1. If the set is known, the number of elements in the set is

5 (B)4 (C)3 (D)2

2. Known points, vectors and vectors.

(A) (B) (C) (D)

3. If the known complex number is satisfied, then ()

(A) (B) (C) (D)

4. If three positive integers can be used as the side lengths of three sides of a right triangle, then these three numbers are called a set of pythagorean numbers. If three different numbers are selected, the probability that these three numbers form a set of pythagorean numbers is ().

(A) (B) (C) (D)

5. It is known that the center of the ellipse E is the coordinate origin, the eccentricity is, the right focus of E coincides with the focus of parabola, and it is the intersection of the directrix of C and E, then

(A) (B) (C) (D)

6. Nine Chapters Arithmetic is a famous mathematical work in ancient China with rich contents. There are the following questions in the book: "There is an inner corner of the wall today, eight feet next week and five feet high. What is the product? " It means: "pile the rice in the corner of the room (as shown in the picture, the rice pile is a quarter cone), the arc length at the bottom of the rice pile is 8 feet, and the height of the rice pile is 5 feet." What is the volume of the rice pile and the piled rice? " It is known that the volume of 1 humus rice is about 1.62 cubic feet, and the pi is about 3. It is estimated that there are () piles of rice.

Huhu

7. The arithmetic series with a tolerance of 1 is known and is the sum of the previous items. If, then ().

(A) (B) (C) (D)

8. If part of the image of the function is shown in the figure, the monotone decreasing interval of is ().

(1)

(2)

(3)

(4)

9, execute the right block diagram, if input, output ().

(A) (B) (C) (D)

10, the function is known, and then

(A) (B) (C) (D)

1 1. After a part of the cylinder is cut off by a plane, it and the hemisphere (radius) form a geometric body. The front view and top view of the geometry are shown in the figure. If the surface area of the geometry is, ().

(A) (B) (C) (D)

12. Let the image of the function and the image of the function be symmetrical about a straight line, and then ()

(A) (B) (C) (D)

Two. Fill-in-the-blank question: This big question is ***4 small questions, with 5 points for each small question.

13, the sum of the first n items in the series, if, then $n = ___.

14. If the tangent of the image of the known function passes through this point, then _ _.

15. If x and y meet the constraints, the maximum value of is _ _.

16. It is called the right focus of the hyperbola, and P is a point on the left branch of C. When the perimeter is the smallest, the area of the triangle is _ _.

Third, answer questions.

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

They are known to be opposite sides of the inner corner.

(i) If, ask

(II) If yes, the area.

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

As shown in the figure, the quadrilateral ABCD is a diamond, g is the intersection of AC and BD,

(1) Proof: aircraft;

(2) If the volume of the triangular pyramid is, find the lateral area of the triangular pyramid.

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

A company needs to know the influence of annual promotion fee X (unit: thousand yuan) on annual sales volume Y (unit: t) and annual profit Z (unit: thousand yuan) in order to determine the promotion fee of a product in the next year. The data of publicity expenses and annual sales volume in recent 8 years are preliminarily processed, and the following scatter chart and some statistical values are obtained.

In the table, =

(1) According to the scatter chart, judge which one is suitable as the regression equation type of annual sales volume Y and annual publicity fee X (only give judgment, no reason);

(2) according to the judgment result of (1) and the data in the table, establish a regression equation of Y about X;

(3) Knowing the relationship between the annual profit Z of the product and X and Y, answer the following questions according to the result of (2):

(1) How much time was spent on publicity in that year, and what were the forecast values of annual sales volume and annual profit?

(ii) What was the publicity expenses in that year, and what was the estimated annual profit?

Attachment: For a set of data, the least square estimate of the slope and intercept of the tropic of cancer is:

20. (The full score of this short question is 12)

It is known that the intersection point and the straight line L with slope k intersect with circle C at two points M and N. 。

(1) Find the value range of k;

(II), where o is the origin of coordinates, find.

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

Set a function.

(i) The number of zeros of the derivative function in question;

(2) Proof: timely.

Please choose one of questions 22, 23 and 24 to answer. If you do too much, score according to the first question. Please write down the question number clearly when you answer.

22. (Full score for this small question 10)

Elective course 4- 1: Selected lectures on geometric proof

As shown, AB is the diameter of O, AC is the tangent of O, and BC passes through points O and E. 。

(i) If D is the AC midpoint, prove that DE is the O tangent;

(II) If so, what is the size?

23. (Full score for this small question 10)

Elective 4-4: Coordinate System and Parameter Equation

In rectangular coordinate system, a straight line and a circle take the coordinate origin as the pole and the positive semi-axis of X axis as the polar axis, and a polar coordinate system is established.

(1) Polar coordinate equation.

(II) If the polar coordinate equation of the line is, the intersection point is and the area is.

24. (Full score for this small question 10)

Elective Course 4-5: Special Lecture on Inequality

Known function.

(i) Finding the solution set of inequality;

(II) If the area of the triangle enclosed by the image and the X axis is greater than 6, find the value range of a. 。