20 10 mathematical answer of the second mode in Haidian district

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Haidian district senior three second semester final exercise.

Mathematics (science)

Reference answer and grading standard 20 10.5

Note: Reasonable answers may be scored as appropriate, but shall not exceed the original score.

The first volume (multiple choice questions ***40 points)

First, multiple-choice questions (this big question is ***8 small questions, each with 5 points and ***40 points)

Title 1 2 3 4 5 6 7 8

Answer B A D C A B A D

Volume 2 (multiple choice questions * * 1 10)

2. Fill in the blanks (this big question is ***6 small questions, with 5 points for each small question, there are two empty small questions, 3 points for the first empty question, 2 points for the second empty question, and 30 points for * * *).

9. 1 10. 1 1.2 ; 12.48 13.

14. [Source: Xue+Ke+Net Z+X+X+K]

; 84.

Third, answer the question (this big question is ***6 small questions, ***80 points)

15. (The full score of this small question is 13)

Solution: (i) Let the tolerance of arithmetic progression be d,

Available, .......................... 2 points.

That is to say,

Solution, 4 points.

∴ ,

Therefore, arithmetic progression's general formula is .............................. 5 points.

(ii) According to the meaning of the question,

∴

, ... 7 points.

Again, 9 points.

Subtract the two formulas to get …11.

, .................... 12.

∴ .....................13.

16. (The full score of this small question is 14)

(a) proof: link delivery, link,

, .............. 1 point

, ……………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

............... 4 points [Source: Zxxk.Com]

(2) As shown in the figure, establish a spatial rectangular coordinate system with the origin,

Then,,,,

, , ,

Five points.

Seven points

The cosine of the angle formed by a straight line on different planes is 8 points.

(iii) side edges,

, ... 9 points.

Try to vector to,

And, moreover,

, make,,

The normal vector is 1 1.

, .................... 13.

It can be seen from the figure that the dihedral angle is acute,

The cosine of dihedral angle is 14 point.

17. (The full score of this small question is 13)

Solution: (I) Let "four people just chose the same park" as event A. .....................................................................................................................................................

Each volunteer has three choices, and the choice of four volunteers is * * * possible ................... 2 points.

The number of equal possible events contained in event A is 3, and

So ...

In other words, the probability that four people choose the same park is .................................................................................................................................................................

(ii) If "Volunteers choose Park A" as Event C, score 6 points.

The number of people who choose Park A among four people can be regarded as the number of events C in four independent repeated trials, so the random variable obeys binomial distribution.

Acceptable values are 0, 1, 2, 3, 4 ................................................... 8 points.

, ...................... 10.

The distribution list is:

0 1 2 3 4

........................ 12.

The expectation is .................. 13.

18. (The full score of this small question is 13)

Solution 1: (I) It depends on the meaning of the problem, so .................................................. 1 min.

Made, obtained, .............................. 2 points.

, with the change of x into the table below:

- 0 + 0 -

minimum value

maximum

.............................., 4 points.

As can be seen from the above table, it is the minimum point and maximum point of the function.

Five points.

(2) ......................................... scored 6 points.

According to the monotone decreasing function in the interval, it is known that it holds true for any constant, [source: Xue+Ke+Net Z+X+X+K]

...................................., seven.

When, obviously, for any constant; .............................., eight.

When, equivalent to,

Because inequality is equivalent to,

.................................., 9 points.

Orders,

Then, there is obviously a constant in the world, so the function is monotonically increasing.

Therefore, the minimum value on the scale is ........................................... 1 1 min.

Because the truth value of any constant is equivalent to the truth value of any constant,

Need and only need, that is, solve, because, therefore.

To sum up, if the function monotonically decreases in the interval, the range of real number A is.

........................ 13.

Solution 2: (1) Same as solution 1

(2) ......................................... scored 6 points.

According to the monotonic decrease of the function in the interval, it can be known that for any constant,

That is, it applies to any constant.

When, obviously, for any constant; …………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………………

The symmetry axis of the function image is,

.................................., 9 points.

If, that is, the function is monotonically increasing, it is necessary for any constant and only needs to be solved, so; ...................... 1 1 min.

If, that is, the image of a function is continuous, if it holds for any constant, there are solutions and contradictions, so it does not hold for any constant.

To sum up, if the function monotonically decreases in the interval, the range of real number A is. [Source: Subject Network]

........................ 13.

19. (The full mark of this short answer is 13)

Solution: (1) From the meaning of the question, the equation of parabola is: .........

(2) Let the linear equation be:

At the same time, cancellation, gain,

..........................., 3 points.

Obviously, suppose,

Then ①

② ................................. 4 points.

Again, so ③ ........................... scored 5 points.

Remove from ① ② ③ to obtain,

Therefore, the equation of the straight line is or ................................. 6 points.

(iii) If, then the midpoint is, because two points are symmetrical about a straight line,

So, in other words, if you get a solution, 8 points.

Substituting it into the parabolic equation, we get:

So, ...................................... scored 9 points.

Simultaneous, elimination, get:

........................ 10.

By, by

That is 12 points.

Substitute the above formula and simplify it, and get

So, that is to say,

Therefore, the minimum length of the long axis of an ellipse is ......................... 13.

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

Solution: (1) From the meaning of the question:

, ............................... 1 min.

................................., two points.

(2), ... 3 points.

, 4 points.

When,,;

When,;

When. [Source: Zxxk.Com]

To sum up, ……………………………………………………………………………………………………………………….

In other words, it exists, which makes it a contraction function of order 4. ...........................................................................................................................................................

(iii) Order or.

The function changes as follows:

8 points for orders, solutions or 3 ..........................

When I), it increases monotonously in the world, so,,.

Because it is a second-order contraction function,

Therefore, ① identity is established;

(2) Existence, which makes it true .......................................... 9 points.

(1) that is, the opposition is real,

From, to: or,

The establishment of Du Heng is necessary and the only necessary ........................... 10.

(2) In other words, existence makes it true.

From: or,