First, multiple choice questions
1.B 2。 D 3。 A 4。 C 5。 B 6。 C 7。 D 8。 B 9。 C 10。 A
Second, fill in the blanks
1 1. 12. 100 13. 14 . a & lt； -1 or a=0 or a >；; 1 15.2 pieces
Third, answer questions.
16. Solution: (1)
(3 points)
and
(6 points)
(2)
Another point (12)
17. The values of the solution (1) and the random variable are 2, 3 and 4.
The total number of basic events for pulling two balls out of the box is C.
Let the four balls be
When =2, the ball is 1. ;
When =3, there are four cases: 1 and 2 and 2, 1 and 2 and 2 * * *.
p(= 3)=；
When =4, the ball touched is
The distribution list is
2 3 4
P
E =2× +3× +4× =3 (6 points)
(2) The function has one and only one zero on the interval (2,3).
. that is
(12)
18. Solution: (1) Connect B C to BC to E, and connect DE, BC CC,
(6 points)
(2) Make BF in F and connect EF.
and
set up
Another point (12)
19. Solution: (1) Ellipse definition is available, available.
And, moreover,
Solution (4 points)
(or solution: a circle with a diameter must have an intersection with an ellipse, that is,
Get from
Solve at this time
If and only if m=2 (8 points)
(3) by
Let the coordinates of point A and point B be, and the coordinates of point Q be.
The two expressions are then subtracted.
①
The part inside the ellipse.
It is also known that
②
① ② The coordinates of point Q can be expressed in the following two forms at the same time.
Point q must be within an ellipse.
and
20. Solution: (1)
therefore
(2)
therefore
Guess from this
The following proof: when, by
get
if
while
When,
When,
In short, the reason is (-( 10)
and
Therefore, when, there is a unique real number solution on (-1, 0), so that.
There is a unique real number solution on.
To sum up,. (13)
2 1. Solution: (1) Order
manufacture
Grading from ① ② (4 points)
(2) Available from (1)
rule
and
and
(3) Orders
rule
while
that is
Solve or
Therefore (14)
Proposer: Shizisong in Huangmei No.1 Middle School.
Examiner: Ding, Huanggang Institute of Educational Science.
Fang Zhongxiang of Hongan Qili High School