The first volume (multiple choice questions and fill-in-the-blank questions ***96 points)
Precautions:
Please be sure to fill in the answers to questions 1 ~ 24 on the corresponding answer sheet in Book 2.
1. Multiple choice questions (4 points for each question, ***48 points) There are four answers to each question below, and only one is correct. Fill in the brackets after the question with the code letters of the correct answer.
1. Analyze the following statements: ① There is a one-to-one correspondence between real numbers and points on the number axis; ② There is no square root; ③ There is only one cube root of any real number; ④ Numbers with the same square root and cube root are 0 and.
The correct one is ()
1。
2. As shown in the figure, in a square grid, the side length of each small square is 1, so in the triangle ABC on the grid, the number of sides with unreasonable side length is ().
A.0 B. 1 C.2 D.3
3. Among the following statements about, the wrong one is ().
A is the irrational number B.3 < < 4.
C is the arithmetic square root of 12. D cannot be simplified.
4. In the following square roots, () has been simplified.
A.B. C. D。
5. The picture on the right can be regarded as an isosceles right triangle that has been rotated several times.
The degree of each rotation can be ()
From 900 to 600 A.D.
From 450 to 300 A.D.
6. Fold a square piece of paper in half as shown in (1) and (2) in Figure 5, then cut it along the dotted line in (3), and finally open and smooth the paper in (4). The generated pattern should be () in the following pattern.
( 1) (2) (3) (4)
A B C D
7. As shown in the figure, in a square grid composed of 4×4 small squares, the ratio of the area of the shaded part to the area of the square ABCD is ().
a . 3:4 b . 5:8 c . 9: 16d . 1:2
8. If the side length of a diamond is 1cm and one of its internal angles is 60, its area is ().
A.B. C. D。
9. If you can find a point in a quadrilateral so that the distance from the point to each side is equal, then the quadrilateral is ().
A. parallelogram, rectangle, diamond B. diamond, rectangle, square
C. diamond, square D. rectangle, square
10. If the length of one side of the parallelogram is 10cm, the length of the two diagonals can be ().
A. 4 cm and 6 cm B.6 cm and 8 cm
C.8cm and 10cm D. 10cm and 12cm.
1 1. As shown in the figure, the axial section ABCD of the cylinder is a square with a side length of 4, and the shortest distance between the midpoint S of the moving point P and BC along the cylinder side is ().
A.B.
C.D.
12. As shown in the figure below, it is possible to change the A pattern into the B pattern through translation and rotation transformation ().
(default triangle congruence)
a，B，B，B，B。
A B C D
Fill in the blanks (4 points for each small question, ***48 points)
13. Among the following numbers:,,, 0.0 1020304 ... there are _ _ _ irrational numbers.
14. As shown in the figure, it is two concentric circles, in which two diameters are perpendicular to each other, and the radius of its great circle is 2, which is the sum of the areas of its shaded parts. (The result is expressed by π).
15. When x
16. Estimated comparison size: (fill in ">", "
; .
17. All quadrilaterals in the figure below are squares, and all triangles are right triangles (excluding composite figures). If the side length of the largest square is, the sum of the areas of squares A, B, C and D is.
18. It is known that smart students can get it without a calculator (1); (2) .
19. As shown in the figure on the right, AB = AC, so the number represented by C is _ _ _ _ _ _ _ _ _.
20. Observe and analyze the following data and fill in the blanks according to the rules: 0, 2, 0, 2, …, (the nth number)
2 1. As shown in the figure below, in □ABCD, diagonal AC and BD intersect at O, AC+BD= 18, BC=6, then the circumference of △AOD is.
22. As shown in the figure, a ladder is 10 meter long and leans against the wall. The top of the ladder is 6 meters above the ground. To make the top of the ladder 8 meters off the ground, the bottom of the ladder should slide horizontally to the left.
23. As shown in figure □ABCD, AE and CF are bisectors of ∠BAD and ∠BCD respectively. According to the existing diagram, please add a condition to make the quadrangle AECF diamond, and then add another condition (only write one, and no other "points" and "lines" can be added in the diagram).
24. The master makes aluminum alloy window frames in the following three steps:
(1) First, cut out two pairs of aluminum alloy window materials that meet the specifications (Figure (1)), so;
(2) If the window frame is placed in a quadrangle as shown in Figure (2), the shape of the window frame is a shape based on.
(3) Lean the square ruler against a corner of the window frame (as shown in Figure (3)) and adjust the frame of the window frame. When the two right angles of the square ruler are seamless with the window frame (as shown in Figure (4)), the window frame is qualified, and the window frame is formed at this time.
( 1)
The first volume of answer sheet
Please fill in the answers to questions 1 ~ 24 in the corresponding positions below: (4 points for each question)
The title is123455678911112.
answer
13. 14. 15. 16. 17.
18. 19.20.
2 1.22.23.
24.( 1)
(2)
Volume II (54 points for solving problems * * *)
Friendly reminder: when solving problems, you should write the necessary text explanation, proof process or calculus steps.
Third, answer the question (this big question ***7 small questions, out of 54 points)
25. Calculation: (4 points for each small question, *** 12 points)
( 1) (2)
(3)
26. Drawing (3 points for each small question, 6 points for * * *)
(1) Draw a figure, move the boat five squares to the right, and then move it down three squares;
(2) Draw a picture after rotating △ ABC 90 clockwise around point A. 。
27.(6 points) Think about it: Are the inverse equations 3= and 7= still valid?
Formulas: 9 = = and 4 = = Is it true? Imitate the above method and simplify the following categories: (1) 2 (2)11(3) 6.
28.(7 points) As shown in the figure, a 36-meter-high giant California redwood was broken in a strong earthquake, and the top of the tree fell 24 meters away from the root. How high do researchers have to climb from the bottom of the tree to see the broken marks?
29.(7 points) As shown in the figure, in □ABCD, AC intersects BD at point O, and points E and F are the midpoint of OA and OC respectively. Please judge the relationship BEtween the line segment be and DF and prove your conclusion.
30.(8 points) Practical operation questions:
Cut an isosceles right triangle ABC along the high line CD (cutting line) on the hypotenuse, and cut a part from this triangle, which can be combined with the rest to form a parallelogram A/BCD (see sketch 1). (If you need drawing in the later query process, there are no restrictions on tools, and you don't need to write drawing and proofing).
Inquiry 1:
(1) Think about it: the basis for judging that quadrilateral A/BCD is a parallelogram is;
(2) Problem solving: According to the above cutting method, please spell out a parallelogram with a different position or shape from the figure 1.
And draw the schematic diagram in fig. 2.
Question 2:
In the isosceles right triangle ABC, please find other cutting lines and spell out different types of special quadrangles.
(1) Try it: you can spell all different types of special quadrangles. Their clipping lines are respectively;
(2) Drawing: Please draw a special quadrilateral sketch in Figure 3.
3 1.(8 points) Observe the changing process of the following graphs and answer the following questions:
As shown in the figure, in △ABC, d is the moving point on the side of BC (point D does not coincide with points B and C). De//AC and AB intersect at point E, and DF//AB and AC intersect at point F. 。
(1) When trying to find out what conditions AD meets, the quadrilateral AEDF is a diamond, and explain the reasons;
(2) Under the condition of (1), the quadrilateral AEDF is a square when △ABC meets any conditions. Why? Hope to adopt!