20 10 national unified entrance examination for colleges and universities (Hubei volume)

Mathematics (Science and Engineering)

This paper is ***4 pages, with three major questions, 2 1 minor questions, and full marks 150. Examination time 120 minutes.

★ Good luck with the exam ★

Precautions:

1. Before answering questions, candidates must fill in their name, candidate number, examination room number and seat number on the answer sheet. And stick the bar code of the admission ticket number horizontally at the designated position on the answer sheet. Use 2B pencil to black the box at the back of Type A test paper on the answer sheet.

2. Multiple-choice answers: After choosing the answer for each question, use 2B pencil to blacken the answer information points of the corresponding question options on the answer sheet. If you need to change it, clean it with an eraser, and then choose other answer labels, which are invalid on the test paper and draft paper.

3. Answer the fill-in-the-blank question and answer the question: use a 0.5mm black signature pen to directly answer the corresponding answer area on the answer sheet. The answers on the test paper and draft paper are invalid.

Candidates must keep the answer sheet clean and tidy. After the exam, return the test paper and answer sheet together.

First, multiple-choice questions: This big question is a small question of *** 10, with 5 points for each small question and 50 points for * * *. Of the four options given in each question, only one meets the requirements of the topic.

1. is an imaginary unit, then =

A.- B.- 1

2. If known, then =

A.B. C. D。

3. Given a function, if, the value range of x is

A.B.

C.D.

4. If the number of regular triangles whose two vertices are on a parabola and the other vertex is the focus of this parabola is n, then

A.n=0 B. n= 1 C. n=2 D. n 3

Test paper type: a

5. Assuming that random variables obey normal distribution, p (< 4) =, then p(0 < < 2)= 1

A.0.6 B.0.4 C.0.3 D.0.2

6. It is known that the odd function and even functions defined on R satisfy (> 0 and). If so, then =

The second century BC.

7. As shown in the figure, three different types of elements K, K and K are connected into a system. When it works normally and at least one of them works normally, the system works normally. Assuming that the probability of normal operation of K, K and K is 0.9, 0.8 and 0.8 respectively, the probability of normal operation of the system is

A.0.960 B.0.864 C.0.720 D.0.576

8. known vectors a=(x+z, 3), b=(2, y-z), and a ⊥ b. If x and y satisfy inequality, the range of z is

A..[-2，2] B.[-2，3] C.[-3，2] D.[-3，3]

9. If real numbers A and B satisfy AND, they are said to be complementary. Remember, then A and B are complementary.

A. Necessary but not sufficient conditions B. Sufficient and unnecessary conditions

C. Necessary and sufficient conditions D. Inadequate and unnecessary conditions

10. Radioactive elements become other elements due to the continuous emission of particles from atoms, and their contents are decreasing. This phenomenon is called decay. It is assumed that during the decay of radioactive isotope cesium 137, its content m (unit: Taber) and time t (unit: year) meet the functional relationship:, where M0 is the content of cesium 137 when t=0. When t=30, the change rate of cesium 137 content is-10In2 (Tebeck/year), then M(60)= 1

A.5 taipeike B.75In2 taipeike

C. 150In2 taipeike d. 150 taipeike

Fill in the blanks: This big question is ***5 small questions, with 5 points for each small question and 25 points for * * *. Please fill in the answers in the position corresponding to the question number on the answer sheet, and fill in the answers in order. You can't give points for wrong answers, unclear handwriting and ambiguity.

The coefficient term contained in the expansion 1 1 be

12.30 bottles of drinks, 3 bottles have passed the shelf life. If you choose two bottles from these 30 bottles, the probability that at least one bottle has passed the shelf life is. (The result is expressed in the simplest score)

13. the problem of "nine-section bamboo" in "nine chapters of arithmetic": there is a bamboo with nine sections. The volume of each section from top to bottom is arithmetic progression, the volume of the upper four sections is 3 liters, and the volume of the lower three sections is ***4 liters, so the volume of the fifth section is liters.

Class a test paper

14. As shown in the figure, the plane of rectangular coordinate system is, and the plane of rectangular coordinate system (coincident with the axis) is.

(i) A point on a given plane whose projected coordinates on the plane are:

(ii) If the equation of the curve on the plane is known, the projection equation of the curve on the plane is.

15. Color the squares connected up and down with black or white. At this point, in all different coloring schemes, the coloring scheme in which black squares are not connected with each other is as shown in the following figure:

From this, it can be inferred that there were * * * kinds of coloring schemes in which black squares were not connected with each other, and there were * * * kinds of coloring schemes in which at least two black squares were connected (the results were expressed by numerical values).

Third, the solution: this big question is ***6 small questions, ***75 points. The solution should be written in words, proof process or calculus steps.

16. (Full score for this small question 10)

The edges opposite to the inner corners of the set are known respectively.

(1) Find the circumference of ...

(2) the value of

17. (The full score of this small question is 12)

Improving the capacity of the river-crossing bridge can improve the traffic conditions of the whole city. In general, the speed V (unit: km/h) on the bridge is a function of the speed X. When the traffic density on the bridge reaches 200 vehicles /km, it will cause congestion and the traffic speed is 0. When the traffic density does not exceed 20 vehicles /km, the traffic speed is 60 km/h, the research shows that; At that time, vehicle speed V was a linear function of vehicle density X. 。

(i) At that time, find the expression of the function;

(2) When the traffic density is high, the traffic flow (the number of vehicles passing an idea on the bridge in unit time, unit: vehicle/hour) can reach the maximum, and the maximum value can be obtained (accurate to 1 vehicle/hour).

18. (The full score of this small question is 12)

As shown in the figure, it is known that the length of each side of a regular triangular prism is 4, which is the midpoint, and the moving point is on the side and does not coincide with this point.

When = 1, verify: ⊥;

(Ⅱ) Let dihedral angle be the minimum value.

19. (The full score of this small question is 13)

It is known that the sum of the first few paragraphs of a sequence is 0 and satisfies:, N*,.

(i) Find the general term formula of the sequence;

(2) If there is N*, it becomes arithmetic progression, that is to judge whether any N*, sum, and, becomes arithmetic progression, and prove your conclusion.

20. (The full score of this short question is 14)

The product of the continuous slopes of two fixed points on a plane is equal to the locus of a point with a non-zero constant. The curve formed by the addition of two points can be a hyperbola of a circle or an ellipse.

(1) Find the equation of curve and discuss the relationship between shape and numerical value;

(2) At that time, the corresponding curves were: for a given, the corresponding curves were, set and yes. Question: Is there a point that makes the area of △ lie? The value of, if it exists; If it does not exist, please explain why.

2 1. (The full score of this small question is 14)

(i) Find the maximum value of a given function;

(Ⅱ) Let …, all positive numbers, prove that:

(1) If …, then …;

(2) If …= 1, then …