In recent years, Fujian college entrance examination has included mathematics.

20 10 Fujian province exam instructions sample paper

(scientific mathematics)

This paper is divided into two parts: the first volume (multiple choice questions) and the second volume (non-multiple choice questions). Among them, Volume 2, 2 1( 1), (2) and (3) are entitled multiple-choice questions, and candidates are invited to answer as required. Other topics are required. The full mark of this volume is 150, and the examination time is 120 minutes.

The first volume (multiple choice questions ***50 points)

1. Multiple-choice question: This big question is a small question of *** 10, with 5 points for each small question and 50 points for * * *. Of the four options given in each small question, only one meets the requirements of the question

1. Complex number equals

A. BC-1+ 1

2. If the complete set U=R is known, then the set is equal to.

A.B.

C.D.

3. The picture on the right is three views of a geometry. According to the data in the figure, the surface area of the geometry can be obtained as follows

A.B.

C.D.

4. In the following function, it satisfies "For any, (0), when" is.

A.= B. =

C.= D。

5. The figure on the right is the program block diagram for calculating the function value, and the items to be filled in at ①, ② and ③ are

A.，，b，

C.，，d，

6. Let, be two different straight lines on the plane, and, be two intersecting straight lines on the plane, then a sufficient and unnecessary condition of is

A. And B. And

C. and D. and

7. In the known geometric series, the range of the sum of the first three terms is

A.B.

C.D.

8. If it is known that it is a real number, the image of the function cannot be

9. The known real number satisfies: If the minimum value of the objective function is, the real number is equal to.

a7 b . 5 c . 4d . 3

10. Definition: A coordinate system consisting of two intersecting but not perpendicular number axes on a plane (the origins of the two number axes coincide and the unit length is the same) is called a plane oblique coordinate system; In the plane oblique coordinate system, if (where, they are the unit vectors on the axis and in the positive direction of the axis, respectively, and r is the origin of the coordinate system), then the ordered number pair is called the oblique coordinate of the point. In the plane oblique coordinate system, if = 120, the oblique coordinate of the point is (1 2), and the point is centered on 65433.

A.B.

C.D.

Fill-in-the-blank question: This big question contains ***5 small questions, each with 4 points and ***20 points. Fill in the answers in the corresponding places on the answer sheet.

1 1. In order to calculate the area of the shadow part as shown in the figure, make a square with a side length of 6 and randomly cast 800 points in the square. It is known that exactly 200 points fall in the shadow part, so the area of the shadow part can be estimated as _ _ _ _ _.

12. If yes, then A 1+A2+A3+A4+A5 = _ _ _.

13. The graphic area enclosed by straight line, x=2, curve and x axis is.

14. There are two ways for a person to go to work, A and B. Starting from home at regular intervals in the morning, there is a probability of being late by taking the A route and a probability of being late by taking the B route; No matter which route you take, as long as you are not late, take the same route next time, or change to another route; Suppose he takes route a on the first day and the probability of taking route a on the third day is.

15. It is known that the center of ellipse C 1 is at the origin, the focus is on the X axis, the vertex of parabola C2 is at the origin, and the focus is on the X axis. Xiao Ming takes several points from curves C 1 and C2 respectively (at least two points from each curve) and records their coordinates (x, y). There is only one due to a recording error.

0 2

three

y 2 0

From this, it can be inferred that the equation of ellipse C 1 is.

3. Solution: This big question is ***6 small questions with a score of ***80. The solution should be written in words, proof process or calculus steps. Fill in the problem-solving process in the corresponding position on the answer sheet.

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

The sides of the three internal angles of are vectors = (,) and ⊥.

(i) the scale of the solution;

(ii) The following four conditions are given:

① ; ② ; ③ ; ④ .

Try to choose more than two conditions to determine and find out the area you have determined.

(Note: You only need to choose one option to answer questions. If you use more than one scheme to answer questions, score according to the first scheme. )

17. (Full score for this small question13) Two students, A and B, participated in the training of the math competition. At present, eight times were randomly selected from several preliminaries they participated in during training, and the records are as follows: A 82 8 1 79 78 95 88 93 84.

B 92 95 80 75 83 80 90 85

(i) Two sets of data are represented by the stem leaf diagram;

(ii) Now, one student should be chosen to take part in the math contest. From a statistical point of view, which student do you think is suitable? Please explain the reasons;

(3) If the frequency is regarded as probability, predict the next three math contest exams of students in A, and record the times when the score is higher than 80 points in these three times, which will be used as the distribution table and the math expectation E. 。

18. (The full mark of this small question is 13) The shapes and dimensions of the bottom and four sides of the P-ABCD of the quadrangular pyramid are shown in the figure.

(1) Write the vertical relationship between four pairs of straight lines and planes in the P-ABCD of the pyramid (without proof);

(ii) In the quadrangular pyramid P-ABCD, if it is the midpoint, verify: planar PCD；;

(3) In the quadrangular cone P-ABCD, let the angle formed by the surface PAB and the surface PCD be evaluated.

19. (The full mark of this small question is 13) Ellipse C with focus F 1(0,-1) and F2(0, 1) passes through point p (,1).

(1) Find the equation of ellipse c; (2) Omission.

20. (Full score for this small question 14) Known function.

(1) Find the extreme value of the function; (2) Omission.

2 1. This question has three multiple-choice questions (1), (2) and (3), with 7 points for each question. Please choose two questions to answer, full score 14. If you do too much, score according to the first two questions.

(1) (The full mark of this small question is 7) Elective 4-2: Matrix and Transformation (omitted).

(2) (The full score of this small question is 7) Elected 4-4: Coordinate System and Parameter Equation.

In polar coordinate system, let a point on a circle have the greatest distance from a straight line.

(3) (The full score of this small question is 7) Elective course 4-5: Selected lectures on inequality.

The known minimum value.

Sample paper reference answer

Multiple-choice question: This question examines the basic knowledge and basic operation, with 5 points for each small question, out of 50 points.

1.D 2。 A 3。 D 4。 A 5。 B 6。 B 7。 D 8。 D 9。 B 10。 A

Fill-in-the-blank question: This question examines the basic knowledge and basic operation, with 4 points for each small question, out of 20 points.

1 1.9. 12.3 1. 13.2 . 14.. 15.。

Third, the solution: this big question is ***6 small questions, with ***80 points. The solution should be written in words, proof process or calculus steps.

16. Solution: (I)∫⊥, ∴-cosBcosC+sinBsinC- =0,

That is, cosBcosC-sinBsinC=-, ∴ cos (b+c) =-. ∫a+b+c = 180，∴cos(B+C)=-cosA

∴cosA=，A=30。

(2) Option 1: Select ① ③ to determine△ ABC. ∫A = 30，a= 1，2C-(+ 1) B = 0。

From the cosine theorem, it is =2, b=, c =.

∴ .

Option 2: Select ① ④ to confirm △ ABC. ∫a = 30，a= 1，B = 45，∴ C = 105。

SIN 105 = SIN(60+45)= SIN 60 cos 45+cos 60 SIN 45 =。

C =。 ∴ in sine theorem.

(Note: If ② ③ is selected, it can be converted into ① ③; If you choose ② ④, you can transform it into ① ④ solution, and omit it. If ② or ③ ④ is selected, the triangle cannot be determined. )

17. Answer: (1) Draw the following stem leaf diagram:

(ii) It is more appropriate to send a team for the following reasons:

A's performance is relatively stable, so it is more appropriate to send A to participate in the competition.

Note: the conclusion and reason of this small problem are not unique. If the examinee can give other reasonable answers from the statistical point of view and give the same score, it is more appropriate to send B to participate in the competition. The reasons are as follows: From a statistical point of view, A has a probability of 85 points or more, and B has a probability of 85 points or more.

(iii) Note that "student A scored more than 80 points in a math contest" is event A, then.

The possible values of random variables are 0, 1, 2, 3, obeying,

So the distribution list of variables is.

. (or)

18. Solution 1:

(i) As shown in the figure, in the quadrangular cone P-ABCD, PA⊥ plane ABCD,

AD⊥ airport, BC⊥ airport, AB⊥ airport. ..

(2) according to the meaning of the question, AB, AD and AP are perpendicular to each other, and the straight lines AB, AD and AP are taken as x, y and z axes respectively.

Establish a spatial rectangular coordinate system, as shown in the figure.

E is the midpoint of PA, and the coordinates of the point of∴ e are,

, , .

Let be the normal vector of planar PCD. By, that is

Take a normal vector of planar PCD.

∵ ,∴ ,

∴‖ Plane PCD. It's also a planar PCD. It's a ∴‖ planar PCD.

(iii) According to (ii), the normal vector of planar PCD is,

Another ∵AD⊥ plane PAB, the normal vector of ∴ plane PAB is,

∴ .

19. Solution: (Ⅰ) Let the elliptic equation be (a >；; B>0), represented by the known c= 1,

And 2a=, so a=, b2=a2-c2= 1, and the equation of ellipse C is x2+= 1.