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Lanzhou City 20 10 Senior Three Diagnostic Examination Answers Science Mathematics
Reference answer

A, multiple-choice questions (this question *** 12 small questions, each small question 5 points, ***60 points. Only one of the four options given in each question meets the requirements of the topic)

1—5 ccdba 6— 10 bccdd 1 1— 12AD

2. Fill in the blanks (4 small questions in this big question, 5 points for each small question, 20 points for * * *)

13.8

14.33

15.

16.

Third, the solution (this big question ***6 small questions, ***70 points, the answer should be written in the proof process or calculus steps. )

17. Solution:

(1) by,

therefore

A is an acute angle.

2 points

But it can be transformed into

That's five points.

(2) By (1)

and

this is

therefore

If and only if the maximum area is 10 point.

18. Solution:

(1) According to the meaning of the question,

Therefore, it can be divided into:

3 points

therefore

That's five points

The above formula also holds, so 6 points.

(2)

9 points

10 point

12 point

19. Solution:

(1) The survival of each tree is independent of each other, and the survival probability of each tree is

2 points

4 points for the solution

(2) If "need to replant" is event A, then A 1: 3 tree did not survive, A2: 1 tree did not survive, A3? : 5 trees didn't survive, A4: 6 trees didn't survive * * * 4 cases, 5 points.

7 points

8 points

(3) According to the meaning of the question, obey binomial distribution 10.

12 point

Or the distribution list is

0 1 2 3 4 5 6

P

=3

20. Option 1: AD//BC According to the meaning of the question,

therefore

So point m is the midpoint of SD, three points.

(1) Proof: link BD to AC to E, link ME, 4 points.

ABCD is a square, e is the midpoint of BD,

M is the midpoint of SD, and ME is the midline.

I/someone. 5 points

Plane ACM

SB// plane ACM. 6 points

(2) From the perspective of the problem, the plane is sad, so there is

and

Plane SCD

Is the angle formed by the straight line AC and the plane SDC at 8 o'clock.

exist

That is, the angle formed by the straight line AC and the plane SDC is 9 degrees.

(3) plane SCD

The plane angle of dihedral angle n-am-c is 10 minute.

Plane AMN 10 point

All merchant ships

auxiliary power unit

The dihedral angle is 12 minute.

Plane SAC plane AMN 12 point

Solution 2: there is AD//BC according to the meaning of the question, so

So point M is the midpoint of SD, and AM is SD.

As shown in the figure, with a as the coordinate origin,

Establish a spatial rectangular coordinate system,

From SA=AB, let AB=AD=AS= 1,

rule

3 points

(1) connect BD and AC to e,

rule

Plane ACM 6 points

(2) from the problem, the plane is sad, so there is CD AM.

you are

Plane SCD,

Is the normal vector of the plane SCD.

The angle formed by the straight line AC and the plane SDC is 9 degrees.

(3) plane SCD

, again

Plane AMN

Is the normal vector of plane AMN.

Let the normal vector of plane AMC be

rule

that is

Let's order then

that is

The dihedral angle n-am-c is 12 minute.

2 1. Solution: (1) The straight AB equation is:

According to the meaning of the question

5 points for the solution

Elliptic equation 6 points.

(2) suppose there is such a

pass by

Get 8 points

Then ①

set up

Then ②

The only possibility is that

That is, a circle with a diameter of CD passes through the origin O (0 0,0).

That is 10.

but

Substitute type 2 into the whole to understand.

It has been verified that, makes ① hold.

To sum up, there is a point that makes a circle with a diameter of CD pass through the origin O (0 0,0)12.

22. Solution: (1) Order

solve

The monotone decreasing interval of is

Develop a solution

The monotone increasing interval of is 4 points.

(2) If, there is no solution.

When, that is,

When, that is,

Is increasing monotonously in the world,

8 points

(3) according to the meaning of the question: namely

set up

Order (house)

When,,

When,

When the maximum value is obtained,

,

So the range of real numbers is 12 points.

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