three

, calculate. (18)

①

+

(

+

②

③

④

⑤

⑥ Solve equation (2x-1) 2 =121.

Mathematics examination paper for the second monthly exam of eighth grade.

Fourth, answer questions. (Select 12. 72 points)

1. As shown in the figure, one side of the folded rectangle AD (the four corners are right angles and the opposite sides are equal) makes the point D fall on the point F on the side BC, and AB is known.

=

8 cm BC

=

10

Cm, find the length of EC

2. As shown in the figure, cut the side of the cone along OA and expand it into a plane figure, which is a fan-shaped OAB.

( 1)

What is the relationship between the length of the sector arc AB and the length of the circumference of the cone bottom? What is the positional relationship between point A and point B on the side of the cone?

(2)

If the angle ∠ AOB = 90, what is the relationship between the radius r of the cone bottom circle and the radius r of the fan-shaped OAB?

(3)

If point A moves once on the side of the cone and then returns to its original position, how should the shortest distance of point A be designed? if

, and ∠ AOB = 90, find the shortest distance of point A.

three

As shown in the figure, the typhoon center of City A is located in B, 320km west of City A, and it moves to the BF direction of 60 northeast at the speed of 40km per hour. The area affected by the typhoon is within 200 kilometers of the typhoon center.

( 1)

Is city A affected by this typhoon? Why?

(2)

If city A is affected by this typhoon, how long will city A be affected by this typhoon?

4. Read the following materials:

As shown in figure (1), the position of △DEC can be changed by moving the length of line BC in parallel along the straight line BC;

As shown in figure (2), take BC as the axis and fold △ABC 180? , you can change to the position of △DBC;

As shown in Figure (3), rotate △ABC 180 around point A? , you can change to the position of △AED.

In this way, a triangle is transformed from another triangle by parallel movement, folding and rotation. This graphic transformation, which only changes the position and does not change the shape and size, is called congruent transformation of triangles.

Answer the following questions:

① In the following figure (3), which method can be used to change △ABE into △ADF?

(2) refers to the relationship between the line segment be and DF in the figure, why?