First, multiple-choice questions: 5 points for each small question, out of 60 points.
1.A
2.D
3.A
4.B
5.A
6.B
7.C
8.A
9.D
10.C
1 1.B
12.C
Fill-in-the-blank: 4 points for each small question, out of 16 points.
13.
14.9
15.288
16. 1+2
Third, answer questions: out of 74 points.
17. (This little question is 13)
Solution: (I) Let A represent that A hits the target and B represents that B hits the target, then A and B are independent of each other, and p (a) =, so that the probability of A hitting the target but B not hitting is
(ii) Let A 1 indicate that A hits k times twice, and B 1 indicates that B hits k times twice 1 time.
According to the meaning of the question
According to independence, the probability of two people hitting the same number of times is
18. (This little question is 13)
Solution: (i) Pass
Therefore, the domain of f(x) is
(2) Based on known conditions
therefore
=
=
=
19. (This little question is 12)
Solution 1: (i) We know B 1C 1⊥B 1D from the definition of a straight triangular prism, and because ∠ ABC = 90, b1.
B 1C 1⊥ airplane A 1B 1D, and get b1c1⊥ b1e. And b/kloc-0.
Therefore, B 1E is the common perpendicular to the straight lines B 1C 1 and a1d.
Yuki people
In Rt△A 1B 1D, A2D= =
Also because
So B 1E=
(2) From (1), we can see that B 1C 1⊥ plane A 1B 1D, while BC ‖ b1,so BC ?. Therefore, the volume v of the quadrangular pyramid is
V=VC-ABDE=
Where s is the area of quadrilateral ABDE. If you answer (19) figure 1, pass E as EF⊥BD, and the vertical foot as F.
Answer (19) Figure 1
In Rt△B 1ED, ED=
And because S△B 1ED=
So EF=
Because of the height of A 1A side of △A 1AE
S△A 1AE=
And because s △ a 1bd = therefore,
S = S△a 1AE-S△a 1AE-S△a 1b 1D = 2-
therefore
Solution 2: (2) If you answer (19) Figure 2, establish a spatial rectangular coordinate system O-xyz with point B as the coordinate origin O, then
(19) Figure 2
A(0， 1，0)，A 1(0， 1，2)，B(0，0，0)
B 1(0，0，2)，C 1(，0，2)，D(0，0，)
therefore
Let e (,y0, z0), then,
therefore
The topic B 1E⊥A 1D has been decided, so B 1E is the common perpendicular to the non-planar straight lines B 1C 1 d.
Let's find the coordinates of point e.
Because B 1E⊥A 1D, that is,
and
Simultaneous (1), (2), solution, that is,.
So ...
(2) BC⊥AB, BC⊥DB, so BC⊥ Aircraft Abe. That is, BC is the height of the four-corner pyramid C-ABE.
Let's find the area of quadrilateral ABDE.
Because SABCD=SABE+ sade
And SABE= =
SBDE=
So SABCD= =
therefore
20. (This little question is 12)
Solution: Let the width of a cuboid be x(m) and the length be 2x.
(m), the height is
.
Therefore, the volume of a cuboid is
therefore
Let v ′ (x) = 0, and the solution is x=0 (excluding) or x= 1, so x= 1.
When 0 < x < 1, v ′ (x) > 0; When 1 < x
So the maximum value of V(x) is obtained at x= 1, and this maximum value is the maximum value of V(x).
Therefore, the maximum volume v = v ′ (x) = 9×12-6×13 (m3). At this time, the rectangular body is 2 m long and 1.5 m high.
Answer: When the rectangular body is 2 m long, width 1 m and height 1.5 m, the maximum volume is 3 m3.
2 1. (This small problem is 12 points)
(1) Solution: Let the standard equation of parabola be, then, therefore,
Therefore, the coordinate of the focal point is (2,0).
The general formula of the directrix equation is.
Therefore, the equation for line l is.
Answer (2 1) chart
(2) Solution 1: As shown in Figure (2 1), if AC⊥l, BD⊥l, and the vertical feet are C and D, we can know from the definition of parabola.
|FA|=|FC|，|FB|=|BD|
Remember that the abscissas of A and B are xxxz, then
| fa | =| AC| = solution,
Similarly, there are solutions.
Remember that the intersection of straight line M and AB is E, then
therefore ...
Therefore.
Solution 2: Setup