Description:

This volume is divided into Volume A and Volume B: Volume A consists of 22 questions in this volume, namely 10 multiple-choice questions, 7 fill-in-the-blank questions, 3 solution questions and 2 additional questions; Volume B consists of the first 20 questions in this paper, namely 10 multiple-choice questions, 7 fill-in-the-blank questions and 3 solution questions.

First, multiple-choice questions (this big question * * has 10 small questions, and each question has only one correct answer. Fill in the serial number of the correct answer in the brackets after the dry question. Multiple choices, no choices, and wrong choices will not be scored, with 5 points for each question and * * * 50 points).

1. The value of the simplified triangular rational formula is ()

A. BC 1

2. If is, it is ()

A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions

C. Necessary and sufficient conditions D. It is neither a sufficient condition nor a necessary condition

3. Let P={}, then the set is ().

A.B.

C.D.

4. Set two mutually perpendicular unit vectors. It is known that =, =, = r+K. If △PQR is an equilateral triangle, then the values of k and r are ().

A.B.

C.D.

5. In the triangular prism ABC-a1b1,if AB= BB 1, the angle between CA 1 and C 1B is ().

A.60 B.75 C.90 D. 105

6. Assuming that arithmetic progression and geometric progression are respectively, the following conclusion is correct ().

A.B. C. D。

7. If the term with the largest coefficient in the binomial expansion of is ()

A. Item 8 B. Item 9

C. Projects 8 and 9 D. Project 1 1

8. If,, then the following relationship is correct ()

A.B.

C.D.

9. The following is a three-dimensional view, so the volume of the three-dimensional is ()

A.B. C. D。

10. The algorithm is as follows:

If the input is A = 144 and B = 39, the output result is ().

A. 144 B.3 C. 0 D. 12

Fill in the blanks (this big question * * *, a total of 7 small questions, fill in the correct answer on the horizontal line after the dry question, 7 points for each blank, 49 points for * * *).

1 1. All real number solutions satisfying the equation are.

12. The minimum positive period of the function is.

13. Let p be a fixed point on the circle, and the coordinates of point A are. When p moves on a circle, the trajectory equation of the point m in the line segment PA is.

14. Suppose there is a point d on the side BC of the acute triangle ABC, let AD divide △ABC into two isosceles triangles, and try to find the range of the minimum internal angle of △ABC.

15. Let z be an imaginary number and the range of the real part of z is.

16. Settings. If so, then the minimum value of k is.

17. Settings. When the zero point of the function is greater than 1, the maximum value in the closed interval with its minimum zero point and maximum zero point as endpoints is.

Third, answer the question (this big question has three small questions, each 17 points, ***5 1 points)

18. Set series,

Q: (1) What is the value of item 20 10 in this series?

(2) In this series, what is the serial number of item 20 1 0 with the value of1?

19. There are 10 red, black and white balls. Now put them all in two bags, A and B. It is required that there are three colored balls in each bag, and the products of the three colored balls in the two bags are equal. How many ways to ask * * *?

20. An ellipse is known, with (0, 1) as the right vertex, and the AB side and BC side intersect with the ellipse at two points B and C. If the maximum value of △ABC area is, then.

Fourth, additional questions: (This big question has two small questions, each with 25 points and ***50 points. )

2 1. Let d, e and f be points on three sides BC, CA and AB of △ABC respectively. Remember. Prove:

22.( 1) Suppose a point on a plane is called a grid point if its coordinates are integers. A curve intersects with grid points (n, m), and the number of grid points on the corresponding curve segment is n. Prove:

.

(2) Let a be a positive integer and prove that:

.

(Note indicates the largest integer not exceeding x)

Reference answer

1. the answer is a.

.

You can also use the special value method.

2. The answer is that B.P. holds, so P holds, and it cannot be inferred that Q must hold.

3. answer: D. draw the number axis, which can be obtained from the geometric meaning of the absolute value.

.

4. answer. C.

Namely.

5. Answer: C. Establish a spatial rectangular coordinate system with a straight line as the axis, a straight line perpendicular to the plane as the axis, and a straight line as the axis. rule

, 。

6. answer: a.

.

7. Answer: D, r= 10, and item 1 1 is the largest.

8. Answer: D. The function is an even function, and it is a decreasing function on (0,), and,

, so.

9. Answer: C. According to the meaning of the question, the stereogram is a combination of a cylinder and a 1/4 ball.

10. Answer B (1)A= 144, B=39, C = 27: (2) A = 39, B=27, C = 12: (3) A = 27. So A=3.

Fill in the blanks (this big question * * *, a total of 7 small questions, fill in the correct answer on the horizontal line after the dry question, 7 points for each blank, 49 points for * * *).

1 1.。

Solve deformation, solve

.

12.。

Answer.

13.。

Let the coordinates of m be

Because point p is on a circle, the trajectory of point p is.

14.30x & lt45 or 22.5

The answer is shown in the figure, (1) ad = AC = BD; (2)DC=AC，AD=BD .

In (1), let the minimum angle be x, then 2x < 90, x.

In (2), let the smallest angle be x and then 3x.

15.。

Solution settings

When there is no solution; When?

16.。

explain

Molecules, so the minimum value of k is 0.

17.0 or q.

Because the function is an even function, we can know from the symmetry and the image that the minimum value of 0 and the maximum value of 0 are the maximum value of 0 or q in the closed interval.

Third, answer the question (this big question has three small questions, each 17 points, ***5 1 points)

18. solution (1) grouping series:

Because1+2+3+…+62 =1953; 1+2+3+…+63=20 16,

Therefore, item 20 10 of the series belongs to the penultimate number of the 63rd group, namely. -10 point

(2) From the above grouping, we can know that there is a 1 in every odd array, so the 20th 1 0 1 appears in the 40 19 group, and the1in the 40th19 group is located at 20/kloc. -17 points.

19. Solution: If the number of red, black and white balls in a bag is 0, then there are, and

(* 1)

-Five points.

Have it at once

. (*2)

So there is. So, one of them has to get 5. Let's assume that by substituting (* 1), we get

. -10.

At this time, you can take y as 1, 2, …, 8, 9 (correspondingly, take z as 9, 8, …, 2, 1) and use the method of ***9. Similarly, when y=5 or z=5, there are nine ways to put them, but sometimes the two ways will be repeated. So, * * * is available.

9× 3-2 = 25 playback modes. -17 points.

20. solution: let's set the equation, then the equation is.

Author:

Author:

So there is

-Five points.

So ...

Order, own

-10 point

Because time is equal to the number.

So when-14 points.

manufacture

-17 points.

Fourth, additional questions: (This big question has two small questions, each with 25 points and ***50 points. )

2 1. The certification score is-5.

. -10.

So,

= 。 -20 points

Therefore, if and only if d and c coincide, the equal sign holds.

Or e coincides with a, or f coincides with b -25 points.

22. It is proved that (1) considers the region, and the number of grid points on this region is nm.

This area consists of area e:

And region f:

On the region e, the grid points on the straight line segment are,

So the number of grid points on the area e is 0. -Five points.

Similarly, the number of lattice points on the region f is. -10.

According to the principle of exclusion,-15 points.

(2) When a is a positive integer, all points () on the curve are lattice points, so N=n in (1). At the same time, substitute the above data into (1).

. -25 points.