Mathematics (science)

1. Multiple-choice question: This big question is a small question of *** 10, with 5 points for each small question and 50 points for * * *. Only one of the four options given in each small question meets the requirements of the topic.

1. is a * * * yoke complex number. If ((is an imaginary unit), then ().

A.B. C. D。

2. The domain of the function is ()

A.B. C. D。

3. Known functions,, if, then ()

A. 1 B. 2 C. 3 D. - 1

4. In the middle and inner corners A, B and C, the corresponding edge is, if, the area ().

The third century BC.

5. The top view of the geometry is shown on the right, and the correct one of the four top views given below is ().

6. Some people have studied the relationship between middle school students' gender and four variables: achievement, vision, IQ and reading, and randomly selected 52 middle school students to get statistical data, such as table 1 to table 4. The most likely variable related to Zeyu's gender is ().

A.b vision, c IQ and d reading

7. Read the following program block diagram and run the corresponding program. The output result after the program runs is ().

a . 7 b . 9 c . 10d . 1 1

8. If ()

A. BC 1

9. In the plane rectangular coordinate system, the axis and the moving points on the axis are respectively. If a circle with a diameter is tangent to a straight line, the minimum area of the circle is ().

A.B. C. D。

10. As shown in the figure on the right, in a cuboid, = 1 1, =7, = 12, a particle shoots from vertex A to a point and meets the surface reflection of the cuboid (reflection obeys the principle of light reflection). The line segment between the second and the first reflection point is recorded as

2. Choose a question: Please choose one of the following two questions to answer. If you do both questions, you will be graded according to the first question, and this question will be scored ***5 points. Of the four options given in each question, only one meets the requirements of the topic.

1 1( 1). (Inequality is selected as a problem) For any, the minimum value is ().

A.B. C. D。

1 1(2). (Coordinate system and parameter equation are selected as questions) If the origin of rectangular coordinate system is taken as the pole and the non-negative half axis of the shaft is taken as the polar axis, the polar coordinates of the line segment are ().

A.B. C. D。

Fill-in-the-blank question: This big question has four small questions, each with 5 points and * * 20 points.

12. 10 products include 7 genuine products and 3 defective products. If four products are selected, the probability of getting 1 defective products is _ _ _ _ _.

13. If the tangent of a point on the curve is parallel to a straight line, the coordinate of the point is _ _ _ _ _ _ _ _.

14. Given that the included angle between unit vector and is, and the included angle between vector and is, then =

15. A straight line with slope intersects an ellipse at the intersection. If it is the midpoint of a line segment, the eccentricity of the ellipse is.

Three. Short Answer Questions

16. Known functions, among which

(1) At that time, find the maximum and minimum values in the interval;

(2) If, the value of.

17, (the full score of this small question is 12)

It is known that two series () whose first term is 1 satisfy.

(1) order, and find the general term formula of the sequence;

(2) If, find the sum of the first n items in the series.

18, (the full score of this small question is 12)

Known function.

(1) extreme value at that time;

(2) If the interval is monotonically increasing, find the range of b 。

19 (the full mark of this small question is 12)

As shown in the figure, in the quadrangular pyramid, it is rectangular and flat.

(1) Verification:

(2) If you ask what the value is, what is the maximum volume of the pyramid? And find the cosine of the included angle between the plane and the plane.

20. (The full score of this short question is 13)

As shown in the figure, the right focus of the hyperbola is known, and the point is on two asymptotes, the axis, ∨ (that is, the coordinate origin).

(1) Find hyperbolic equation;

(2) The straight line passing through a point intersects with the straight line of a point and intersects with the straight line of a point, which proves that the point is constant when it moves on the floor, and finds this constant value.

2 1. (Out 14) Divide these 2n consecutive positive integers into two groups, A and B, n in each group, with the minimum number of group A being 0 and the maximum number being 0; The minimum number of people in group b is, and the maximum number is, remember.

(1) Find the distribution table and mathematical expectation at that time;

(2) Let the value of the event represented by c be exactly equal to the value of, and find the probability of the occurrence of event c;

(3) For the event c in (2), express the opposite event of c, judge the size relationship of sum, and explain the reasons.