A, multiple-choice questions (this question *** 12 small questions, each small question 5 points, ***60 points. Only one of the four options given in each question meets the requirements of the topic)
1—5 ccdba 6— 10 bccdd 1 1— 12AD
2. Fill in the blanks (4 small questions in this big question, 5 points for each small question, 20 points for * * *)
13.8
14.33
15.
16.
Third, the solution (this big question ***6 small questions, ***70 points, the answer should be written in the proof process or calculus steps. )
17. Solution:
(1) by,
therefore
A is an acute angle.
2 points
But it can be transformed into
That's five points.
(2) By (1)
and
this is
therefore
If and only if the maximum area is 10 point.
18. Solution:
(1) According to the meaning of the question,
Therefore, it can be divided into:
3 points
therefore
That's five points
The above formula also holds, so 6 points.
(2)
9 points
10 point
12 point
19. Solution:
(1) The survival of each tree is independent of each other, and the survival probability of each tree is
2 points
4 points for the solution
(2) If "need to replant" is event A, then A 1: 3 tree did not survive, A2: 1 tree did not survive, A3? : 5 trees didn't survive, A4: 6 trees didn't survive * * * 4 cases, 5 points.
7 points
8 points
(3) According to the meaning of the question, obey binomial distribution 10.
12 point
Or the distribution list is
0 1 2 3 4 5 6
P
=3
20. Option 1: AD//BC According to the meaning of the question,
therefore
So point m is the midpoint of SD, three points.
(1) Proof: link BD to AC to E, link ME, 4 points.
ABCD is a square, e is the midpoint of BD,
M is the midpoint of SD, and ME is the midline.
I/someone. 5 points
Plane ACM
SB// plane ACM. 6 points
(2) From the perspective of the problem, the plane is sad, so there is
and
Plane SCD
Is the angle formed by the straight line AC and the plane SDC at 8 o'clock.
exist
That is, the angle formed by the straight line AC and the plane SDC is 9 degrees.
(3) plane SCD
The plane angle of dihedral angle n-am-c is 10 minute.
Plane AMN 10 point
All merchant ships
auxiliary power unit
∽
The dihedral angle is 12 minute.
Plane SAC plane AMN 12 point
Solution 2: there is AD//BC according to the meaning of the question, so
So point M is the midpoint of SD, and AM is SD.
As shown in the figure, with a as the coordinate origin,
Establish a spatial rectangular coordinate system,
From SA=AB, let AB=AD=AS= 1,
rule
3 points
(1) connect BD and AC to e,
rule
Plane ACM 6 points
(2) from the problem, the plane is sad, so there is CD AM.
you are
Plane SCD,
Is the normal vector of the plane SCD.
The angle formed by the straight line AC and the plane SDC is 9 degrees.
(3) plane SCD
, again
Plane AMN
Is the normal vector of plane AMN.
Let the normal vector of plane AMC be
rule
that is
Let's order then
that is
The dihedral angle n-am-c is 12 minute.
2 1. Solution: (1) The straight AB equation is:
According to the meaning of the question
5 points for the solution
Elliptic equation 6 points.
(2) suppose there is such a
pass by
Get 8 points
Then ①
set up
Then ②
The only possibility is that
That is, a circle with a diameter of CD passes through the origin O (0 0,0).
That is 10.
but
③
Substitute type 2 into the whole to understand.
It has been verified that, makes ① hold.
To sum up, there is a point that makes a circle with a diameter of CD pass through the origin O (0 0,0)12.
22. Solution: (1) Order
solve
The monotone decreasing interval of is
Develop a solution
The monotone increasing interval of is 4 points.
(2) If, there is no solution.
When, that is,
When, that is,
Is increasing monotonously in the world,
8 points
(3) according to the meaning of the question: namely
set up
Order (house)
When,,
When,
When the maximum value is obtained,
,
So the range of real numbers is 12 points.
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