3. The reciprocal of is _ _ _ _ _, and the absolute value is _ _ _ _.
4. Calculation:;
5. When a = 3 and A-B = 1, the value of the algebraic expression a2-ab is _ _ _ _ _.
6. As shown in Figure 2, the side length of each small square in the grid is 1.
The area of the quadrilateral is;
7. It is known that in a diamond-shaped ABCD, if its area is 12 and one diagonal AC=3, the other diagonal BD = _ _ _ _ _ _ _ _.
8. As shown in the figure, in ABC, ∠ ACB = 90, ∠ B = 30, D is the midpoint of the hypotenuse AB, and AC=3cm, then CD = _ _ _ _ _.
9. As shown in the figure, after a rectangular piece of paper is folded along EF, the points D and C are at the positions D ′ and C ′ respectively. If ∠ EFB = 65, ∠ AED' = _ _ _ _ _.
10. The carpenter made a door frame with two equal long wooden strips and two equal short wooden strips, as shown in the figure. Now I'll give you a rope long enough. Please tell me that the shape of this door frame can be verified by _ _ _ _ _ _ _ _ _ _ _ _ _ _.
Second, believe in your choice! (There are 10 small questions in this big question, with 3 points for each small question and 30 points for * * *).
1 1. Among the real numbers, 0.3131113 …, -3. 14, and the irrational number is …
a . 1； B.2C.3D.4
12. The following equation is ................................................ ().
A.； b； c . a6÷a3 = a2； d .(a3)2 = a6；
13, the following proposition is wrong: ............................................. ()
A. The two bottom sides of the isosceles trapezoid are parallel and equal; The two diagonals of an isosceles trapezoid are equal.
C. The two angles of the isosceles trapezoid with the same bottom are equal. D. The isosceles trapezoid is an axisymmetric figure.
14. In the following statement, the correct number is ..................................... ().
① Real numbers include rational numbers, irrational numbers and zero; ② If the ratio of three sides of a triangle is equal, the triangle is an isosceles right triangle; (3) the power of the power, the cardinal number is constant, and the exponent is added; (4) The square root and cube root are equal to the sum of their respective numbers;
A. I; B. one; C. one; d . 1；
15. As shown in the figure, the cylinder is 8 cm high and the bottom surface is 4 cm in diameter. An ant moves from the surface of a cylinder.
Climb from point A to point B for dinner, and the shortest distance (take =3) is ...................... ().
A. 10/0cm B.12cm C.14cm D. cannot be determined.
16. As shown in the figure, it is a rotationally symmetric figure. To make it coincide with itself after rotation, at least it should be wrapped around it.
The angle at which the center rotates counterclockwise is ................................ ().
A.30 B. 60 C. 120 D. 180
17. The correct one in the following statement is ................................. ().
A. The diagonals of rectangles are perpendicular to each other. Diagonal lines of diamonds are equal.
C. The diagonals of a square are equal and equally divided. D. diagonal bisection of isosceles trapezoid.
18. As shown in the figure, in the parallelogram ABCD, CE is perpendicular to AB, ∠ D =,
Then the size of ∠BCE is ........................... ().
A.B. C. D。
19. In the known quadrilateral AB=CD, AB‖CD, AB = CD, the perimeter is 40, and the ratio of two adjacent sides is 3: 2, then the length of the larger side is ................................................................. ().
10 C. 12 D. 14
20. As shown in the figure, the side length of the square ABCD is 1, e is any point on BC, and EF⊥AC is in F.
EG⊥BC is in G, then the value of EF+EG is ............................ ().
A.2 B. C.3 D
Third, challenge your skills! (This big question is out of 60 points)
2 1.( 1) (5 points in this question) Decomposition factor: 64x2- 16xy+y2.
(2) (5 points for this question) Simple calculation: 1998.
Solution:
(3) (6 points for this question) Simplify first, then evaluate:, where a=
Solution:
22. (6 points in this question) Draw a picture by hand: Given Δ ABC and point O, draw Δ def, so that Δ def and Δ ABC are symmetrical about point O. 。
Solution:
23. (5 points for this question) Please pay attention to the following points:
(x2- 1)÷(x- 1)= x+ 1
(x3- 1)÷(x- 1)= x2+x+ 1
(x4- 1)÷(x- 1)= x3+x2+x+ 1
(X5- 1)÷(x- 1)= x4+x3+x2+x+ 1
…………
(1) Can you get the general result of (xn- 1) ÷ (x- 1)?
(2) According to this result: 1+2+22+...+262+263.
Solution:
24. (6 points in this question) As shown in Figure 15, in the isosceles trapezoid ABCD, AD‖BC and BD share ∠ABC,
Ad = 5 cm, try to find the length of CD.
Solution:
25 (6 points in this question) As shown in Figure 14, both δδACD and δδBCE are equilateral triangles, and δδNCE can coincide with δδMCB after rotation. Please answer:
(1) What is the center of rotation?
(2) How many degrees has it rotated? Find two pairs of congruent triangles in the graph. (without proof)
(3) If NE = 10 cm, what is MB?
Solution:
26. (6 points in this question) As shown in the figure, in δ ABC, BD divides ∠ABC, DE‖BC and EF‖AC equally. Try to determine the relationship between CF and BE, and explain the reasons.
Solution:
27. (This question is 10) There are two problems with this question.
(1) As shown in the figure, in Rt△ABC, ∠ACB=900, and CD⊥AB in D, let AC=b, BC=a, AB=c, CD = H, try to explain that the triangle composed of a+b, H, c+h is a right triangle.
Solution:
(2) If,
The value.
Solution: