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(Applicable to 20 1 1 Ningxia, Hainan and Henan college entrance examination new curriculum reform)

Investigation and test of 20 1 1 college entrance examination in Haikou, Hainan Province

Mathematics test questions (text)

Precautions:

1. The examination papers in this exam are divided into examination papers and answer sheets. This is a test paper. Please write the answers and solutions in the designated position on the answer sheet. Answers in test papers and other positions are invalid.

2. The full mark of this volume is 150, and the examination time is 120 minutes.

Reference formula:

Standard deviation conic volume formula of sample data.

Where is the sample average, where is the bottom area, and which is higher.

Cylindrical volume formula Sphere surface area and volume formula

Where is the area of the bottom surface, the height and the radius of the ball.

Volume one multiple-choice questions

A, multiple-choice questions (this big question * * 12 small questions, each small question 5 points, ***60 points. Of the four options given in each small question, only one meets the requirements of the topic; After choosing the answer for each question, please blacken the answer label of the corresponding question on the machine-readable card with 2B pencil. If you need to change it, clean it with an eraser, and then choose another answer label, which is invalid in this volume. )

1. Set up a complete work,

The set represented by the shaded part in the figure is ()

A.B.

C.D.

2. If the complex number is purely imaginary, then the value of the real number is ().

A.1b. or1c.d. or 3

3. In a physical examination, the visual acuity data of four students were 4.6, 4.7, 4.8 and 4.9 respectively. If two students are randomly selected at a time, the probability that their eyesight differs by 0.2 is

A.B. C. D。

4. There are four propositions about plane vectors:

(1) If ∨, then make;

② If，then or

(3) There are real numbers that are not all zero, which makes;

4 if, then.

The correct proposition is ()

A.①③b。 ①④c。 ②③d。 ②④

5. Given that circle A: and fixed straight line:, and moving circle P is circumscribed with circle A and tangent to straight line, the locus equation of the center of moving circle P is ().

Asian Development Bank.

6. If known, the value of is ()

A. The second century BC

7. If the variables meet the constraints, the maximum value of the objective function is ().

a . 7b . 8c . 10d . 23

8. Let two non-overlapping planes be two non-overlapping straight lines, and give the following four propositions:

(1) If;

(2) If, then;

3 If, then;

4 if, then.

The correct proposition is: ()

A.①②b。 ①③c。 ①②③D。 ②③④

9. Expand the abscissa of all points on the function image to twice the original (the ordinate is unchanged), and then shift the obtained image to the left by one unit. The corresponding analytical formula of the obtained image is ().

10. The block diagram of a program is shown in the figure, and the output value after the program runs is ().

a . 3b . 4

c . 6d . 8

1 1. The three views of a geometric figure are shown in the figure, so the volume of this geometric figure is ().

a . 32b . 33 c . 34d . 35

12. The given function is satisfied on r, and the tangent equation of the curve at this point is ().

A.B. C. D。

Volume 2 Non-multiple choice questions

2. Fill in the blanks: (This topic is entitled ***4 small questions, with 5 points for each small question and 20 points for * * *, and the answer is filled in the designated position on the answer sheet)

13. Set a vector, if the vector and the vector * * * line, then.

14. In, its three sides are known, and the area of the triangle is, then the angle c =.

15. It is known that the equation of ellipse C is that hyperbola D and ellipse have the same focus as their intersection point, then the eccentricity of hyperbola is.

16. Assuming that the function increases monotonically in the interval [1, 2], the value range of is.

Three. Solution: (This big question is ***5 small questions, and the score is ***60. The solution should be written in words, proof process or calculation steps. Please write down the process of answering questions in the designated position on the answer sheet)

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

In arithmetic progression, the preceding paragraph and geometric progression are both positive numbers, and the common ratio is.

(i) Seek;

(2) seeking.

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

There are 1000 students in the third grade of a school. Through investigation and study, 750 of them often take part in physical exercise (called Class A students), and the other 250 do not often take part in physical exercise (called Class B students). At present, stratified sampling method (divided into two layers according to Class A and Class B) is used to randomly select 100 students from this grade.

(1) In statistical methods, the midpoint value of this set of data (for example, the midpoint value of an interval is 165) is often used as a representative. On this basis, the average height data of this 100 student is calculated;

(2) Take the height as high as 170cm as the standard, and draw the following table for 100 students:

2×2 contingency table of physical exercise and height reaching the standard

Total height up to standard and total height up to standard.

take an active part in

physical exercise

Not actively participating

Physical exercise 15

Total 100

(i) Complete the above table;

(2) How confident is physical exercise and reaching the height standard (K value is accurate to 0.0 1)?

Reference formula: K=, reference data:

p(Kk)0.40 0.25 0. 15 0. 10 0.05 0.025

k 0.708 1.323 2.072 2.706 3.84 1 5.024

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

In the quadrangular pyramid P-ABCD, that is, in the plane, the bottom ABCD is a diamond with a side length of 2, e is the midpoint of AD, and f is the midpoint of PC.

(i) Verification:

(ii) verification: EF// plane PAB.

(iii) Find the distance from point E to plane PBC.

20. (The full score of this short question is 12)

In the plane rectangular coordinate system, the sum of two points is known, and the alignment is: The fixed point on the plane is always satisfied.

(i) finding the equation of the trajectory of the moving point;

(ii) setting an intersection curve of a straight line passing through the fixed point (the straight line is not coincident with the axis) at two points,

Prove that the intersection of a straight line and a straight line is always on a straight line.

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

Known function. ()

(i) At that time, find the maximum and minimum values in the interval [1, e];

(2) Extreme value of the solution

Fourth, the topic (choose one of the following three answers, please indicate the question number when answering; If you do more, you will be included in the total score according to the first question, with a full score of 10. Please write down the answer process in the designated position on the answer sheet)

22. (Full score for this small question 10) Elective course 4- 1: Selected lecture on geometric proof.

As shown in the figure, it is known that AB is the diameter ⊙O, C and D are the two points above ⊙O, CE⊥AB is in E, BD is in G, CE is in F, and CF = FG.

Prove: (I) C is the midpoint;

(ⅱ)BF = FG。

23. (Full score for this small question 10) Elective course 4-4: Coordinate System and Parameter Equation.

It is known that the pole of polar coordinate system coincides with the origin of rectangular coordinate system, and the polar axis coincides with the positive semi-axis of the axis of rectangular coordinate system. The parameter equation of a straight line is (parameter), and the polar coordinate equation of a curve is.

(i) Finding the rectangular coordinate equation of the curve;

(Ⅱ) Let a straight line and a curve intersect at two points and find the distance between the two points.

24. (The full mark of this small question is 10) Elective course 4-5: Selected lectures on inequality.

Set a function.

(i) Finding the solution set of inequality;

(ii) If the solution set of inequality is not empty, the range of seeking truth from numbers.

First, multiple choice questions

1—5 bcdba 6— 10 adbcd 1 1— 12BC

Second, fill in the blanks

13.2 14. 15. 16.

Third, answer questions.

17. Solution: (1) can be obtained from the known.

Solve or (give up)

........................ scored six points.

(2)

.............. 12 point

18. Solution: (1) The average value of the data is:145× 0.03+155× 0.17+165× 0.30+175.

(Ⅱ) (ⅰ)

Total height up to standard and total height up to standard.

Take an active part in physical exercise

Do not actively participate in physical exercise 10 15 25

Total 50 50 100

(ⅱ)K= 1.33

Therefore, there is a 75% confidence that physical exercise is related to reaching the height standard. -12 points.

19. Proof: ∴AB=2, AE= 1.

∴BE⊥AE

Plane PAD⊥ plane ABCD, the intersection line is AD,

∴BE⊥ Plane mat-4 points

(ii) Take the midpoint g of BC and connect GE and GF.

Then GF//PB, EG//AB,

and

∴ Aircraft EFG// Aircraft PAB

∴EF// aircraft PAB-8 points

(3) BC ∫ AD ∨ AD ∴ Plane PBC

The distance from a to the plane PBC is equal to the distance from e to the plane PBC.

By (1) AE⊥ plane PBE

∴ aircraft PBE⊥ aircraft PBC

Plane PBE∩ plane PBC=PB[

If EO⊥PB is in O, EO is the distance from E to PBC.

And PE= ∴PB=2.

pass by

∴- 12 point

20. Solution (i) assumes that,

By, that is, the equation of trajectory is. -Four points.

(ii) If the slope of the straight line is, then the straight line:, let,.

Get together, get together,

Then, it was observed that,

That is to say,

Straight line:, straight line:,

Li Lian:

Solution:; So the intersection is on a straight line:

If the axis time, might as well get,, then at this time,

Straight line:, straight line:,

Combine, solve,,

That is, the intersection point is also on the straight line: up. -12 points.

2 1. Solution: (1) At that time,

For [1, e], there is a ∴ increasing function in the interval [1, e].

∴,-4 points

(2) (x>0)

(1) When, immediately,

Therefore, (0, +∞) is a monotonically increasing function.

So, it's worthless.

(2) When and immediately

Order, get (give up)

When it changes, the changes are as follows:

+ 0 -

As can be seen from the above table,

.............. 12 point

Fourth, the topic (choose one of the following three answers, please indicate the question number when answering; If you do more, it will be included in the total score according to the question type, with a full score of 10. Please write down the answer process in the designated position on the answer sheet. )

22. Proof: (Ⅰ) ∵ CF = FG

∴∠GCF =∠CGF

∵AB is the diameter of⊙ O.

∴AC⊥BD CE⊥AB

∴∠GCF =∠ABC=∠CBD+∠GBA

And ∠GCF=∠A+∠GBA.

∴∠CBD=∠A

∴BC=CD, which is the midpoint of point C-6.

(ii) Through (I)CBD =∠A =∠BCF.

∴BF=CF and CF=FG

∴ BF = FG- 10 integral

23. Solution: (i) Multiply from both sides,