Nanjing City, Jiangsu Province in 2009, Grade Three, Grade One Measurement Examination.

Math test questions 2009.3

Reference answer

fill (up) a vacancy

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Second, answer the question.

1`5, (the full mark of this question is 14)

Solution: (1) (Let "players belong to only one team" as event A, then the probability of event A.

(2) If "players belong to at most two teams" is event B, the probability of event B is

Answer: (omitted)

16, (the full mark of this question is 14)

Solution: (1) Lian, quadrilateral rhombus,

Yes, the midpoint,

and

(2) If, at an appropriate time, the intersection point is the midpoint of the median line of the regular triangle, the center of the regular triangle, and the side length of the diamond is, then.

Namely:

17, solution:

( 1)

The range of interval values is

(2) ,

18, solution: (1) According to the meaning of the question, it is:.

The standard equation of parabola is:

(2) Let the center coordinate be and the radius be.

The chord length cut by the center of the circle on the axis is

The equation for the center of the circle is:

Thus become: ①

Equation ① applies to any.

Therefore, there are the following solutions:

Therefore, the circle passes through the fixed point (2,0).

19, when solving (1),

So the tangent point is (1, 2), and the slope of the tangent line is 1.

So the tangent equation of the curve is:.

(2) (1) When,

, and constantly build. In an increasing function.

So when,

(2) When,

( )

(i) When time is instantaneous, it is positive in time, so it is increasing function in interval. So at this time.

(ii) When, that is when is negative and when is positive. So it is a decreasing function in the interval and a increasing function in the field.

So at this time.

(iii) When; That is, it is negative in time, so it is a decreasing function in the interval [1, e], so it is negative in time.

To sum up, when, when and when is the lowest value.

So the minimum value at this time is; At that time, when the minimum value is

And, moreover,

So the minimum value at this time is.

When the minimum value is, when the minimum value is,

So the minimum value at this time is

So the minimum value of this function is

20. Solution: (1) Let the tolerance of the series be, then,

According to the title, Du Heng holds.

That is, it applies to constants.

So, that is: or

, so the value of is 2.

(2)

So,

(1) When it is odd, and,.

Multiply to keep consistent.

(2) When it is an even number,

Multiply like this

, so. Therefore, it is also timely.

So the general formula of the series is.

When it is an even number,

When it is odd, it is even,

therefore

The First Survey and Test of Senior Three in Nanjing in 2009

Reference answers to other math problems

2 1, choose to do the problem.

Elective course: special lecture on geometric proof

Proof: because we cut off O at the point, so

Because, so ... ...

And A, B, C and D are four * * * circles, and so on.

Here we go again, so

this is

That is:

B. Elective Course 4-2: Matrix and Transformation

Solution: set by the problem, let it be any point on a straight line,

Under the corresponding transformation of the matrix,

Yes, that's it.

Because this point is on a straight line, therefore, that is:

So the equation of the curve is

C. Elective courses 4-4; Coordinate system and parametric equation

Solution: the parametric equation of a straight line is a parameter), so the general equation of a straight line is

Because it is any point on the ellipse, it can be set in it.

So the distance from a point to a straight line is

So when, when, get the maximum.

D. Elective Course 4-5: Special Lecture on Inequality

Proof: So

Required questions: Questions 22 and 23 10, * * * 20.

22. Solution: (1) Let the radius of the circle be.

Because the circle is a circle, so

So, that is:

So the trajectory of a point is an ellipse with focus, and let the elliptic equation be one of them, so

So the equation of the curve

(2) Because the straight line passes through the center of the ellipse, we can know from the symmetry of the ellipse,

Because so

Then, you might as well set a point above the axis.

So, that is, the coordinates of the point are or.

So the slope of the straight line is 0, so the sum of squares path of the straight line is 0.

23. (1) When,

The original equation becomes

Lingde

(2) because of this

(1) When? Left =, right

Left = right, the equation holds.

(2) Assuming that the equation holds, i.e.

So, when,

left

It's on the right.

Therefore, when the equation holds.

To sum up ① ②, when,