I. Multiple-choice questions: This big question is a * *12 small question, with 5 points for each small question and 60 points for * * *. Only one of the four options given in each question meets the requirements of the question. Jin Hao succeeded.
1. (rational) If the set m = {z | z =1-(1-i1+i) 4n, n ∈ n}, then the set m is equal to ().
A.? B.{0} C. {0,2} D. {2}
If the set m = {(x, y) | x2+y2 ≤ 0, x, y ∈ r}, then the set m is equal to ().
A.? B.{0} C. {(0 (0,0)} D. {0,0} Made in Jin Hao.
2. In the regular triangle ABC with the side length of 1, if the vectors Ba→ = a and BC→ = b, then | a+b | = ().
A.7 B. 5 C. 3 D.2
3. If Proposition A: A, B and C are arithmetic progression; Proposition B: Ma+P, MB+P and MC+P are arithmetic progression, where M and P are constants, then A is B ().
A. Sufficient and unnecessary B. Necessary and insufficient D. Necessary and sufficient conditions D. Neither sufficient nor necessary
4. Given acute angles α and β, and satisfying SIN α = 12sin (α+β), the correct relationship between α and β is ().
A.α& gt; βb .α& lt; β C. α=β D. α≥β
5. It is known that the straight line MX+3y-4 = 0 and the circle (x+2) 2+y2 = 5 intersect at points A and B. If |AB|=2, the value of m is
() A.52B.54C.52D.0, 54C
6. The function y = cos 2 (x-π12)+sin 2 (x+π12)-1is ().
A. odd function with a period of 2π B. Even function with a period of π C. odd function with a period of π D. Even function with a period of 2π.
7. If straight lines A and B make an angle of 60 with plane α, and A and α, B? α, then the range of the angle θ formed by A and B is ()
A.B. C. D。
(text) inequality1-3 | x | x >; The solution set of 0 is ()
A.(0, 13)∩(-∞,- 13) B. (- 13,0)∩( 13,+∞) C.( - 13, 13) D. (-∞,- 13)
Fill in the blanks (the full mark of this question is 16, 4 points for each small question, and ***4 small questions. Please fill in the answer directly in the line after the question)
13. If (2x-3) 6 = A0+a1(x-1)+A2 (x-1) 2+…+A6 (x-1) 6, then A66.
14. If the function y=f(x) defined on R has an inverse function, the images of the functions y = f (x+a)+b and y = f- 1 (x+a)+b are symmetric about the straight line _ _ _ _ _ _ _. Jin Hao succeeded.
15. the straight line l passes through the parabola y2 = 2px(p & gt;; 0), which intersects with the parabola at two points, P and Q. Draw vertical lines PR and QS from P and Q to the alignment respectively, and set feet R and S. If | PF | = A and | QF | = B, then | RS | = _ _ _ _ _ _ _ _
16. There is an irregular hexahedral box (six faces are of different sizes). Now we need to paint the six sides of the box red, yellow and blue, one color has three sides, the other color has two sides, and the other color is 1 side. There is _ _ _ _ _ _ _ _ _ _ _ _
Third, answer questions (this big question * * 6 small questions, ***74 points. The solution should be written in words, deduction steps or calculation process)
17.( 12 point) The known plane vectors OA → = (1 7), OB → = (5, 1), OP → = (2, 1), and point M is the moving point on the straight line OP. The coordinates of MB→ OM→ when the minimum value is taken.
18.( 12 minutes) As shown in the figure, in the planar quadrilateral ABCD, AB = BC = CD = A, ∠ B = 90, ∠ BCD = 135, and the quadrilateral is folded into a straight dihedral angle along the diagonal AC. Jin Hao succeeded.
(1) Verification: AB⊥ Plane bcd
(2) Find the included angle between plane ABD and plane ACD.
19.( 12 points) (rational) The known series {an} and {bn} satisfy: a 1= 1, a2=a (a is a constant), bn=an? an+ 1(n= 1,2,3,…)。
(1) If {an} is a geometric series, find the sum sn of the series {bn} and the first n terms;
(2) When {bn} is a geometric series, classmate A said: {an} must be a geometric series; Student B said: {an} must not be a geometric series. Do you think their statement is correct? Why?
(Text) The first term a 1= 1 of the geometric series {an} is known, and the sequence {bn} satisfies the first term b 1=a (a is a constant).
And bn= an? an+ 1(n= 1,2,3,…)。
(1) formula for finding the general term of series {an}; Made in Jin Hao
(2) Find the first n terms of the sequence {bn} and Sn (written as an expression about n).
20.( 12 points) One rule of the "Pass Game" stipulates that the dice must be thrown n times in the nth pass, and if the sum of the points thrown n times is greater than 2n- 1+ 1 (n ∈ n *), it is considered as a pass.
(1) What is the probability of this game getting through the third level?
(2) (Reason) If n≤3 is specified, ask someone's expectation for the number of customs clearance.
Find the probability that someone will only pass the first level.
2 1.( 12 minutes) It is known that the function f (x) = x4-4x3+AX2- 1 decreases monotonically in the interval.
(1) Find the value of a; Jin Hao's Works
(2) It is proved that the image of f(x) is symmetric about x= 1;
(3) Is there a real number b, so that the image of the function g (x) = bx2- 1 and the image of the function f(x) have exactly three intersections? If it exists, request the range of real number b; If it does not exist, please explain why.
22.( 14 point) In the plane rectangular coordinate system, O is the coordinate origin, given two points A( 1 0) and B (0,2), point C satisfies.
OC→ = α OA→+β OB→, where α, β∈R, α 2+β 2 = 1.
(1) Find the trajectory equation of point C; Made in Jin Hao
(2) The straight line L passing through point D (2,0) and the trajectory of point C intersect at two different points M and N, and M is between D and N, remember.
λ λ λ= |DM→||DN→|, and find the range of λ.