First, multiple-choice questions (this big question * * 10 small questions, 3 points for each small question, 30 points for * * *)

1, the following figures are irrational ().

-0.333 ...,,,, 3, 3. 1 4 1 5, 2.0101... (there is/kloc between two adjacent1

0), 76.0 123456 ... (The decimal part consists of consecutive positive integers).

A.3 B.4 C. 5 D.6

2, the following statement is correct ()

A. rational numbers are only finite decimals. Irrational numbers are infinite decimals

C. infinite decimals are irrational numbers. D. scores

3, the following statement is wrong ()

The square root of A. 1 is1B. The cube root of–1is-1.

C is the square root of 2. D.–3 is the square root.

4. If the specified error is less than 1, the estimated value of is ().

A.3 B. 7 C. 8 D. 7 or 8

5. As shown in Figure 2, the cylinder is 8 cm high and the bottom radius is 2 cm. An ant starts from point a.

The shortest crawling distance (∏ = 3) is () when climbing to point B to eat.

A, 20cm B, 10cm C, 14cm D, uncertain.

6. Xiaoming wants to know the height of the school flagpole. He found that the rope on the flagpole was higher than the ground 1 m. When it pulled the lower end of the rope away by 5 m, it was found that the lower end just touched the ground, so the height of the flagpole was ().

(a) 8cm (b)10cm (c)12cm (d)14cm.

7. The lengths of the following three groups of line segments are ①9, 12 and15 respectively; ②7、24、25; ③32、42、52; ④3a、4a、5a(a & gt； 0); ⑤m2-n2, 2mn, m2+n2(m, n is a positive integer, m >；; N) where () can form a right triangle.

Groups a and 5; Group b and group 4; Group c and group 3; Groups d and 2

8. An isosceles triangle with waist length 13 and base length 10, with an area of ().

A.65 B.60 C. 120 D. 130

9, the following formula is correct ()

A, B, C, D,

10, after school, Xiaohong and Xiaoying broke up after school and went home in the southeast and southwest directions respectively. If Xiaohong and Xiaoying walk at a speed of 40m/min, Xiaohong 15 minutes will get home, Xiaoying will get home in 20 minutes, and the straight line distance between Xiaohong and Xiaoying is ().

A.600 b.800 m C.1000 m D. Not sure.

Two. Fill in the blanks: (2 points for each question, ***20 points)

1 1, in △ABC, ∠ C = 90, AB = 5, then++= _ _ _ _.

12. in the known Rt⊿ABC, a=3, b=4 and c=.

The square root of 13 is _ _ _ _; The cube root of 0.2 16 is _ _ _ _.

14, the arithmetic square root is equal to its own number is _ _ _ _; The cube root equals its own number is _ _ _ _.

The reciprocal of 15 is; The number whose absolute value is equal to is.

16, the volume of a cube becomes 27 times, and its side length becomes _ _ _ _ times.

17. If the square root of a positive number is 2a- 1 and -a+2, then a=

18, meet-

19, if it makes sense, the smallest integer that can be taken is

20. In ⊿ABC, if the lengths of its three sides are 9 12 and 15 respectively, then the area of a rectangle composed of two such triangles is.

Third, answer questions:

2 1, simplification: (20 points for this question)

( 1) (2)

(3) ( + )( )+ 2 (4)

(5)(-2+ )(-2- )-( - )2

22. As shown in the figure, the side length of each small square in the square grid is 1. By arbitrarily connecting the vertices of these small squares, some line segments can be obtained. Please draw such a line segment in the picture and choose one of them to explain the reason for drawing it like this. (6 points)

23. A ladder with a length of 10 meter leans against the wall. The vertical height of the top of the ladder from the ground is 8 meters. After the top of the ladder slides 2 meters, will the bottom slide 2 meters horizontally? Try to explain why. (6 points)

25. In order to enrich children's spare time, a community should build a library on the straight line where AB is located, as shown in the figure. There are two schools in this community at point C and D, CA⊥AB at point A and DB⊥AB at point B. It is known that AB=25km, CA= 15km and DB= 10km. Question: How many kilometers away from Point A should Library E be built to make it equal to two schools? (6 points)

26. As shown in the figure, two ships, A and B, set out from Port A at the same time. Party A sails 40 to the northeast at the speed of 16 knots, and Party B sails 50 to the southeast. Three hours later, A arrives at Island C and B arrives at Island B. If the two islands are 60 nautical miles apart, what is the speed of B? (7 points)

27. Exploratory conjecture: (8 points)

1. Make sure the following is correct. If you think it is valid, please mark the correct number in (), if it is invalid, please mark the wrong number.

① ( ) ; ② ( )

③ ( ); ④ ( )

(1) What laws did you find after your judgment? Please use the formula containing n to express the law and explain the value range of n?

(2) Please use your mathematical knowledge to illustrate the correctness of the formula you wrote.

28. As we all know,

Value (9 points)

29.(8 points) As shown in Figure 4, in △ABC, the bisector of ∠B and ∠C intersects with F. If F crosses, it is DE∨BC, AB is in D and AC is in E.

Try to write down the conclusions you can draw (at least three) and choose one to reason.