Class: Student ID: Name: Score:

First, multiple choice questions

1. The following groups are the lengths of three sides of a triangle, and the group that can form a right triangle is ().

A.B. 7， 12， 15 C. 13， 16，20 D. 8，24，25

2. The following statement is true ()

A. irrational numbers include positive irrational numbers and negative irrational numbers. B. Real numbers only include rational numbers and irrational numbers.

C. irrational numbers are infinite decimals. D. a number without a root sign is a rational number.

3. The following graphics, both axial symmetry graphics and central symmetry graphics is ()

A. parallelogram, diamond and square

C. isosceles trapezoid, rectangle and square D. regular triangle, rectangle and circle

4. Among the following properties, the one with diamonds but without rectangles is ().

A. the sum of internal angles is equal to 3600 b. Diagonal lines bisect a set of diagonal lines.

C. Diagonal lines are equal D. Adjacent angles are complementary.

5. The following graphics with the same shape and size can't be densely covered ()

A. regular hexagon B. regular polygon C. parallelogram D. isosceles triangle

6. The following propositions: ① The diagonal of the parallelogram is bisected; ② The quadrilateral whose diagonal is bisected is a parallelogram; ③ The diagonal of the square is vertical; (4) the quadrilateral with vertical diagonal is a square, of which the correct one is ().

A.4b 3c 2d 1

7. In the following categories, the correct one is ()

A.B. C. D。

8. In the rotation of graphics, the following statement is wrong ().

A. Every point on the graph moves at the same angle. B the edges of any two points on the graph are equal to the edges from them to the two points.

C the distance between the centers of rotation of each point on the graph is equal. There may be fixed points on the diagram.

9. The quadrant of point P (-4, 1) in the plane rectangular coordinate system is ().

a4 b . 3 c . 2d . 1

10. A tourist climbed 2.4 kilometers/hour, rested 1 hour, and then climbed to the top of the mountain 1 hour. The functional relationship between tourists' climbing time and mountain height is shown in Figure ().

A B C D

Second, fill in the blanks

The square root of 1 4 is, the cube root of 8 is, and the arithmetic square root is.

2. The right side of a right triangle is 3 cm long and the hypotenuse is 5 cm long, so the height on the hypotenuse is 0.

3. The sum of the internal angles of pentagon is, and the sum of the external angles of decagon is.

4. As shown in the quadrilateral ABCD, diagonal AC and BD intersect at

Point o, when the condition is met,

It is a parallelogram. (Just fill in one condition that you think is correct)

5. If there is a straight line, y = 2； when x = 1; When x = 0 and y = 3, the expression of the straight line is.

6. For a function, y decreases with x.

7. The coordinates of point A (3,2) relative to the axis symmetry point B of X are.

8. The circumference of a diamond is 40 cm, and the diagonal length is 12 cm, so the area of this diamond is.

9. It is known that the intersection angle of two diagonals of a rectangle is 600, and the short side of the rectangle is 4cm, so its diagonal is cm and its long side is cm.

Third, calculation

1.2.

Fourth, as shown in the figure, the quadrilateral ABCD is a rectangle, and the diagonal lines AC and BD intersect at the extension line E of O, CE‖DB and AB, which proves that AC = CE.

Verb (abbreviation of verb) is shown in the figure. It is known that in △ABC, AD divides ∠BAC, DE‖AC and DF‖AB equally.

(1) Try to prove the shape of quadrilateral AEDF.

⑵ When △ABC meets any conditions, the quadrilateral AEDF is a square. Why?

Six, a food factory sells biscuits to city A, if the railway consignment, 0.58 yuan per kilogram, if the road transport, 0.28 yuan per kilogram, need to travel subsidies to 600 yuan.

(1) The factory sells X kilograms of biscuits to City A, and the freight is y 1 yuan for railway and y2 yuan for highway. Write the relationship between the costs y and x of the two transportation schemes respectively.

(2) How many kilograms of biscuits are sold to City A, and are the costs of the two distribution schemes the same?

⑶ Assuming that the weight of biscuits sold is 2500 kg, discuss which distribution scheme is more cost-effective.

7. It is known that A is 3km south of B, and A and B are moving in a straight line at a constant speed in the positive direction. The relationship between their distance S(km) from A and their travel time t(h) is shown in the figure, where l 1 represents the movement process of A and l2 represents the movement process of B. According to the image, answer:

(1) Which is A and which is B?

(2) How long did it take A to catch up with B?

(3) Find the functional expression of l 1, l2?

(4) When the distance is 3km again, it is explained by calculation.