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Jiangsu college entrance examination, mathematics, questions 15, 16, 17, 18,19,20. What knowledge points does the topic include?
15. (The full score of this small question is 14)

Yes, it is known.

(1) Verification:;

(2) If the value of a is found.

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

F

As shown in the figure, in a straight triangular prism, is the point on the side (point D is different from point C) and is the midpoint.

E

Verification: (1) plane; [Source: Xue Ke. com]

(2) straight line plane ADE ..

(Question 16)

D

C

A

B

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

As shown in the figure, establish a plane rectangular coordinate system xOy, where the X axis is on the ground plane, the Y axis is perpendicular to the ground plane, and the unit length is 1 km. A gun is located at the origin of coordinates. It is known that the trajectory of the projectile after launching is on the curve expressed by the equation, where k is related to the launching direction. The range of the gun refers to the abscissa of the impact point of the projectile.

(1) Find the maximum range of the gun;

(2) There is a flying object (regardless of size) in the first quadrant with a flying height of 3.2 kilometers. When the abscissa A does not exceed, how much can a shell hit it? Please explain the reason. [Source: Xue+Ke+Net Z+X+X+K] [Source:]

X (km)

Y km

O

(Question 17)

18. (Full score for this small question 16)

It is known that A and B are real numbers, and 1 and are two extreme points of the function.

(1) Find the values of a and b;

(2) Set the derivative function of the function and find the extreme point;

(3) Let, where the number of zeros of the function is found.

19. (Full score for this small question 16)

A

B

P

O

x

y

(Question 19)

As shown in the figure, in the plane rectangular coordinate system x Oy, the left and right focal points of the ellipse are 0, 0, and both are known on the ellipse, where E is the eccentricity of the ellipse.

(1) Find the eccentricity of the ellipse;

(2) Let A and B be two points on the ellipse above the X axis, and they are straight lines.

Parallel to a straight line and intersecting at point p.

(i) If yes, find the slope of the straight line;

(2) Verification: it is a fixed value.

20. (Full score for this small question 16)

It is known that the sum of two series whose terms are positive satisfies:

(1) hypothesis, verification: the series is arithmetic progression;

(2) Let sum be a geometric series and the value of sum.

This is the general form of the 20 12 college entrance examination, which is similar every year.