Note to candidates:

1. Before answering questions, candidates must clearly fill in their names and college entrance examination admission ticket numbers on the answer sheet, and stick bar codes in the designated areas.

2. There are * * * 23 questions in this volume, with full marks of 150 and examination time of 120 minutes.

1. Fill-in-the-blank question (the full score of this big question is 56) * * There are 14 questions in this big question. Candidates should directly fill in the corresponding numbered blanks on the answer sheet, and each blank will get 4 points, otherwise it will get 0 points.

The inverse of the function f (x) = x3+1 is f-1(x) = _ _ _ _ _.

2. known sets A={x|x≤ 1}, B={x|≥a}, A∪B=R,

Then the range of the real number A is _ _ _ _ _ _ _ _ _ _ _.

3. If the algebraic cofactor of element 4 in the determinant is greater than 0, then the condition that X satisfies is _ _ _ _ _ _ _ _ _ _ _.

4. If the program block of an algorithm is as shown on the right, the relationship between the output Y and the input X is _ _ _ _ _ _ _ _ _ _ _ _.

5. As shown in the figure, if the base length of the regular quadrangular prism ABCD-A1B1C1D1is 2,

If the height is 4, the angle formed by the non-planar straight line BD 1 and AD is _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.

The result is expressed by the inverse trigonometric function value.

6. If the spheres O 1 and O2 represent the area ratio, then their radius ratio is = _ _ _ _ _ _ _ _ _.

7. If the real numbers x and y are known to be satisfied, the minimum value of the objective function z=x-2y is _ _ _ _ _ _ _.

8. If the right-angled side length of an isosceles right-angled triangle is 2, the geometric volume of the Zhou Suocheng rotating on the straight line of the right-angled side is.

9. If the intersection point A (1, 0) is a straight line with an inclination of, and it intersects the parabola at two points, then =.

10. The minimum value of this function is.

1 1. If a school wants to select three volunteers for the Shanghai World Expo from five boys and two girls, the probability that the selected volunteers are not less than 1 is (the result is expressed by the simplest score).

12. It is known that the two focuses of an ellipse are points on the ellipse, and. If the area of is 9, then.

13. Known functions. Arithmetic progression with 27 terms satisfies the tolerance. If, then when k=,.

14. A street in a certain place presents an east-west and north-south network, and the distance between adjacent streets is 1. The intersection of two streets is called a grid point. If a rectangular coordinate system is established with two mutually perpendicular streets as the axis, and the following grids (-2,2), (3, 1), (3,4), (-2,3) and (4,5) are newspaper retail stores, please determine one grid as the publishing station, so that the sum of the distances of the five retail stores along the street is the shortest.

Two. Multiple-choice question (the full score of this big question is 16) This big question * * * has 4 questions in total, and each question has one and only one correct answer. Candidates should black out the small squares representing the answers on the corresponding numbers on the answer sheet, and get 4 points for choosing the right one, otherwise get 0 points.

15. Given that straight lines are parallel, the value of k is ().

(A) 1 or 3 (B) 1 or 5 (C)3 or 5 (D) 1 or 2.

16, as shown in the figure, it is known that the bottom surface of a triangular pyramid is a right triangle, with right-angle side lengths of 3 and 4 respectively, and the side length passing through the right-angle vertex is 4 and perpendicular to the bottom surface. The front view of the triangular pyramid is ().

17. The midpoint trajectory equation of point P(4, -2) continuous with any point on the circle is [A] ().

(A) (B)

(C) (D)

18. During the occurrence of a public health incident, a professional organization thought that the sign that the incident did not have a large-scale group infection for a period of time was "10 day, and no more than 7 suspected cases were added every day". According to the data of suspected cases added by A, B, C and D in the past 10 day, it must be [A].

(a) A: The overall average is 3 and the median is 4. (B) B: the overall average value is 1, and population variance is greater than 0.

(c) C: the median is 2 and the mode is 3. (D) D: The overall average is 2, and population variance is 3.

3. Answer (out of 78) *** 5 questions in this big question. To answer the following questions, you must write the necessary steps with corresponding numbers in the designated area on the answer sheet.

19. (The full mark of this question is 14)

It is known that the complex number (a, b )(I is the imaginary unit) is the root of the equation. Complex number () is satisfied, and the value range of u is found.

20. (The full score of this question is 14) There are two small questions in this question. The full score of the first 1 question is 6, and the full score of the second one is 8.

Given that ABC's angles a, b and c are a, b and c respectively, set a vector,

,

If//,verify that ABC is an isosceles triangle;

(1) If ⊥, the side length C = 2 and the angle C =, find the area of Δ δABC.

2 1. (The full score of this question is 16) There are two small questions in this question, and the full score of 1 small question is 6, and the full score of the second small question is 10. Sometimes you can use functions.

Describe the degree of mastery of learning a subject. Among them, the number of times to learn a certain subject () indicates the degree of mastery of the subject knowledge, and the positive real number A is related to the subject knowledge.

(1) proves that when x 7, the growth of proficiency f(x+ 1)- f(x) always decreases;

(2) According to experience, the values of A corresponding to subjects A, B and C are (1 15, 12 1), (12 1, 127 respectively.

(127, 133). When you study a subject for six times, your mastery is 85%. Please determine the corresponding theme.

22. (The full score of this question is 16) There are three small questions in this question. The full score of 1 is 4, the full score of 2 is 4, and the full score of 3 is 8.

It is known that the center of hyperbola C is the origin, the right focus is F, an asymptote M:, and let a straight line L pass through the direction vector of point A..

(1) Find the equation of hyperbola c;

(2) If a straight line passes through the origin and the distance from A to L is 0, find the value of k;

(3) It is proved that there is no point Q on the right branch of hyperbola C, and the distance from it to straight line L is 0.

23. (The full score of this question is 18) There are three small questions in this question. 1 has a full score of 5, 2 has a full score of 5 and 3 has a full score of 8.

Arithmetic progression with a known tolerance of d is geometric progression with a common ratio of q.

(1) If yes, does it exist? Please explain the reasons;

(2) If (a, q is constant, aq 0) exists for any m, try to find the necessary and sufficient conditions that a and q satisfy;

(3) If you try to determine all P so that one of the sum series of a continuous P exists in this series, please prove it.

Shanghai (Mathematical Literature) Reference Answer

Fill in the blanks

1.2.ɑ≤ 1 3.4.

5 6.2 7.-9 8.

9. 10. 1 1. 12.3

13. 14 14(3,3)

Second, multiple choice questions

Title15161718

Code name C B A D

Third, answer questions.

19. solution: the root of the original equation is

Twenty questions. Proof: (1)

That is, where r is the radius of the circumscribed circle of triangle ABC,

It's an isosceles triangle

Solution (2) According to the meaning of the question,

According to cosine theorem,

2 1 question. The proof (1) is timely,

When the function monotonically increases, and

So the function monotonically decreases.

As time goes on, the growth of proficiency always decreases.

(2) The meaning of the question is clear.

arrange

Get a score of ... 13

So this course is subject B. 14.

22. The solution (1) sets the hyperbolic equation as follows

The equation for solving the frontal hyperbola is

(2) straight line, straight line

From the meaning of the problem, the meaning of the problem, the meaning of the problem and the meaning of the problem.

(3) Prove that 1 sets a straight line parallel to the origin.

Then when the distance between the straight line and,

The asymptote of hyperbola is

The right branch of the hyperbola is at the lower right of the straight line,

The distance from any point on the right branch of hyperbola to a straight line is greater than.

Therefore, there is no point on the right branch of the hyperbola, so its distance from the straight line is

Proof 2 Suppose that the distance from a point on the right branch of a hyperbola to a straight line is,

rule

By (1)

Settings,

When,;

Replace with (2).

,

The equation has no positive root, that is, the assumption is not valid.

Therefore, there is no point on the right branch of the hyperbola, so its distance from the straight line is

23. The solution of (1) is derived.

Upon completion, you can get

And are integers.

No, it makes the equation hold.

(2) So, when?

That is, where is an integer greater than or equal to.

Otherwise, if, where is an integer greater than or equal to,

Obviously, among them,

The necessary and sufficient condition is that, where is an integer greater than or equal to.

(3) Settings

When it is even, the left side of the formula is even and the right side is odd.

When it is an even number, the formula does not hold.

Arrange by type

When? That fits the question.

When it is odd,

By, by

When it is an odd number, at this time, there must be a sum to make the above formula hold.

When it is odd, all propositions hold.

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