1, the negation of the proposition "arbitrary" is (c)
A does not exist. B does exist.
C has d for arbitrary.
2. If the definition domain is and the value domain is, the minimum value of the interval length is (b).
In 2 BC.
3. arithmetic progression's general formula is: if the sum of the first items is, then the sum of the 10 items before the series is (a).
120 D. 100
4. It is known that A, B and C are three points on the plane, O is the outer center, and the moving point P satisfies.
, then the trajectory of P is set (D)
A, the center of a heart, b, the center of gravity, c, and the midpoint of D AB.
5. If it is an even function, then the locus equation (b) of the point ().
6. The even function defined on satisfies and is a decreasing function on. Of the following five propositions about, the correct number of propositions is (C).
① is a periodic function; ② Image symmetry; (3) It is a decreasing function;
(4) increase its role in the world; ⑤ .
2 (B)3 (C)4 (D)5。
II. Fill in the blanks (this big question * * 10 small question, 5 points for each small question, 5 points for * * *).
7. The known sets A = {- 1, 3, m} and B = {3, 4}. If b is a, the value of real number m is 4.
8. In the triangle ABC, if the maximum internal angle of the triangle is equal to.
9. The function about is known. If the image is always above the axis, the value range of is.
10, and the side lengths opposite to the three internal angles A, B and C of △ABC are A, B and C respectively. Let's set a vector. If so, the size of angle C is
1 1, if it is the sum of all digits, such as,, then; Remember,,,, and then 1 1.
12, if the general term formula of series {an} an =, remember, try to find the value and infer =.
13. For a function, among all the constants M that hold ≤M, we call the minimum value of m the supremum of the function, and the supremum of the function is 2.
14. The function has only one common point with the straight line in the interval, and the chord length obtained by cutting the straight line is, then the values of a set of parameters that meet the conditions can be.
15, the number of intersections between the image of the function and the image of the function is 3.
16, a proofreader designed five multivariate evaluation indexes for the selection of civilized classes, and calculated the comprehensive scores of each class through empirical formulas. The higher the S value, the better the evaluation effect. If all indicators of a class are displayed during the self-check, the value of an indicator will be increased by 1 unit in the next stage, which makes the value of S increase the most, so this indicator should be C. (fill in a letter).
Three. Problem solving (this big question is ***6 small questions, and ***85 points. The solution should be written in words, proof process or calculus steps)
17 (full mark of this question 12) Let the propositional function be the subtraction function on, and the range of the propositional function is. If "sum" is a false proposition and "or" is a true proposition, the range of values is obtained.
Answer: You got 3 points.
, in the range of ... 7 points.
And it's fake, or true, true or false.
If it's true, 9 points.
If it is true, 1 1 min.
In a word, it's still ............................................................... 12.
18 (the full mark of this small question is 12) exists, and the inner angle and edge are known. Let the area of the inner corner be.
(1) Find the analytic formula and domain of the function;
(2) Find the maximum value.
Solution: sum of interior angles of (1)
....................... 1 min.
.........................., 4 points.
.......................... scored six points.
(2) 8 points.
............. 1 1 min
When it is timely, y gets the maximum ........................ 12.
19 (the full mark of this small question is 13) The domain of the known function is and the range is; Function.
(i) Find the minimum positive period and maximum value of the function g(x);
(ii) When the sum g(x) =5, find tan x. 。
Solution: f (x) = a (1-cos2x)-sin2x+b
=-a (cos2x+sin2x)+a+b =-2asin (2x+)+a+B.-2 points.
∫x∈,∴2x+，sin(2x+)？ Obviously, a=0 is irrelevant. -Three points.
(1) When a > 0, the value range is, that is, 5 points.
(2) When a < 0, the range is 6 points.
(I) when a > 0, g(x)=3sinx? 4cosx=5sin(x 1)，∴T=2？ ，g(x)max = 5；
When a < 0, g(x)=? 3sinx？ 2cosx= sin(x2)，
∴ T=？ ，g(x)max=。 Eight points.
(2) From the above situation,
When a > 0, g(x)=5sin(x 1), and tan? 1=? , g(x)max=5, then x 1 = 2k? + (k∈Z)。
So x=2k? + 1(k∈Z)，x∈(0，？ ),∴tanx=cot？ 1=? . 10 point
When a<0, the maximum value of g (x) =
To sum up, tan x =-.
20 (the full mark of this question is 13) It is known that the vector m =( 1, 1), the angle between the vector n and the vector m is, and m? I don't know
(1) Find the vector n;
(2) If the angle between vector N and vector a = (1, 0) is, and vector b = (), where A and C are the internal angles of △ABC, and A, B and C are arithmetic progression in turn, try to find the range of | N+B |.
(1) solution: If, by, get-2 points.
∫ The included angle between vector and vector is,
∵∴-4 points.
If the score is ∴ or-6.
(2) Solution: From the perspective of vectors, we can know that
From 2B=A+C, B=, A+C=, 0 < a.
If, then
-10.
When ∫0 < A 1, the inequality holds for a positive integer not less than 2, and the value range of x is found.
Solution: (Ⅰ), f (x) > 1.
Let x =- 1 and y=0, then f (-1) = f (-1) f (0) ∫ f (-1) >1.
∴ f (0) =1....................................... 2 points.
If x > 0, then f (x-x) = f (0) = f (x) f (-x).
Therefore, x ∈ r f (x) > 0 .............................................. 4 points.
Let x 1 < x2.
Therefore, f(x) subtracts the function.
(Ⅱ)①
According to the monotonicity of f(x), an+ 1=an+2, so {an} arithmetic progression.
②
This is an increasing sequence. ..........................................................................................................................................................................
When n≥2,
................... 14 o'clock
that is
And a > 1, ∴ x > 1.
Therefore, the value range of x is (1, +∞) ...................15 points.