I. Multiple-choice questions (this big question is a total of * *12 small questions, with 5 points for each small question and 50 points for * * *).
The value of 1.sin2 ()
A. less than 0 b. greater than 0 c. equal to 0 d. does not exist.
2. It is called a point on the terminal edge of the corner, and then = ()
a、— 10 B、C、D、
3. If the set is known, then ()
A, B, C, D,
4.( )
A.B. C. D。
5. In order to get the image of function y = cos2x+π 3, just put the image of function y = sin2x ().
A. translate 5π 12 length unit to the left. B. Translate 5π 12 length unit to the right.
C. translate 5π6 length units to the left. D. translate 5π6 length units to the right.
6. If known, the value of is ()
a6 b . 7 c . 8d . 9
7. Three numbers, the size relationship is ().
A.B.
C.D.
8. If U is a complete set and M, P and S are three subsets of U, then
The set represented by the shaded part is ()
a 、( M∩P)∩S； b 、( M∩P)∪S；
c 、( M∩P)∩(CUS) D 、( M∩P)∩(CUS)
9. The number of solutions of the equation sin π x = 14x is ().
a . 5 b . 6 c . 7d . 8
10. As shown in the figure, the function f (x) = asinω x (a > 0, ω >; 0) periodic images,
Then the value of f (1)+f (2)+f (3)+f (4)+f (5)+f (6) is equal to ().
A.2 B.22 C.2+2 D.22
2. Fill in the blanks (this big question is ***4 small questions, 5 points for each small question, 25 points for * * *, and fill in the correct answer on the horizontal line)
1 1. Given the central angle of the sector is 72, the radius is 20cm, and the sector area is _ _ _ _ _ _.
12. If the image of the function passes through a fixed point, the coordinate of the point is.
13. sinθ =1-a1+a, cos θ = 3a-11+a. If θ is the second quadrant angle, the value of real number A is _ _ _ _ _ _.
14. If 1+sin2θ = 3s inθ cos θ, then Tan θ = _ _ _ _ _ _
15. If the function defined on satisfies and, then _ _ _ _ _ _ _ _.
Third, solve the problem (this big question ***6 small questions, ***75 points, write the process or calculus steps to solve the problem)
16. (The full mark of this question is 10) Find the domain of the function y = 16-x2+sinx.
17. (The full mark of this question is 10) It is known.
(1) If it is the third quadrant, simplify (2) and evaluate.
18, (full mark of this question 13) setting function, and.
( 1); (2) When, find the maximum value.
19. (The full mark of this question is 14) A hotel has 100 beds of the same specification. According to experience, when the hotel bed price (that is, the daily rent per bed) does not exceed 10 yuan, all the beds can be rented out, and when it is higher than 10 yuan, it will increase by 65,438 yuan. (2) The hotel costs 575 yuan per day, and the bed rental income must be higher than the cost, the higher the better. If the bed price is used, the net income of hotel bed rental (that is, income after daily expenses are removed) is used.
(1) as a function and find its domain;
(2) Try to determine the number of beds in this hotel, which not only meets the above two conditions, but also maximizes the net income.
20. (The full mark of this question is 14) The picture on the right is the image of the function f (x) = sin (ω x+φ) in a certain period, among which, try to deduce the minimum positive period of (1)f(x) according to the picture; (2) monotonic increasing interval of f (x);
(3) The set of values of x that makes f(x) the minimum. (4) Find the analytical formula of f(x).
2 1. (The full mark of this question is 14) The minimum value of the function f (x) =1-2a-2acoxx-2sin2x is g (a) (a ∈ r).
(1) find g (a); (2) If g (a) = 12, find the maximum value of a and f(x) at this time.
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