Mathematics Test
Precautions:
1. This paper is divided into two parts: test paper and answer sheet. The test paper has 4 pages and 24 small questions. Examination time 120 minutes, full score 120 minutes.
Before answering the questions, please be sure to fill in your name and admission ticket number on the test paper, and fill in the candidate information on the answer sheet.
3. Multiple choice questions must be filled in with 2B pencil in the multiple choice answer area of the answer sheet; Non-multiple-choice questions must be answered with a 0.5 mm black signature pen in the answer area specified for each question on the answer sheet. Anything written or filled in the test paper is invalid.
At the end of the exam, the examination paper and the answer sheet should be handed in together.
A, multiple-choice questions (this topic is entitled *** 10 small questions, 3 points for each small question, 30 points for each small question. Only one of the four options given in each small question meets the requirements of the topic. Please fill in the correct option in the corresponding position on the answer sheet).
The reciprocal of 1 -2 Yes:
A, 2 B, c, -D, does not exist.
2. The following operations are correct:
a 、\b 、-
c、D 、- -
3. Place a right triangle and a ruler as shown. If ∠ α = 43, the times of ∠βare:
a、43 B、47 C、30 D、60
4. When solving the equation (-1) -5(-1), we can regard-1 as a whole. If-is set, the original equation can be transformed into-and solved. When = 1, it is-and solved; When =4, that is,-,the solution is =5, so the solution of the original equation is:,. Then the solution of equation-is obtained by this method:
a、 1、3 B 、-2、3 C 、-3 、- 1 D 、- 1、-2
5. Linear function and inverse proportional function (? ≠0) image as shown in the figure, if >, the value range is:
A, -2 < < 0 or > 1 b, -2 < < 1 c, 1 d,
6. A school organized several teachers and students to carry out social practice activities in Enshi Grand Canyon. If the school rents 45 buses, the remaining 20 people have no seats; If you rent a 60-seat bus, you can rent two less, and the last bus is not full. The number of people taking the last bus with 60 seats is:
a、200-60 B、 140- 15 C、200- 15 D、 140-60
7. As shown in the figure, straight lines AB, AD and ⊙ are tangent to points B and D, C is the upper point of ⊙, and ∠ BCD = 140, then the number of times of ∠A is:
a、70 B、 105 C、 100 D、 1 10
8. The three views of the geometry are shown in the figure. According to the relevant data in the figure, the transverse area of the geometric figure is:
a、B、2 C、3 D、4
9. As shown in the figure, AD is the bisector of △ABC and DF⊥AB, the vertical foot is F, DE=DG, and the areas of △ADG and △AED are 50 and 39 respectively, so the area of △EDF is:
a、 1 1 B、5.5 C、7 D、3.5
10. Xiaoming's father rode a motorcycle and drove Xiaoming on the expressway at a constant speed. The number of milestones that Xiao Ming sees at regular intervals is as follows:
Time12: 0013: 0014: 30
The number on the tablet is two digits, and the sum of the numbers is 6. Ten digits and single digits are just the opposite of what you saw at 12:00, and there is a 0 in the middle of the two digits you saw at 12:00.
So the two digits you see at 12:00 are:
a、24 B、42 C、5 1 D、 15
Fill in the blanks (this big question is ***6 small questions, each with 3 points, *** 18 points. Please fill in the answer in the position corresponding to the question number on the answer sheet. If the handwriting is unclear, ambiguous or the answer is incomplete, you won't score).
1 1. By the end of 20 10, the total registered population of Enshi Prefecture was about 4,040,850, which was expressed by scientific counting method (two significant figures were reserved);
12. Decomposition factor:-=;
13. As shown in the figure, the vertex of delta is at the origin, the point is in the first quadrant, and the point is on the positive axis.
On the half axis, and =, ∞= 60, the inverse proportional function (>; 0) image.
After passing the point, rotate the point clockwise by △ 120, and the vertex just falls on.
On the image of, the value of is;
14. If the inequality is 0, the point is the moving point on the parabola symmetry axis.
(1) Find the coordinates of points, and find a point on the diagram in 1 to minimize the sum of the distances from point to point;
(2) If the minimum value of △ perimeter is 0, find the analytical formula and vertex coordinates of parabola;
(3) As shown in Figure 2, there is a moving point on the line segment that moves from one point to another at a speed of 2 units per second (which is not coincident with the end point and the point). If the point is ∑ and the moving time is set to seconds, try to express the area of △ as a function of time. When it is what value, there is a maximum value, and find the maximum value;
(4) Under the condition of (3), when a parallel line passing through the axis intersects a parabola at two points, ask: Can a circle and a straight line passing through three points be tangent to that point? Please prove your conclusion. (Option Tu Tu 3)