find the functional relationship between D and T, and directly write the value range of the independent variable T. 。

(3) Under the condition of (2), if B is BR⊥AC in R, and the ray BR passes through the straight line EF in Q, what is the value of T, and the quadrilateral whose vertices are O, P, F and Q only loves parallelogram? And find the length of QR at this time.