Science Mathematics (Compulsory+Elective Ⅱ) (Shaanxi Volume)
volume one
1. Multiple-choice questions: Of the four options given in each question, only one meets the requirements of the topic (this big question * * 12, with 5 points for each question and 60 points for * *).
1. Let the solution set of inequality be m and the domain of function be n, then.
(a) World Intellectual Property Organization
18. (The full score of this small question is 12)
As shown in the figure, AB= 1 and ∠ABC=60 in a straight triangular prism.
(i) Evidence:
(2) Find the size of dihedral angle A-B ... 5.u.c.o.m
18. (The full score of this small question is 12)
The solution 1 (1) proves that the triangular prism is a straight triangular prism.
By sine theorem.
, again
(2) The solution is shown in the figure, which intersects with point D and connects BD.
From the theorem of three vertical lines
Plane angle of dihedral angle
exist
Solution 2 (1) proves that the triangular prism is a straight triangular prism,
, ,
According to sine theorem
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As shown in the figure, a spatial rectangular coordinate system is established.
rule
(2) The solution, as shown in the figure, can take the normal vector of the plane.
Let the normal vector of the plane be,
rule
Might as well bring it
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19. (The full score of this small question is 12)
The amount of consumer complaints in a food enterprise in one month is expressed by, and the probability distribution of random variables is as follows:
0 1 2 3
p 0. 1.3 2a a
(i) Find the mathematical expectation of the sum of the values of a;
(2) Assuming that the number of consumer complaints in 1 month and February does not affect each other, find the probability that the enterprise was complained twice by consumers in these two months. 5.u.c.o.m
Problem 19, the probability distribution property of the solution (1) is 0. 1+0.3+2a+a= 1, and the solution a=0.2.
The probability distribution of is
0 1 2 3
P 0. 1 0.3 0.4 0.2
(2) Let event A mean that * * * has been complained twice in two months, and the event means that it has been complained twice in one month and two months, and it has been complained 0 times in another month; This incident means that "there were 12 complaints every month for two months".
Through the independence of events
Therefore, the probability that the enterprise has been complained twice by consumers in these two months is 0. 17.
20. (The full score of this short question is 12)
Known function, in which
If the extreme value is found at x= 1, the value of a is found;
The monotone interval of search;
(iii) If the minimum value of is 1, find the range of a ... 5.u.c.o.m
20. Solution (1)
Find the extreme value at x= 1 and get the solution.
(Ⅱ)
∵ ∴
(1) When the interval is monotonically increasing, the interval is
2 when,
pass by
∴
(iii) When (ii) 1,
When, from (Ⅱ) ②, the minimum value is obtained at.
To sum up, if the minimum value is 1, the range of a is
2 1. (The full score of this small question is 12)
It is known that the equation of hyperbola C is eccentricity, and the distance from the vertex to the asymptote is.
(1) Find the equation of hyperbola c;
(2) As shown in the figure, P is a point on hyperbola C, and points A and B are on two asymptotes of hyperbola C, which are located in the first and second quadrants respectively. If yes, find the range of the area. 5.u.c.o.m
2 1. (The full score of this small question is 14)
As we all know, the equation of hyperbola C is
The distance from the vertex of eccentricity to asymptote is
(1) Find the equation of hyperbola c;
(2) As shown in the figure, P is a point on hyperbola C, and points A and B are on two asymptotes of hyperbola C, which are located in the first quadrant and the second quadrant respectively.
Answer 1 (I) From the meaning of the question, the vertex of hyperbola C reaches the asymptote.
∴
The equation of hyperbola c is
(Ⅱ) From (Ⅰ), we know that the two asymptote equation of hyperbola C are
Let's do it together
The coordinates of the point p are obtained as follows
Substitute the coordinates of p point into simplification.
Set ∠AOB
and
commemorate
pass by
When, the area of △AOB takes the minimum value of 2; When the area of △AOB is the maximum, the value range of △ AOB's is
Solution 2 (I) is the same as solution 1.
(Ⅱ) Let the equation of straight line AB be the reason for knowing the meaning of the question.
The coordinates of point a are from {
The coordinates of point b are from {
The coordinates of the point p are obtained as follows
Substitute the coordinates of point p.
Let q be the intersection of straight line AB and Y axis, then the coordinate of point Q is (0, m).
= 5 . u . c . o . m
The following is the same as answer one.
22. (The full score of this short question is 12)
The known sequence satisfies.
Guess the monotonicity of the sequence and prove your conclusion;
(2) Evidence: World Intellectual Property Organization
22 questions
Certificate (1) by
By conjecture: the sequence is a decreasing sequence.
The following is proved by mathematical induction:
(1) When n= 1, the proved proposition holds. (2) Assuming that n=k, the proposition holds, that is,
Then puzzle it.
=
that is
That is to say, when n=k+ 1, the proposition also holds. Combining (1) and (2), the proposition holds.
(2) When n= 1, the conclusion holds.
When it is timely, it is easy to know.
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