1. If the complete set U={ 1, 2,3,4,5}, the set M = {1, 2,3} and n = {3 3,4,5}, then m ∩ (UN) = ().

A.{ 1，2} B.{4，5} C.{3} D.{ 1，2，3，4，5}

2. The imaginary part of the complex number z=i2( 1+i) is ().

A. 1 BC-1 BC

3. If the positive sequence {an} is proportional, a 1+a2=3 and a3+a4= 12, then the value of a4+a5 is ().

A.-24 B. 2 1 C. 24 D. 48

4. An assembly is front in three views and square in front view.

The side length is 2, and the top view is a regular triangle and an inscribed circle.

Then the combined volume is ()

A.2 B。

C.2+ D。

5. If a hyperbola focuses on two vertices of a square and the other two vertices are on the hyperbola, then its eccentricity is ().

A.2b+ 1 c . d . 1

6. In quadrilateral ABCD, "=2" means "quadrilateral ABCD is trapezoidal" ().

A. sufficient and unnecessary conditions B. necessary and insufficient conditions C. necessary and sufficient conditions D. neither sufficient nor necessary conditions

7. Let p take a random value, and the probability that the equation x2+px+ 1=0 has a real root is ().

A.0.2 B. 0.4 C. 0.5 D. 0.6

8. The known function f (x) = asin (ω x+φ) (x ∈ r, a >；; 0，ω& gt； 0，|φ| & lt； )

The image (part) of is shown in the figure, then the analytical formula of f(x) is ()

A.f(x)=5sin(x+) B.f(x)=5sin(x-)

C.f(x)=5sin(x+) D.f(x)=5sin(x-)

Fill in the blanks: (5 points for each small question, * * * 30 points)

9. Lines corresponding to Y = kX+1 and A( 1, 0) and B( 1,1) are common.

* * * point, then the value range of k is _ _ _ _ _.

10. The coefficient of the m term in the record expansion is, if, then = _ _ _ _ _ _ _

1 1. Let the four zeros of the function be, then;

12, let a vector, if the vector and the vector * * * line, then

1 1 ..

14. for any real numbers x and y, define the operation x*y=ax+by+cxy, where

A, B and C are constant real numbers, and the operation on the right side of the equal sign is the addition in the usual sense.

Multiplication operation. It is known that 2* 1=3, 2*3=4, and there is a nonzero real number m,

So for any real number x, there is x*m=2x, then m=.

Third, answer questions:

15. (The score of this question is 10) Known vector =(sin(+x), cosx), = (sinx, cosx), f (x) =.

(1) Find the minimum positive period and monotone increasing interval of f(x);

⑵ If f(A)= is satisfied in triangle ABC, find the value of angle A. 。

16. (This title is 10) as shown in the figure: straight triangular prism (side ⊥ bottom) ABC-a1b1c1,

∠ ACB = 90, AA 1=AC= 1, BC=, CD⊥AB, and the vertical foot is D.

(1) Verification: BC∑ plane AB1c1;

⑵ Find the distance from B 1 point to A 1CD surface.

17. (This title is 10) The travel company provides five tour routes for four tour groups, and each tour group can choose one of them.

(1) How many ways can four tour groups choose different routes?

(2) Find out the probability of choosing just two lines;

(3) Find the mathematical expectation of choosing the number of A-line tour groups.

18. (The score of this question is 10) The sequence {an} satisfies a1+2a2+22a3+…+2n-1an = 4n.

(1) Find the general term an;

⑵ Find the first n terms of series {an} and Sn.

19. (The score of this question is 12) The function f(x)=alnx+bx, and f( 1)=-1, and f'( 1)=0.

(1) Find f (x);

(2) Find the maximum value of f(x);

(3) If x>0, y>0, it is proved that: lnx+lny≤

20. (this question 14 points) is set as the left focus and the right focus of the ellipse respectively. If the sum of the distances from point A( 1,) to F 1 and F2 on ellipse C is equal to 4.

(1) Write the equation and focus coordinates of ellipse C;

⑵ The straight line passing through point P( 1,) intersects the ellipse at two points D and E. If DP=PE, find the equation of straight line d E;

⑶ The straight line passing through point Q (1, 0) intersects the ellipse at two points M and N. If the area of △OMN is the largest, the equation of straight line MN is found.

2 1. (This is called 14) For any positive real number a 1, a2, …, an;

Verification1/a1+2/(a1+a2)+…+n/(a1+a2+…+an)

Answers to 09 Senior Three Mathematical Simulation Test Questions

First, multiple choice questions:. ACCD bada

Fill in the blanks: This question mainly examines the basic knowledge and basic operation. 4 points for each small question, *** 16 points.

9. 10.5 1 1. 19 12.2 13. 14.3

Third, answer questions:

15. This topic examines the formulas and properties of vector, double angle and composite trigonometric functions, and requires students to use what they have learned to solve problems.

Solution: (1) f (x) = sinxcosx++cos2x = sin (2x+)+ ...

T=π，2 kπ-≤2x+≤2 kπ+，k∈Z，

Minimum positive period is π, monotonically increasing interval [kπ-, kπ+], k ∈ z. .....................

(2) by sin (2a+) = 0,

∴2A+=π or 2π, ∴A= or ...............

16. This topic mainly examines the position relationship of spatial lines, lines and planes, the calculation of spatial distance angle, the ability of spatial imagination, reasoning and demonstration, and the ability of students to flexibly use graphics, establish spatial rectangular coordinate system and solve problems with vector tools.

(1) proves that BC∑b 1b 1 of straight prism ABC-a1,

BC plane A B 1C 1, b1c/plane aB 1C 1, ∴B 1C 1∥. ………………

(2) (Solution 1) ∵CD⊥AB and ABB 1A 1⊥ plane AB C plane,

∴CD⊥ Aircraft ABB 1A 1, ∴CD⊥AD and CD⊥A 1D,

∴∠A 1DA is the plane angle of dihedral angle a1-cd-a,

At Rt△ABC, AC= 1, BC=,

∴AB= and ∴AC2=AD×AB. CD⊥AB

∴ad=,aa 1= 1,∴∠da 1b 1=∠a 1da=60，∠a 1b 1a = 30 ,∴ab 1⊥a 1d

And CD⊥A 1D, ∴AB 1⊥ plane A 1CD, let A 1d ∩ AB 1 = p, ∴ b/kloc.

b 1P = a 1b 1cos∠a 1b 1A = cos 30 =。

That is to say, the distance from the point to the surface is ...........................................

(2) (Solution 2) By VB1-a1CD = VC-a1b1d =×× =, and cos∠A 1CD=×=,

S△A 1CD=×××=, let the distance from B 1 to plane A 1CD be h, then× h=, h = is what we want.

(3) (Solution 3) Take the straight lines of CA, CB, CC 1 as the X, Y and Z axes respectively (as shown in the figure), then A (1, 0,0), A 1 (1, 0/kloc-0.

C(0，0，0)，C 1(0，0， 1)，

B(0，，0)，B 1(0，， 1)，

∴D (,0)=(0, 1), let the normal vector of the plane A 1CD =(x, y, z), then

，take =( 1，- 1)

The distance from the point to the surface is d = ..............................

17. This topic mainly examines the basic knowledge and basic operation ability of permutation, the probability calculation of typical discrete random variables, and the distribution table and expectation of discrete random variables.

Solution: (1) There are: A54= 120 ways for four tour groups to choose different routes. …

(2) The probability that only two lines are selected is: P2= …

(3) Let the number of tour groups in Route A be ξ, then ξ ~ b (4,)

∴ Expected E ξ = NP = 4× = ...................

Answer: (1) There are 120 kinds of lines * * *, (2) The probability that just two lines are selected is 0.224, and (3) The expected number is 0.8. ..................

18. This question mainly examines the basic knowledge of series, the mathematical thought of classified discussion and the ability of candidates to creatively solve problems by comprehensively applying what they have learned.

Solution: (1) a1+2a2+22a3+…+2n-1an = 4n,

∴ a1+2a2+22a3+…+2nan+1= 4n+1= 3x4n, ∴ an+1= 3x4n.

When n= 1, a 1=4, ∴ to sum up, an= what you want; ………………………

(2) When n ≥ 2, Sn=4+3(2n-2), and when n= 1, S 1=4 also holds.

∴ Sn = 3× 2 N-2 .............................................................................................................................................................

19. This topic mainly examines the basic knowledge of functions and derivatives, the treatment of function properties and the synthesis of inequalities, and also examines the ability of candidates to prove inequalities with scale functions.

Solution: (1) is given by b = f (1) =- 1, f'( 1)= a+b = 0, ∴ a = 1, ∴ f (. ……………

⑵∫x & gt； 0，f′(x)=- 1 =，

x

0 & ltx & lt 1

x= 1

x & gt 1

f′(x)

+

-

f(x)

↗

maximum

↘

∴f(x) obtains the maximum value of-1 at x= 1, that is, the maximum value is-1; ……………

(3) lnx≤x- 1 is a constant from (2),

∴lnx+lny=+≤+= holds. ...

20. This topic examines the basic ideas and methods of analytic geometry. The solution method of curve equation and curve properties requires candidates to correctly analyze the problem and find a better solution direction. At the same time, we should give consideration to the ability of arithmetic and logical reasoning, and require the rational evolution of algebra and the correct analysis of the maximum problem.

Solution: (1) The focus of ellipse C is on the X axis.

The sum of the distances from point A to point F 1 and F2 on the ellipse is 4, and 2a=4, that is, a = 2.

Point A( 1,) is on the ellipse, so b2= 1, so C2 = 3；;

So the equation for ellipse c is, ...

⑵ p is in the ellipse, ⑵ the straight line DE intersects the ellipse,

∴ Substitute d (x 1, y 1) and e (x2, y2) into the equation of ellipse C to get.

X 12+4Y 12-4 = 0, x22+4y22-4 = 0,2 (x1-x2)+4× 2× (y1-y2) = 0, and the slope is k.

∴DE equation is y- 1=-1(x-), that is, 4x+4y = 5；; ………

(3) The straight line MN is not perpendicular to the Y axis, ∴ Let the MN equation be my=x- 1, and substitute it into the equation of ellipse C.

(m2+4)y2+2my-3=0, let M(x 1, y 1), N(x2, y2), then y 1+y2=-, y 1y2=-, and △ 0 has been created.

S△OMN=|y 1-y2|=×=, let t=≥, then

S△OMN=，(t+)′= 1-t-2 & gt； 0 holds for t≥ constant, t+ takes the minimum value, and S△OMN takes the maximum value. When t = ∴., it is expected to be adopted.