A, multiple-choice questions (this question has *** 10 small questions, each small question 3 points, out of 30 points. There is only one correct answer to each small question).
The reciprocal of 1 Yes ()
A.B. C. D。
2. The following statement is true ()
The square root of a.9 is 3.b. Translate the point to the right by 5 unit lengths to the point.
C is an irrational number D. The symmetry point of a point about the axis is
Zhai Zhigang, an astronaut of Shenzhou VII, left his footprints in the vast space, which made the people of China deeply proud. The extravehicular spacesuit he wore cost 30 million yuan, which is () yuan according to scientific notation.
a、3× 103 B、0.3× 108 C、3× 107 D、3× 108
4 the vertex coordinate of parabola is ()
a 、( 2，8) B 、( 8，2) C 、(-8，2) D 、(-8，—2)
5. As shown in figure 1, it is a geometric body composed of six small cubes with side length of 1 unit. The small cube A moves along its horizontal line at a speed of 1 unit per second. During its movement, the () of the geometry will not change.
A, front view b, top view c, left view d and three views
6. As shown in Figure 2, the two right-angled sides BC = 6 and AC = 8 of right-angled triangular paper ABC are folded in half along the DE to make point A and point B coincide, then the value of tan∠CBE is ().
a、247 B、73 C、724 D、 13
7. As shown in Figure 3, the fan-shaped OAB is the side spread of the cone. If the sides of small squares are all 1cm, then the radius of the bottom of the cone is () cm.
A.B. C. D。
8. It is known that the image of the function is symmetrical about the straight line x= 1, and some images are given in the figure.
Points a (x 1, y 1) and b (x2, y2) are on the function image, and -2.
A.y 1 & gt； y2 b . y 1 & lt； Y2 C.y 1=y2 D. Unable to determine.
9. Two students, A and B, count the frequency of a certain result in an experiment, and estimate the probability by frequency. The statistical chart drawn as shown in the figure may be ().
A. throw a regular hexahedral dice, and there is a probability of 4 points.
B. Take out any ball from a bag containing four white balls and two red balls, and get the red ball.
C. flip a coin, and the probability of tails appears.
D the probability of writing any integer divisible by 2.
10, the image of quadratic function is roughly as shown in the figure,
Among them, () has positive value.
A. 1
Fill in the blanks (6 small questions in this question, 4 points for each small question, out of 24 points).
1 1. To make A a rational number, please write a qualified real number A: _ _ _ _ _ _ _ _
12. In the function, the value range of the independent variable is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.
13. According to the information in the figure, the solution of x < 14x is.
14. There is a circular lawn with a radius of 4 meters in the campus. Some students walked out of a path AB on the lawn and took a "shortcut", as shown in figure ∠ AOB = 120. These students trample on flowers and plants in order to walk less.
15, as shown in the figure, in the parallelogram, is the point where the edge intersects the point. If e is the midpoint of BC, then the ratio of △BEF to parallelogram area is
16. As shown in the figure, fan-shaped paper with radius of 1 and central angle continuously rolls to the right on the positive semi-axis of X axis, and point A falls at the positions of A 1, A2, A3, … in turn, then the abscissa of A2009 is _ _ _ _ _ _ _.
Iii. Answering questions (there are 8 small questions in this question, 6 points for each question from 17 to 19, 8 points for each question from 20th to 2nd/kloc-0, 22 to 23rd 10, 24th 12, * * 66 points).
17. (6 points for this question)
(1) (2) Solving inequalities
18. (6 points in this question) As shown in the figure, the vertex D of the square ABCD is a straight line A, and the vertical lines passing through A and C are points E and F respectively.
① Verification: △ AED △ DFC
② If AE = 2 and CF = 1, the circumference of the square ABCD is.
19 (6 points in this question) At the New Year's Day party, there was an out-of-box game with prizes. Take three boxes with the same appearance, one with prizes in it and the other two empty boxes. The rules of the game are: take out these three boxes after mixing each game, and the students who participate in the game will randomly open one of them. If there is a prize, they will win it. If there is an empty box, they will execute a program.
(1) If a person participates in the game, the probability of winning the prize is _ _ _ _ _ _,
(2) What is the probability that two people participate in the game and both of them execute the program? Verify your results with a tree diagram or list.
20. (8 points in this question) As shown in the figure, each small square in the grid paper is a square with a side length of 1 unit.
After the plane rectangular coordinate system is established, the vertices of △ABC are all on the grid points, and the coordinates of point B are (1, 0).
① Draw △A 1B 1C 1 of the axis symmetry of △ABC about X,
② Draw △A2B2C2 obtained by rotating △ ABC 90 counterclockwise around the origin O,
③ Is △ a1b1c1an axisymmetric figure with △A2B2C2? If it is an axisymmetric figure, draw all the symmetry axes;
2 1.(8 points) In order to reduce energy consumption and environmental pollution, the General Office of the State Council issued the Notice on Restricting the Use of Plastic Shopping Bags in Production and Sales (hereinafter referred to as "Plastic Restriction Order"), which was officially implemented on June 1 2008. Xiaoyu went to a market on June 8 to learn about the use of shopping bags after the plastic limit order. It is understood that according to the load-bearing capacity of plastic shopping bags, the market provides plastic bags with different quality of 0./kloc-0 yuan, 0.2 yuan and 0.3 yuan. The following two pictures are incomplete statistics obtained from this survey (if each person only uses one shopping bag at a time). Please answer the following questions according to the information in the picture:
(1) The total number of shoppers in this survey is ▲;
(2) Please complete the histogram and explain that the central angle corresponding to the 0.2 yuan part in the fan chart is ▲.
The central angle corresponding to the 0.3 yuan part is ▲ degrees;
(3) If there are 3000 people shopping in this market on June 8th (if each person only uses one shopping bag at a time), please estimate the number and amount of plastic shopping bags sold in this market.
22 (full mark of this question 10) A new type of water slide in Holiday Travel Paradise is shown in the figure, in which the line segment PA represents a platform 5m above the water surface (axis) (point P is on the axis). Slide AB can be regarded as a part of the inverse proportional function image, and slide BCD can be regarded as a part of the quadratic function image. The connection point B of the two slideways is the vertex of parabola BCD, the distance from point B to the water surface is BE=2m, and the distance from point B to the axis is 5m. When Xiao Ming slides from top to bottom to point C, the distance from the water surface CG= m,
The horizontal distance from point B is CF=2m.
(1) Find the analytical formula of inverse proportional function and the range of its independent variables.
(2) Find the analytic formula of quadratic function and the range of its independent variables.
(3) When Xiaoming glides from point A to point D on the water, try to find the horizontal distance d of his gliding.
23. (The full mark of this question is 10) As shown in figure 1, it is a household trash can with its foot on it. Figure 2 is a schematic diagram of its internal structure. EF is a fixed circular tube axis MN, and both ends are spheres that can always slide up and down the circular tube. Point A is the fulcrum of horizontal bar BN rotation. When stepping on horizontal bar BG, N moves to N'. Points b, a, n and GD are known.
(1) When the crossbar steps down to B', find the height of N rising.
(2) The design requirement of the trash can is that the lid of the trash can must rotate 75 around the O point. Does the production at this time meet the requirements? Please provide a justification for the answer.
(3) In the production process, you can move the fulcrum A (no matter how the point A moves, when you step on the crossbar BG, the point B always falls on the point B'). How to move the fulcrum (left or right, how far) to meet the design requirements? (The result of this small problem is accurate to 0.0 1 cm)
24. (The full mark of this question is 12) The side length of the square OABC is 2. Put it in a rectangular coordinate system as shown in the figure. Point M(t, 0) is a moving point on the X axis, connecting BM, and making a square BMNP on the right side of BM.
(1) When t=4, find the coordinates of point p;
(2) Connect CP, the area of triangle CBP is S, and find the functional relationship between S and T;
(3) The analytical formula of straight line DE is y=2x+b, which intersects with X axis at point D and Y axis at point E,
Whether there is a point p that makes the triangle PDE an isosceles right triangle,
If it exists, find the coordinates of point P. If it does not exist, please explain the reason.
Math answer sheet
First, multiple-choice questions (3 points for each question, ***30 points)
The title is 1 23455 6789 10.
Answer d, d, c, c, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b, b. B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
Fill in the blanks (4 points for each question, 24 points for * * *)
1 1 etc. 12.x 1 13.x