Seek the answer to the mathematics examination paper of the joint examination of eight schools in Jiangxi Province in 2009!

The first volume (multiple choice questions ***60 points)

I. Multiple-choice questions (this is a small question entitled * *12, with 5 points for each small question and 60 points for each small question. Of the four options given in each question, one and only one is correct)

1. If it is equal to ()

A.B. C. D。

2. Divide the samples with the capacity of n into several groups. If the frequency and frequency of a certain group are known to be 40,0.125 respectively, then the value of n is ().

A.640 B.320 C.240 D. 160

3. {an} is known to be a positive arithmetic progression. If so, the sum of the first 1 1 items of the sequence {an} is ().

A.8 B.44 C.56 D.64

4. The range of the function is ()

A.B. C. D。

5. Let a, b∈R, then "a+b= 1" is the () condition of "4ab≤ 1".

A. Sufficient and unnecessary B. Necessary and insufficient

C. Sufficient conditions D. Conditions that are neither sufficient nor necessary

6. If the function has an extreme point on r, the range of real number A is ().

A.B.

C.D.

7. Let m and n be natural numbers not greater than 6, then the number of hyperbolas represented by the equation is ().

a . 16 b . 15 c . 12d

8. Assuming that the angles formed by two plane vectors are equal, then

= ( )

A.b.6 or C.6 D.6 or

9. If the left focus of hyperbola is F 1, the vertex is A 1, and A2 and P are any points on the right branch of hyperbola, then two circles with line segment diameters of PF 1 and A 1A2 must be ().

A. Intersection B. Internal connection C. External connection C. Separation

10. Let the definition of function f(x) be an even function on R, then the following conclusion is correct ().

A.B.

C.D.

The orthographic view of the 1 1. cube is shown on the right, and its expanded view is ().

12.△ABC, the opposite sides of angles A, B and C are respectively. If the longest side of △ABC is 1, the length of the shortest side is ().

A.B. C. D。

Volume 2 (60 points for non-multiple choice questions * *)

Fill in the blanks (4 points for each small question, *** 16, and the answer is filled in the horizontal line of the answer sheet)

13. If x > 1 and the inequality holds, the range of real number k is.

14. It is known that the term containing x3 in binomial expansion is the fourth term, so the value of n is.

15. There are two places in the circle of 60 north latitude, and their arc length in the latitude circle is the radius of the earth), so the spherical distance between these two places is.

16. If x and y are satisfied, the maximum value of z=x+2y is

Third, answer the question (this big question is ***6 small questions, ***74 points. The solution should be written in words, proving the process or calculation steps. )

17. (The full score of this small question is 12)

In △ABC, let

(1) Verification: △ABC is an isosceles triangle;

(2) if the value range.

18. (The full mark of this question is 12)

known function

(1) If f(x) is an upper increasing function, find the range of the number A;

(2) If x=3 is the extreme point of f(x), find the minimum and maximum value of f(x).

19. (The full score of this small question is 12)

As shown in the figure, in a quadrangular pyramid P-ABCD with a diamond bottom, ∠ ABC = 60, PA=AC=a, PB=PD=, point E is on PD, and PE: ED = 2: 1.

(1) Prove PA⊥ Plane ABCD

(2) Find the dihedral angle θ with AC as the edge and EAC and DAC as the surface;

(3) Is there a point f on the edge PC that makes BE// plane AEC? Prove your conclusion.

20. (The full score of this short question is 12)

Dice is a cube with uniform quality, and its six faces are engraved with 1, 2, 3, 4, 5 and 6 points respectively. Now there are three dice made of wood, bone and plastic on the table. Repeat the following operation until there are no dice on the table: throw all the dice on the table, and then remove those odd dice.

(1) Find the probability of completing the above operations twice;

(2) Find the probability of completing the above operations for more than three times.

2 1. (The full score of this small question is 12)

The sum of the first n terms of the series {an} whose known terms are all positive numbers is Sn, and the first term is a 1, which becomes arithmetic progression.

(1) Find the general term formula of sequence {an};

(2) If

22. (The full score of this short question is 14)

It is known that the left and right foci of an ellipse are F 1, F2, the right vertex is a, and p is any point on the ellipse C 1. Let hyperbola C2 take the focus of ellipse C 1 as the vertex and the vertex as the focus, and b be any point of hyperbola C2 in the first quadrant, and

(1), find the eccentricity of ellipse;

(2) If the eccentricity of ellipse holds.

The entrance examination of senior three in eight schools in Jiangxi Province.

Reference answers to mathematics (literature) examination questions

First, multiple-choice questions (5 points for each question, ***60 points)

The title is123455678911112.

The answers are BBB, BBA, BBA, BBA, BBA.

Second, fill in the blanks

13. 14.9 15. 16.⑦

Third, answer questions.

17.( 1) Because

So |AB|=|BC|, so △ABC is an isosceles triangle. (6 points)

(2) because,

18. Solution: (i) If increasing function is on it, then there is.

And (if and only if x= 1, take the equal sign), so a≤3(6 points).

(2) If the root of = 3x2-2ax+3 = 0 is x=3, a=5 can be obtained.

So the root of = 3x2- 10x+3 = 0 is x=3 or x= (truncation), and f (1) =- 1.

On F (3) =-9, f(5)= 15, x ∈ [1, 5] ∴f(x) has a minimum value of f (3) =-9 and a maximum value of f (5) =1.

19. Proof: Because the bottom ABCD is a diamond, ∠ ABC = 60, AB=AD=AC=a, in △PAB,

From PA2+AB2=2a2=PB2, we can know that PA⊥AB.

Similarly, PA⊥AD, so PA⊥ plane ABCD. (3 points)

(II) EG//PA and AD in g,

Take PA⊥ plane ABCD.

Know the EG⊥ plane ABCD. Let GH⊥AC be in H, connect, er,

Then EH⊥AC and ∠EHG are the plane angles of dihedral angle θ.

And PE: ed = 2: 1,

(III) Solution 1 Take A as the coordinate origin, straight lines AD and AP as the Y axis and Z axis respectively, and the straight line passing through point A perpendicular to the plane PAD as the X axis, thus establishing a spatial rectangular coordinate system, as shown in the figure. The coordinates of the relevant points are as follows.

A(0，0，0)，B( a，- a，0)，C( a，a，0)。

D(0，a，0)，P(0，0，a)，。

Let point f be a point on the edge PC, then

、

That is, when f is the midpoint of PC, * * * plane.

And BF plane AEC, so when f is the midpoint of the edge PC, BF// plane AEC. (12).

Solution 2 When f is the midpoint of the edge PC, the BF// plane AEC is proved as follows.

The first proof is to take the midpoint m of PE, then FM, and then FM//CE. ①.

E is the midpoint of MD.

Connect BM and BD, let BD∩AC=O, then O is the midpoint of BD.

So BM//OE. ②

According to ① and ②, plane BFM// plane AEC.