1. Multiple choice questions (3 points for each question, *** 18 points) There are four options for each of the following questions, of which there is only one correct answer. Please fill in the correct answer in the corresponding position on the answer sheet.
The reciprocal of 1. 120 12 is ().
A.20 12b。 -20 12c . 120 12d。 -120 12 display analysis 2. Figure 1 is a right-angled prism metal block with a square bottom, which needs to be cut off in design.
A.B. C. D。
Dominance analysis 3. The solution set of inequality group {x- 1 < 0-2x ≤ 4 is expressed as () on the number axis.
A.B. C. D。
Display analysis 4. As shown in the figure, it is known that the diameter AB of the chord CD⊥ is at point E, connecting OC, OD, CB and DB, and the following conclusion must be correct ().
A.∠CBD= 120
B.BC=BD
C. Quadrilateral OCBD is a parallelogram.
D. The quadrilateral OCBD is a diamond.
Display analysis 5. The math test scores of six students in a study group are 50 points, 100 points, 60 points, 70 points, 80 points and 60 points respectively, so the median and mode of this score are () respectively.
A.60，60，B.70，60，C.70，80，D.65，60。
Display analysis 6. As shown in the figure, in the plane rectangular coordinate system, after △ABC rotates 90 clockwise around the rotation center, △A? b？ c？ The coordinate of its rotation center is ()
A.( 1.5， 1.5) B.( 1，0) C.( 1，- 1) D.( 1.5，-0.5)
Display parsing
II. Fill in the blanks (3 points for each question, ***27 points)
7. Calculation: (-2x3) 2 = 4x6. Display analysis 8. In quadrilateral ABCD, AB=DC and AD=BC. Please add another condition to make quadrilateral ABCD rectangular. The condition you added is that the diagonal lines are equal. (Write any one) Display Analysis 9. In order to visit grandpa in hospital, Li Ming went to the supermarket to buy apples and oranges. There is just no money, assuming that apples buy X kilograms and oranges buy Y kilograms, then the functional relationship between Y and X is y =-85x+8. Display analysis 10. Place a right triangle and a rectangular ruler as shown. If ∠ α = 54, the degree of ∠βis 36. Display analysis 65438. B≠0) and the image of the linear function y2=kx(k≠0) intersect at the origin and point A. When y 1 < y2, the corresponding value range of x is x 0. The display analysis is 12. In a school extracurricular activity, Xiao Ming jumped 90 in the same time. Then the equation about x can be listed as 90x = 120x+20. The display analysis is 13. As shown in the figure, there are two turntables A and B which can rotate freely, wherein the turntable A is divided into four equal parts and the turntable B is divided into three equal parts, and each part is marked with numbers. Now Party A and Party B rotate one of the turntables at the same time, and the probability that the product of the two numbers pointed by the pointer is even after the turntable stops (when the pointer points to the boundary line) is 23. The display analysis is 14. As shown in the figure, line segment AB=6, point C is a point above AB, and point D is the midpoint of AC. When AC=4, the sum of the areas of three squares is the smallest. The display analysis is 15. As shown, in the plane rectangular coordinate system. The relationship of the straight line BC is y= 12x+2, with the BA⊥x axis, the vertical foot is a (4 4,0), the point P is a point on the X axis, and the length of PB is ⊙M. When ⊙ m is tangent to the straight line BC, the coordinate of the point P is (6,0) to show the analysis.
Third, answer the question (this big question * * 8 small questions, ***75 points)
16. Simplify before evaluating: (12-x+ 1)÷x-3x2-4? Xx2+4x+4, where x =- 1. Display analysis 17. As shown in the figure, in a right-angled ABCD, AD=2AB, point F is the midpoint of AD, △AEF is an isosceles right triangle, ∠ AEF = 90, and BE, DE and AC are connected.
(1) Verification: △ EAB △ EFD;
(2) Find the value of ACDE. The display analysis is 18. According to relevant data, the total resident population of a city has increased from 4 million ten years ago to 4.5 million now. The statistical chart of the education status of the specific permanent population is as follows (some information is not given):
Answer the following questions:
(1) Calculate the number of permanent residents with junior high school education in this city and complete the histogram;
(2) Compared with ten years ago, how much has the proportion of high school education increased among the permanent residents in this city?
(3) If 1 students are randomly selected from the current resident population in this city, what is the probability that their education happens to be a university? Display analysis 19. As shown in the figure, there are two buildings, A and B, on both sides of a small river l 1∑L2. In order to measure the distance between A and B, Xiao Ming starts from point B, chooses a point C along the direction perpendicular to the bank l2, then drives 24 meters along the straight line perpendicular to BC to reach D, and measures ∠ CDA. The distance between b (reference data: sin 56 ≈ 45tan56 ≈ 32sin67 ≈1415tan67 ≈ 73262 = 676272 = 729) shows the analysis 20. As shown in the figure, it is known that the straight line Y = KX+B (k) 1), the point c is a point on the straight line y=kx+b(k≠0) above the X axis, the point c is a parallel line of the X axis, and the hyperbolas Y = KX (x < 0) and Y =-KX (x > 0).
(1) Fill in the blanks: k=- 1, b =- 1.
(2) If point C is on the straight line y=2, judge the positional relationship and quantitative relationship between line segment BD and line segment AE, and explain the reasons. Display analysis 2 1. As shown in figure 1, the vertex of the right angle ∠PE=PF coincides with the vertex C of the square ABCD, and two right angles PE and PF intersect with the straight lines of AB and AD at points E and F, so it is easy to get △ PBB.
(1) As shown in Figure 2, if the point P is on the diagonal AC of the square ABCD, and other conditions remain unchanged, is the conclusion in (1) still valid? Explain the reasons;
(2) As shown in Figure (3), the square ABCD in Figure (2) is changed to rectangular ABCD, and other conditions remain unchanged. If AB=m and BC=n, write the value of PEPF directly.
Display analysis 22. As shown in the figure, there is a tennis launcher launching a tennis ball into the air at a horizontal ground point A, and the flight path of the tennis ball is parabola, and the landing point on the ground is B. Someone puts a cylindrical bucket without a cover vertically upward at point C (near point B) on the straight line AB, trying to make the tennis ball fall into the bucket. It is known that AB = 4m, AC = 3m, the maximum flying height of tennis ball om = 5m, and the diameter of cylindrical bucket is 0.
(1) If five cylindrical barrels are placed vertically, can tennis balls fall into the barrels?
(2) When several cylindrical barrels are placed vertically, can tennis balls fall into the barrels?
VIP display analysis 23. As shown in the figure, ∠ B = 90, ad∨BC, and point E in trapezoidal ABCD are the midpoint PF⊥BC, AB=AD=BE=2cm, and the moving point PC starts from point B and moves at a constant speed of 1cm/s along the dotted line B → A → D → E.
Let the area of △PFQ be s and the moving time of point p be x (s) (0 < x < 6).
(1) When point P moves on AB, the shape of △PFQ can be directly judged;
(2) In the process of movement, what special quadrilateral can the quadrilateral PQCD become? (Answer directly, without proof) Write the value range corresponding to X;
(3) Find out the functional relationship between S and X, and show the analysis.