1. Fill in the blanks: This big question is a *** 14 small question, with 5 points for each small question and 70 points for * * *. Please fill in the answer in the printed position on the answer sheet.
1, and the minimum positive period of the function is ▲
2, let (imaginary unit), then the modulus of complex number is ▲
3. The equation of two asymptotes of hyperbola is ▲
4. The set * * * has ▲ subsets.
5. The figure on the right is the flow chart of an algorithm, and the output value is▲ (the flow chart is temporarily missing).
6. Sampling and counting the five training results of two design athletes A and B (unit: ring), the results are as follows:
Athletes' first, second, third, fourth and fifth times.
A 87 9 1 90 89 93
B 89 90 9 1 88 92
Then the variance (smaller equation) of athletes' performance with relatively stable performance is ▲
7. At present, a certain type of virus is recorded as, in which positive integers, (,) can be arbitrarily selected.
Then the probability of taking all odd numbers is ▲
8. As shown in the figure, in a triangular prism, they are
Let the volume of a triangular pyramid be a triangular prism.
If the product is, then ▲
9. The area of the triangle enclosed by the tangent of parabola and two coordinate axes is (inclusive).
Triangle interior and boundary). If the point is any point in the area, the value range of is ▲
10, give way in,,,
If (is a real number), the value of is ▲
1 1 is called odd function as defined above. When, then the solution of inequality.
The setting interval is expressed as▲
12. In the plane rectangular coordinate system, the standard equation of an ellipse is, the right focus is, the right directrix is, one endpoint of the short axis is, the distance from the origin to the straight line is, and the distance from it is.
If so, the eccentricity of the ellipse is ▲
13. In the plane rectangular coordinate system, the set point is a moving point on the image of function ().
If the shortest distance between points is, then the values of all real numbers that meet the conditions are ▲
14, in positive geometric series,,, satisfies.
The value of the largest positive integer is ▲
Second, answer: this big question ***6 small questions, * * * 90 points. Please answer in the designated area on the answer sheet. Write a written description, proof process or calculation steps when answering.
15, (the full score of this small question is 14)
Known,
(1) If yes, please verify:
(2) Set the value of, if.
16, (the full score of this small question is 14)
As shown in the figure, in the triangular pyramid, the plane plane,
Overacting, drooping feet,
A point is the midpoint of an edge.
Verification: (1) plane;
(2) 。
17, (the full score of this small question is 14)
As shown in the figure, in the plane rectangular coordinate system, points and straight lines.
Let the radius of a circle be and the center of the circle be at the top.
(1) If the center of the circle is also on a straight line, the intersection point is tangent to the circle.
Equation for finding tangent;
(2) If there is a point on the circle, let's find the center of the circle.
Standard range of values.
18, (the full score of this small question is 16)
As the picture shows, there are two paths for tourists to get down from a tourist attraction. One is to walk in a straight line, and the other is to take the cable car along the cableway first, and then walk in a straight line. At present, two tourists A and B come down from the mountain, and A walks at a constant speed. After starting from A, B arrives by cable car, stops there and walks at a constant speed. Suppose that the speed of the cable car moving in a straight line at a uniform speed is, and the length of the mountain road is, after measurement, …
(1) Find the length of the trajectory;
(2) How many minutes after B leaves, what is the shortest distance between B and A on the cable car?
(3) In order to make two tourists wait for each other for no more than minutes,
In what range should B's walking speed be controlled?
19, (the full score of this small question is 16)
Let arithmetic progression, the first term of which is, and the tolerance is, which is the sum of the previous terms. Remember, where is a real number.
(1) If, and in geometric series, prove: ();
(2) In the case of arithmetic series, it is proved that:
20. (Full score for this small question 16)
Let function, where is a real number.
(1) If it is a monotonically decreasing function and has a minimum value in, the value range of;
(2) If it is a monotonous increasing function in the world, try to find out the number of zeros and prove your conclusion.