First, multiple-choice questions: BBDBA BBBCB AC
Fill in the blanks:13.614.15.1.16.23.
3. Solution: This big question is ***6 small questions, with a score of ***70. The solution should be written in proof process or calculus steps.
17. Solution: (1)∫, and the angle with the vector is
∴ , ∴ ,
Say it again. That is.
(2) From (1):
∴
∵ ,
∴ ,
∴ ,
∴ when = 1, A=
Then go ∴AB=2
18. Solution: (1)P=
(2) The value of the random variable is 0, 1, 2, 3.
According to the probability formula of n independent repeated tests
The distribution list of random variables is
0 1 2 3
Mathematical expectation is
19. Proof (1)
DC DC airport.
DC police station DC advertisement,
PDA is the plane angle of dihedral angle p-CD-B.
So PDA = 45 pa = ad = 3,
APD=45。 PA AD。
PA AB, pa plane ABCD ..
(2) proof 1: extend DA and CE to point n and connect PN,
Just fold it.
,
You can also know from (1) that,
It's the plane angle of dihedral angle, ............. 9 points.
In a right triangle,
, .
That is, the sharp dihedral angle formed by the plane PEC and the plane PAD is 30.
Prove 2: establish a spatial rectangular coordinate system as shown in the figure,
rule
,
Set to the normal vector of the plane, then
, you can set the normal vector of the plane,
. .
20. Answer: (1) According to the meaning of the question
(2) According to the meaning of the question, there are exactly two different real roots in the world.
manufacture
So it is a decreasing function on [0, 1] and a increasing function on it.
2 1. Solution: (1) Linear equation and simultaneous.
(2) Set the coordinates of the midpoint m of the chord AB as follows.
So the locus of the midpoint m of the chord AB is centered,
The focus is on the axis, the major axis is 1, and the minor axis is ellipse.
(3) Let the equation of straight line AB be
Substitution finishing
The straight line AB passes through the left focus f of the ellipse, and the equation has two unequal real roots.
Remember the midpoint
rule
Perpendicular bisector NG's equation is
Lingde
The value range of abscissa of G point is
22. Solution: (1) Release
(2) ①
②
(1) minus (2), deformation,
And because the tense formula also holds.
Therefore, the sequence is a geometric series with common ratio,
therefore
(3),
therefore