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20 12 Pudong New Area College Entrance Examination Forecast

Key Points and Grading Criteria of Answers in Mathematics Examination Paper (Liberal Arts)

1. Fill in the blanks (the full score of this big question is 56) * * There are 14 questions in this big question. Candidates should directly fill the scores in the numbered spaces on the answer sheet, and get 4 points for each blank space, otherwise get 0 points.

The focal coordinate of 1. parabola is _ _ _ _ _ _ _ _.

2. Complex number (where it is imaginary unit), then = _ _ _ _ _ _

3.。

4. The projection of the vector in the vector direction is _ _ _ _ .3

5. If set, set and then =__0 or 1_.

6. Given the surface area ratio of three balls, the volume ratio of these three balls is _ _ _ _ _.

7. In delta, if,,, then.

8. If the real number is known and the inequality group is satisfied, the maximum value of is _ _ _ .20.

9. Two travelers A and B experience city life, get on the same train from one subway station and get off at a random subway station in front of 10, so the probability that they will not get off at the same station is _ _ _ _ _ _ _.

10. Execute the program block diagram on the right. If the input n is 4, the output p = _ _ _ .3.

1 1. If a line and a curve have two intersections, the range of real numbers is _ _.

12. Given the sequence, the first term, if the root and quadratic equation are satisfied, then the first n terms of the sequence are sum.

13. The domain of a known function is that if there is a constant, if there is, this function is called a function. The following functions are given: ①; ②; ③; ④ The serial number of the function is. (Answer: ② ④)

14. The development of the mobile phone industry gave birth to the new word "beauty" on the Internet. A student is going to make its corresponding image on the computer, as shown in the figure. When students form line segment AB, they hope to transform the image of the function properly and get the function curve. Please write the resolution function corresponding to curve segment AB.

Second, multiple-choice questions (the full score of this big question is 20) This big question has four questions, and each question has one and only one correct answer. Candidates should black out the small squares representing the answers on the corresponding numbers on the answer sheet, and get 5 points for choosing the right one, otherwise get 0 points.

15. As we all know, the non-zero vector "function is even function" is "(c)".

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

C. Sufficient conditions are neither sufficient nor necessary.

16. Let sum be a complex number, and the following propositions must be true: () d.

A. If, then B. If, then

C. If, is a positive real number, then D. If, is a positive real number, then

17. If hyperbola and hyperbola have the same focus, the following four conclusions are given:

①; ②;

③; ④;

All the correct conclusions are numbered () B.

A.①② B、①③ C、②③ D、①④

18. If the function is known and the number of roots satisfying the equation is () c.

a，0 b，2 c，4 d，6

Three. Answer the question (the full score of this big question is 74 points). There are 5 questions in this big question. To solve the following problems, you must write down the necessary steps in the area designated by the corresponding number on the answer sheet.

19. (The full score of this question is 12) There are two small questions in this question. The full score of the first 1 question is 6, and the full score of the second one is 6.

Known function,

(1) Find the monotone increasing interval of the function;

(2) After translating the function image to the right, the image of the function is obtained and the solution of the equation is obtained.

Solution (1),

Author:

Monotonic increasing interval of is;

(2) As we all know,

By, by,

20. (The full score of this question is 14) There are two small questions in this question. The full score of the first 1 question is 6, and the full score of the second one is 8.

As shown in the figure, in a quadrangular pyramid, the bottom is a square, and and are the midpoint respectively.

(1) Find the angle formed by a straight line on a different plane;

(2) At that time, find the volume of the four pyramids.

The solution (1) ∵ is the midpoint respectively.

∴.

∴ is the angle or complementary angle formed by a straight line on different planes.

Bottom surface,

∴ is an isosceles right triangle,

∴,

The angle formed by straight lines on different planes is.

⑵ Solution: From ⑵ and ⑵, we can know.

From the meaning of the question, it is an isosceles right triangle.

This point is also the midpoint, and the distance from this point to the bottom is.

The volume of the pyramid is.

2 1. (The full score of this big question is 14) This big question * * has three small questions, and the full score of 1 small question is 4, the full score of the second small question is 5 and the full score of the third small question is 5.

It is known that the left focus and the right focus of an ellipse are respectively that one endpoint of the major axis and two endpoints of the minor axis form three vertices of an equilateral triangle. A straight line passes through a point at an oblique angle and intersects an ellipse at two points.

(1) If, find the elliptic equation;

(2) Find the area of the ellipse in (1);

(3) is any point on the ellipse. If there is a real number, try to determine the relationship.

The answer (1) consists of known, available,

∵,∴,,

∴.

(2) Let, a straight line,

Substitute into elliptic equation,,,

∴.

(3) From the known elliptic equation ①,

The coordinates of the right focus are,

The linear equation is ②,

From ① ②:,

Suppose, then,,,

Set, get,

The point is on the ellipse,

∴,

Tidy up,

③,

And the point is on the ellipse, so ④, ⑤,

From ③ ④ ⑤ type.

22. (The full score of this big question is 16) This big question * * * has three small questions, and the full score of 1 small question is 4, the full score of the second small question is 6, and the full score of the third small question is 6.

Remember that the sum of the previous paragraph of the sequence is. The sum of known vectors is satisfied.

(1) Find the general term formula of the sequence;

(2) seeking;

(3) Set and find the sum of the first paragraphs of the sequence as.

Solution (1)

∴=

∴;

(2) The sequence is a periodic sequence with a period of 3, and

Therefore.

(3).

At that time,

∵ =.

∴ ;

At that time,

;

At that time,

therefore

23. (The full score of this big question is 18) This big question * * * has three small questions, and the full score of 1 small question is 4, the full score of the second small question is 6 and the full score of the third small question is 8.

Given a function, if any real number always has a non-zero constant in the defined domain, and given a non-zero constant, the function is called a periodic function with a period of. If it is always true, the function is called an incremental periodic function with a period of.

(1) Try to judge whether this function is a 2-level class increasing period function with a period of 1. And explain the reasons;

(2) The known function is a 2-class increasing period function with a period of 1, and the range of the real number is realistic;

(3) You can choose one of the following two questions to answer. Question (1) is 6 points, and question (2) is 8 points. If you choose two questions, we will grade you according to question (1).

(i) It is known that it is a periodic function of the superior, and at that time it is a monotonically increasing function over the range of real numbers.

(2) It is known that at that time, if the function is a quasi-periodic function with an upper period of 4 and its range is a closed interval, then the range of the value of the real number is real.

explain

(1)∫, i.e.

∴, namely

In other words, it applies to everything,

Therefore, it is a 2-class period-increasing function with a period of 1.

(2) In terms of meaning,

In other words, it applies to everything,

∵

∴ ,

So, order,

Is increasing monotonously in the world,

So,