1. Fill in the blanks. 1. 2.； 3.5;
4.2; 5. (reason), (text); 6.；
7.； 8.； 9.；
10. (Richard) 0, (Wen) 2; 1 1.c； 12.；
13. (Richard), (Wen) 3; 14.①④.
Two. Multiple choice questions.15.b; 16.a； 17.d； 18.C
Three. Solve the problem. 19. Solution: (1) From the known situation, (2 points)
Again, (4 points) ∴ (6 points)
(2) (reason) by (if and only if the equal sign holds) (2 points)
∴(4 points)
That is, if and only if the maximum value of (5 points) area is. (6 points)
(2) (Text) From the sine theorem,, (2 points) ∴, (4 points)
∴, that is, the area of the circumscribed circle is. (6 points)
20. Solution: (1) Let the equation be, and the coordinates of the intersection of sum are,
Point, by, (2 points)
Get, according to the meaning of the question, (4 points)
Therefore, the trajectory equation is. (7 points)
(2) (Science) from (1), (2 points)
By (4 points)
Solved, (6 points) noticed, ∴.(7 points)
(Text) (2) Known by (1), (2 points)
Youde (4 points)
Solution (6 points) Note, ∴.(7 points)
2 1. solution: scheme ①: * * repair the entrance and exit of ordinary highway and two interchanges,
Required funds 10000 yuan; (3 points)
Scheme 2: take the left and right symmetrical points and connect the intersections.
When building the entrance, it needs the shortest distance, and * * * needs funds:
Ten thousand yuan; (6 points)
Scheme ③: Build roads along the connecting roads, and the entrance is being built, which requires funds:
Ten thousand yuan (9 points)
Because the comparison size is (12 points), scheme (3) is selected. (14).
22. Answer: (1)∵ is an even function, so it holds for everyone, (2 points) means it holds for everyone, (4 points).
(2) obtained from (1), namely. (2 points)
So the minimum value of (3 points) is. (5 points) If and only if.
(3) The solution 1 is given by equation ()
It can be converted into, obtained from ② or,
By ( 1)，make，then，or
Then. (2 points)
When monotony increases, ∴,
∴, then equation () has one and only one solution; (3 points)
When,,
When equation () has one and only one solution; (4 points)
When equation () has two solutions;
If or at that time, equation () has no solution. (5 points)
In a word, when, function and image have two different things in common;
When or, the image of function and has only one common point;
When or, the image sum of the function has no common point. (7 points)
Solution 2: ()
(2 points)
(3 points)
(4 points)
(5 points)
, ,
. (7 points)
(Text) According to Equation ()
It can be converted into, obtained from ② or,
Order, then, or
Obtained from ①, set (2 points)
∴ In due course,, (4 points)
When ∴ does not exist,
When, or,
If, then, it does not meet the meaning of the question, give up, if, then, it meets the meaning of the question, (5 points)
When or, function and image have only one thing in common. (7 points)
23. Solution: (1), ∴ (3 points)
(2), and
, namely
∴ Geometric series, who takes the first term as the specification, (2 points).
∴.(4 points) ∴.(8 points)
(3) (Cause) comes from (2),
∴, (1 min)
rule
∴ is a decreasing sequence, ∴, (3 points)
To achieve arbitrary constancy,
Just, just, (5 points)
Therefore, ∴, or,
If and when, it applies to any constant,
The minimum positive integer value of ∴ is. (7 points)
(Text) From (2),. ( 1)
If any constant holds, the constant holds (3 points)
At the right time, there is a maximum value of 4, so. (5 points)
In addition, the existence of ∴ makes it arbitrary. So ... (7 points)