1. In real numbers, the rational number is ().
A.B. C. D。
2. Among the following four figures, the negative one is ().
A.B. C. D。
3. The following statement is true ()
The cube root of a is the cube root of B.
C. negative numbers have no cubic root D.
4. The arithmetic square root of is ()
A.B. C. D。
5. The cube root of a number is, and the square root of this number is ()
ABC or d or
6. The following calculations are correct ()
A.
B.
C.
D.
7. Among the following statements about, the wrong one is ().
A. is irrational number B.
The arithmetic square root of C. is D. It is the simplest quadratic square root.
8. If the formula is meaningful in the real number range, the value range of is ().
A.B. C. D。
9. If the fractional part of is, the value of is ().
A.b. is an irrational number, and C.D. cannot be sure.
10. As shown in the figure, on the number axis, the numbers represented by two points are sum respectively, so there are * * * points between the two points representing integers.
A.B. C. D。
1 1. If both right sides of a right triangle are magnified, then the hypotenuse is magnified ().
A times b times c times d times
12. As shown in the figure, the side length of the square is. On the number axis, draw an arc with the origin as the center and the length of the diagonal as the radius, and the positive half axis of the intersecting axis is at a point, then the real number represented by this point is
A.B. C. D。
13. The graph is a beautiful pythagorean tree, in which all quadrangles are squares and all triangles are right triangles. If the sides of a square are 0, the area of the largest square is 0.
A.B. C. D。
14. The length of three sides of a triangle,, is satisfied, then the triangle is ().
A. right triangle B. acute triangle C. obtuse triangle D. isosceles triangle
15. Observe the following equations:,,, and answer the following questions: The last digit of is ().
A.B. C. D。
Second, fill in the blanks (***6 small questions; *** 18.0)
16. Calculation:.
17. In,, ① If,, then; ② If, then.
18. The hypotenuse of a right triangle.
19. The length of three sides of a triangle is, and the height of the longest side of this triangle is.
20. As shown in the figure, in a rectangle, if the point is on the edge, then one edge will be folded so that the point just falls on the point of the edge, and the crease is. If is, the length is.
2 1.,,, Please use an equation containing (and a positive integer) to express their laws:.
Third, answer questions (***7 small questions; ***57.0 points)
22. Find values in the following categories.
( 1) ;
(2) .
As we all know, there is a quadrangular open space in a development zone. As shown in the picture, it is planned to plant turf on this open space. According to the calculation, if RMB is needed per square meter of turf, how much does it cost to plant turf in this open space?
24. Known: As shown in the figure, at the midpoint of,, is, the length.
25. As shown in the figure,, is the square and the point on the side, and, is the midpoint. Connect and ask what triangle it is. Please explain the reason.
26. As shown in the figure, the middle is the height of the side. According to the above data, can you get the area? Just try it.
27. As shown in the figure, the side length of each small square in the square grid is, and the vertices of the small squares are called grid points. Draw the following figures in the square grid:
(1) is a line segment of length, where, and are both on the grid;
(2) Square with area, where,, and are all on the grid.
28. As shown in the figure, fold one side of the rectangle so that the point falls on the point on the side, and find:
The length is (1);
(2) length.
?
answer
Multiple choice question:
1.D 2。 C 3。 D 4。 B 5。 C
6.D 7。 D 8。 D 9。 C 10。 C
1 1.B 12。 B 13。 C 14。 A 15。 B
Fill in the blanks:
16.
17.；
18.
19.
20.
2 1.
Answer the question:
22.( 1)
22.(2)
23.( 1)
Connect.
Yes,.
In,,,
So,
So this is a right triangle.
.
So it costs (yuan) to plant turf.
A: It costs RMB to plant turf in this clearing.
24.( 1) inches,
Self-Pythagorean Theorem: (negative).
Yes, the midpoint,
.
In,,
Self-Pythagorean Theorem: (negative).
25.( 1) is a right triangle. The reason for this is the following：
The side of a square is the midpoint,
,,.
,,.
.
This is a right triangle.
26.( 1) Because it is too high,
So sum is a right triangle.
According to Pythagoras theorem,
rule
In, according to Pythagorean theorem, we get
rule
therefore
27.( 1) The diagram is what you want. (The answer is not unique)
27.(2) A square as shown in the picture is what you want. (The answer is not unique)
28.( 1) can be obtained by folding.
Yes,
Because,
So,
So ...
28.(2) The meaning of the question can be concluded that the length that can be set is, then.
In, it is solved by Pythagorean theorem.
Therefore, the length is.