High score: Mathematical answers of module exams in Shengli No.1 Middle School and No.3 High School in Dongying City, Shandong Province.

Zhongshan City unified examination at the end of the first semester of the 2009-20 10 school year.

Mathematics examination paper (science)

This volume is divided into two parts: the first volume (multiple choice questions) and the second volume (non-multiple choice questions), with a score of *** 150. Examination time 120 minutes.

Precautions:

1. Before answering the first volume, candidates must scribble their names, test numbers, seat numbers and test subjects in pencil on the answer sheet.

2. After choosing the answer for each question, black the answer label of the corresponding question on the answer sheet with a pencil. If you need to change it, clean it with an eraser and choose another answer. You can't answer the question.

You can't use the calculator.

4. After the exam, return the answer sheet, and don't hand in the test paper.

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

1. Multiple choice question: (This big question has ***8 small questions, each with 5 points and ***40 points. Only one of the four options given in each small question meets the requirements of the topic. )

1. Known

A.B. C. D。

2.=

A.b .– 1 c . d

3. Given two straight lines M and N and two planes α and β, there are four propositions below:

1) If; 2) ;

3) ; 4) .

The number of correct propositions is

A.0 B. 1 C.2 D.3

4. The image of function y=sinx is shifted by a vector and coincides with the image of function y=2-cosx, that is

A.B. C. D。

5. As shown in the figure, it is known that the bottom surface of the triangular pyramid is a right triangle, with right-angle side lengths of 3 and 4 respectively, and the side length passing through the right-angle vertex is 4, which is perpendicular to the bottom surface. The front view of the triangular pyramid is as follows

6. Variables X and Y have observed data (,) (I = 1, 2, …, 10), and the scatter plot is1; There are observation data (,) (I = 1, 2, ..., 10), and the scatter plot is obtained. 2. Judging from these two scatter charts.

A. variables x and y are positively correlated and u and v are positively correlated.

B. the variable x is positively correlated with y, and u is negatively correlated with v.

C. the variable x is negatively correlated with y, and u is positively correlated with v.

D. the variable x is negatively correlated with y, and u is negatively correlated with v.

7. During the occurrence of a public health incident, a professional organization thinks that the sign that the incident has not suffered from large-scale group infection for a period of time is "continuous 10 days, and no more than 7 suspected cases are added every day". The data of suspected cases added in the past 10 days according to A, B, C and D must be consistent with this mark.

A. One place: the overall average is 3, and the median is 4.

B.b: the overall average value is 1, and population variance is greater than 0.

C c: the median is 2 and the mode is 3.

D D: The overall average is 2, and the population variance average is 3.

8. Take any three vertices of the parallelepiped ABCD-A ′ B ′ C ′ D ′ as vertices to make triangles, and randomly select two triangles from them, then the probability p that these two triangles are not * * * faces is

A.B. C. D。

Volume 2 (multiple choice questions * * 1 10)

Fill in the blanks: (There are 6 small questions in this big question, with 5 points for each small question and * * 30 points. )

9. If the complex number Z satisfies z (1+I) = 1-I (I is an imaginary unit), then its * * * yoke complex number = _ _ _ _ _.

10. The negation of the proposition ""is.

1 1. In the binomial expansion, the coefficient of the inclusion term is _ _ _ _ _.

12. Of all the points on the plane that satisfy the inequality group 1≤x+y≤3,-1 ≤ x-y ≤ 1, x≥0, y≥0, the coordinates of the point where the objective function z=5x+4y takes the maximum value are

13. Arrange all positive integers into a triangular array;

According to the above arrangement, the third number from left to right is.

14. in order to know the average sleep time of the elderly aged 70-80 in a certain area (unit:

Hours), 50 elderly people were randomly selected for investigation. The table below shows these 50 old people.

The frequency distribution table of people's sleep time every day.

serial number

(i) Grouping

(Sleep time) Group median ()

frequency

Frequency (number of people)

( )

1 [4,5) 4.5 6 0. 12

2 [5,6) 5.5 10 0.20

3 [6,7) 6.5 20 0.40

4 [7,8) 7.5 10 0.20

5 [8,9) 8.5 4 0.08

In the analysis of the above statistics, the right side is a part of the calculation algorithm.

Flow chart, the output value of s is.

Three. Solution: (This big topic is ***6 small questions, and the score is ***80. The solution should be written in words, proof process or calculus steps. )

15. (The full score of this small question is 12)

Known: function (). Solve inequality:.

16. (The full score of this small question is 12)

Given the directional quantity, define the function.

(1) is the minimum positive period, the maximum value and the corresponding x value;

(2) When, find the value of x 。

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

In an international table tennis match, two players A and B met in the final. According to past experience, the probability of player A winning a single game is 0.6. This game adopts the best of five games system, that is, the player who wins three games first wins and the game is over. Let the global games not affect each other, let ξ be the number of games in this game (excluding the number of games that player A loses to B), and find the probability distribution and mathematics of ξ.

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

As shown in the figure, the bottom surface of the quadrangular pyramid S-ABCD is square, and each side

The length of the side is twice the length of the bottom side, and p is the point on the side SD.

(i) Verification: communication ⊥ self-destruction;

(ii) If SD⊥ plane PAC, find out the size of dihedral angle P-AC-D;

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

It is known that the sum of the first n terms in the sequence is Sn,

And sn+ 1 = 2sn+n+5 (n ∈ n *).

(i) Prove that the sequence is a geometric series;

(2) order.

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

It is known that A, B and C are three different points on a straight line, and O is the point outside the straight line, and the vector,, satisfies, remember.

(1) Find the analytical formula of the function;

(2) If,, prove the inequality;

(3) If the equation about has exactly two different real roots in the world, find the value range of the number.

Zhongshan City unified examination at the end of the first semester of the 2009-20 10 school year.

Math Test Paper (Science) Answers

First, multiple choice questions

DACB·BCDA

Second, fill in the blanks

9. I; 10. 1 1. 10; 12.(2, 1);

13.； 14.6.42

Third, answer questions.

15. Solution: 1) If, that is, the solution,

That is, the inequality holds, that is;

2) when, that is, because, so.

From 1) and 2), the original inequality solution set is.

16. Solution: (1)

When, take the maximum value.

(2) When, that is,

Solve,.

17. Solution: As a random variable ξ, the number of games in which player A beats player B has four values: 0, 1, 2, 3.

1) When ξ=0, there are * * * three games in this game, and player A loses three games in a row.

p(ξ= 0)=( 1-0.6)3 = 0.064；

2) When ξ= 1, in the four games of this game, A loses four games, and A wins one game in the first three games.

p(ξ= 1)=；

3) When ξ=2, there are five games in this game, with A losing five games and A winning two games in the first four games.

p(ξ= 2)=；

4) When ξ=3, this game has * * * three games, or four games, or five games. Among them, Party A won three games in a row; * * * In the fourth game, A won the fourth game, and A won two games in the first three games; * * * In the fifth game, A won the fifth game, and A won two games in the first four games;

P(ξ=3)= =0.68256

The probability distribution list of ξ is:

ξ 0 1 2 3

p 0.064 0. 1 152 0. 13824 0.68256

Eξ=0？ P(ξ=0)+ 1？ P(ξ= 1)+2？ P(ξ=2)+3？ P(ξ=3)

=0? 0.064+ 1? 0. 1 152+2? 0. 13824+3? 0.68256=2.43926? 2.4394.

18. Solution 1:

(I) even BD, let AC pass through BD in O, from the meaning of the title. In the square ABCD, so, get.

(ii) Let the side length of a square be.

Again, so,

Lian, known from (1),

So, w and, so.

It is the plane angle of dihedral angle.

Know, know,

So,

That is, the size of dihedral angle is.

Solution 2:

(Ⅰ); Lian, located in, can be seen from the meaning of the question. Take O as the coordinate origin, and establish the coordinate system as shown in the figure.

If the side length of the bottom surface is, it is high.

So,,,

, ,

So,

Therefore, this way

(2) From the topic, we can know that the normal vector of a plane and the normal vector of a plane, if the dihedral angle is, then the size of the dihedral angle is

19. Solution: Solution: (i) From the known VII

Subtract two expressions to get.

That is, therefore

When n= 1 and S2=2S 1+ 1+5, ∴ appears again.

So there is always

Again/therefore

That is, the geometric series is the first term and 2 is the norm.

(ii) Starting from (i)

therefore

20. Solution: (1)

A, b, c three-point * * * line,

(2), then