(Examination time: 120 minutes) Volume: Yi Zhu, New China.
Fill in the blanks (1 ~ 10 is 1,1~14 is 2, * * 28).
1, (1) in □ABCD, ∠A=44, then ∠B=, ∠C=.
(2) If the circumference of □ABCD is 40cm and AB:BC=2:3, then CD=, AD=.
2. If the side length of the cube is expanded by 2 times, the volume will also be expanded by 2 times.
Enlarge the volume of a ball by 27 times, and the radius will be enlarged by 10 times.
3. The side length of a square with diagonal length of 2 is: Its area is.
4. Simplification: (1) (2), (3) = _ _ _.
5. Estimation: (1)∽_ (error is less than 1), (2)∽_ (accurate to 0. 1).
The square roots of 6 and 5 are, the square root of 0 is, and the cube root of -8 is.
7. As shown in figure 1, 64 and 400 are square areas respectively, then the square area represented by the letters in the figure is.
8. As shown in Figure 2, the length of the unknown side of the right triangle =.
9. As we all know, a triangle with three sides is a triangle.
10, the minute hand on the clock rotates around the axis. /kloc-After 0/5 minutes, the minute hand angle is.
1 1, as shown in Figure 3, right-angled trapezoid, ∠ b = 90, AD ‖ BC, AB = BC = 8, CD = 10, then the area of the trapezoid is.
12. As shown in Figure 4, given that AC = AD and ∠ B = 72 in ABCD, ∠ AC=AD = _ _ _ _ _ _ _
13. In Figure 5, how did Figure A become Figure B: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
14. You can spell _ _ _ _ _ _ _ kinds of parallelograms with two identical trigonometric rulers (the one with an angle of 30).
Second, multiple-choice questions (15 ~ 25 questions, 2 points for each question, ***22 points)
15, which of the following movements belongs to rotation is ()
A. Basketball in the process of rolling B. Pendulum swing of clocks and watches
C. the movement of the balloon in the air D. the process of folding a figure in half along a straight line
16, as shown in Figure 6, is a rectangular concrete playground in our school. If a student wants to walk from Angle A to Angle C, he should at least walk ().
140
17, the following statement is true ()
A. rational numbers are only finite decimals. Irrational numbers are infinite decimals
C. infinite decimals are irrational numbers. D. scores
18. Among the following conditions, the condition that a quadrilateral ABCD cannot be judged as a parallelogram is ().
A.AB‖CD，AB=CD B. AB‖CD，AD‖BC
C.AB=AD，BC=CD D
19, in the following array, the number that is not Pythagoras is ().
A 3、4、5 B 9、 12、 15 C 7、24、25 D 1.5、2、2.5
20. The number one-to-one corresponding to the points on the number axis is ()
A. natural number B. rational number C. irrational number D. real number
2 1. Xiaofeng's mother bought a 29-inch (74 cm) TV set. The following statement is about 29 inches.
The correct one is ()
A. Xiaofeng thinks it refers to the length of the screen; B Xiaofeng's mother thinks it refers to the width of the screen;
C. Xiaofeng's father thinks it refers to the circumference of the screen; D. The salesman thinks it refers to the diagonal length of the screen.
22. Xiaogang intends to measure the depth of a river. He inserted a bamboo pole at the bottom of the water 1.5m from the shore. The bamboo pole is 0.5m higher than the water surface, and the top of the bamboo pole is pulled to the shore. The top of the pole is just flush with the water on the shore, so the depth of the river is ().
A.2m； B. 2.5mC. 2.25mD. 3m。
23, diagonal vertical and equal quadrilateral must be ().
A, square b, rectangle c, diamond d, whose shapes cannot be determined.
24, the following statement is incorrect ()
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.
25, the length of the two diagonal lines and one side of the parallelogram can be taken in turn ().
A.B. 6，4，3 C. 6，4，6 D. 3，4，5
III. Answers (26 ~ 33 questions ***50 points)
26.(4 points) Fill in the following figures in the corresponding set (only fill in the serial number).
( 1)3. 14(2)- (3)- (4) (5)0
(6) 1.2 122 1222 1… (7) (8)0. 15
Irrational number set {…};
Rational number set {…}
27. Simplification (3 points for each small question *** 12 points)
( 1).(2).
(3).(4).
28, painting questions (6 points)
As shown in the figure, the side length of each small square in the square grid is 1, and some line segments can be obtained by arbitrarily connecting the vertices of these small squares. Please draw such a line segment in the picture.
29.(5 points) Use 250 square floor tiles of the same size to pave a living room of 40 square meters. What is the side length of each square floor tile?
30.(5 points) When a fire broke out in a high-rise residential building, the fire truck immediately rushed to a place 9 meters away from the building (from the back of the building to the wall of the building) and lifted the ladder to the fire window, as shown in the figure. It is known that the length of the ladder is15m, and the bottom of the ladder is 2m from the ground. How high is the window of the household where the fire broke out?
3 1, (6 points) Xiaozhen came up with a method to measure the width AB of the pond: first, draw two straight lines AC and BC from both ends A and B of the pond to intersect at point C, then take two points E and G from BC to make BE = CG, and then pass E and G as EF‖GH‖AB, and AC intersects at f and h to measure EF. Why?
32.(5 points) Given the quadrilateral ABCD, choose any combination of three conditions from the following conditions to make the quadrilateral ABCD rectangular, and write all the situations: (only fill in the serial number)
( 1)AB‖CD(2)BC‖AD(3)AB = CD(4)∩A =∩C(5)∩B =∩D
(6)≈A = 90(7)AC = BD(8)≈B = 90(9)OA = OC( 10)OB = OD
Please write five groups,,,,.
33.(7 points) Xiaodong thinks that it is the same after learning, so he thinks that a simplified process: = is correct.
(3 points) Do you think his simplification is correct? If not, please write the correct simplification process;
(2 points) explain the conditions for establishment;
(3) (2 points) Ask whether it is established, and if it is, explain the conditions for its establishment.