Multiple choice
1. Then ()
2 1004 b .-2 1004 c . 22008d .-22008
A
Analyze it.
2. Define set operations: If, the sum of all elements in the collection is ().
A.0 B.2 C.3 D.6
D
3.A, b∈R is known, A >；; B, then the following inequality is ()
A.a2 & gtB2 b .()a & lt； ()b C.lg(a-b)>0d . >； 1
4. Given the condition: =, if the straight line is tangent to the circle, then it is.
() condition
A. Sufficient and unnecessary conditions B. Necessary and insufficient conditions
C. sufficient and necessary conditions D. neither sufficient nor necessary conditions
A
Analysis: A straight line is tangent to a circle.
5. The set of known sets T= ()
A, B, C, D,
A
Analysis, because, so choose (a).
6. Set, which is equal to ()
A.B. C. D。
D
Analysis, select (d)
7. Given a circle, a point (-2,0) and a point (2,0), if the point is observed from the point, the value range is (), so that the line of sight will not be blocked by the circle.
A.(-∞,- 1)∪(- 1,+∞)
B.(-∞,-2)∪(2,+∞)
C.(-∞,)∪(,+∞)
D.(-∞,-4)∪(4,+∞)
C
The analysis is shown in the figure. So the value range of is (c).
8. (Text) ()
A.B. C. D。
D
Analyze it.
(Li) Four representatives were selected from five men and four women, among whom at least two boys, at least 1 girl, went to four different factories for investigation. Different distribution methods are ().
A.b . 400 c . 480 W . W . k . s . 5 u . c . o . m . d . 2400
D
Analyze it.
9. The function satisfies the conditions of any positive integer A and B, and. rule
The value of is ()
In 2007
B
Analysis because, therefore, that is, so.
10. If the function is known, the value of the sum of any real numbers is ().
A. greater than 0 b. less than 0 c. equal to 0 d. uncertain
A
The analytic function is an odd-numbered function, which monotonically increases in R. You might as well set it, and then, so, so, so.
1 1. In order to improve traffic and celebrate the 60th anniversary of the National Day, a certain area is ready to open a,
The bus line between the two places. Given that the distance between A and B is 15km, the planning requirements of public transportation are: the distance between two adjacent stations is equal, the distance between cars passing through each station is 3min, and the design speed of cars is 60km/h, then at least () cars need to be put into operation between A and B. ..
a . 9 b . 10 c . 1 1d . 12
B
Because it runs every 3 minutes, the speed is 60 kilometers per hour, and the distance between two adjacent stations is 3 kilometers, so it takes 6 stations from A and B, that is, 6 cars, plus 4 cars from B to A, so * * * needs 10 cars.
12. It is known that the sum of the first n terms of arithmetic progression {a} is S. If so, then this series {a} is absolute.
The item with the smallest pairing value is ()
A B C D
C
Analysis because,, so, so, so.
So the item with the smallest absolute value in this series {a} is.
fill-in-the-blank question
13. Execute the program block diagram on the right. If yes, output.
Analyze it.
14. (Text) When the enclosed area is calculated by the random simulation method, two groups of uniform random numbers within the range of 0~ 1 are generated by the calculator, and then the translation and expansion transformation are carried out. The experiment has been carried out 100 times, and the number of samples in the required area for the first 98 times is 65, and the random numbers of the last two experiments are known. The conclusion of this simulation is that
10.72
Parse the area surrounded by from, get: and.
Inside, from, get:, the main points are also related to
In the enclosed area, therefore, the area obtained by this simulation is.
The curve represented by polar coordinate equation is
A straight line and a circle
Analysis,
And then still.
15. (Text) A master needs to make a workbench with plywood. The workbench consists of a main part and an accessory part. The main part is fully enclosed, and the auxiliary part is a retaining wall to prevent the workpiece from slipping off the workbench. Three views of its general shape are shown on the right (unit length: cm). According to the size in the figure, the plywood area used for the workbench is (plywood loss and plywood thickness are ignored in the manufacturing process).
As can be seen from the three views, the workbench is a cube with a side length of 80, which is surrounded by a rectangle and two right-angled triangular plywood, as shown in the right figure, and the area of plywood used.
If 1N can stretch the spring 1cm, in order to stretch the spring 6cm, it is necessary to do work J.
0. 18
Analysis, so, so.
16. (Text) If: known, the range of the function is
Analysis, in which. Make the feasible region, that is, because the function is monotonically increasing in the world, so.
(Richard), then the minimum value is
eight
Analysis hypothesis derived from Cauchy inequality;
An equal sign holds if and only if they are in the same direction. So, the minimum value of is 8.
answer the question
17. As shown in the figure, the known points and moving points in the upper half of the unit circle.
(1) If, find the vector;
(2) The maximum value to find.
Analysis (1) According to the meaning of the question, (excluding 1 or 2 endpoints is also correct),
, (just write 1),
Because, therefore, the solution,
So;
⑵,
. The maximum value was obtained at that time.
18. (Text) In the 60 years since the founding of New China, especially in the 30 years since the reform and opening up, China's economy has grown rapidly and people's living standards have improved steadily. The annual electricity consumption and GDP data of a certain place in 2006-2008 are as follows:
Date: 2006, 2007 and 2008
Electricity consumption (x billion kwh)111312
GDP growth rate (year (percentage))
Using the data in the table, we can get (1), and try to find the linear regression equation of y about x;
(2) According to previous statistics, every one percentage point increase in local GDP every year will drive 1 000 jobs. Affected by the financial crisis, it is estimated that the electricity consumption will be 800 million kWh in 2009, and 200,000 local people will be newly employed in 2009. Please estimate the employment rate of these new employees.
The analysis (1) is obtained from the data, so. So the linear regression equation of y about x is;
(2) At that time, it was predicted that the local GDP growth in 2009 could drive the local newly-employed population to 6,543,800+0.7 million, and the employment rate of these newly-employed population was estimated.
There are 8 employees in a company, 5 of whom have participated in one or more skill trainings, and 3 others.
I haven't participated in any skill training, and now I want to choose three employees from eight to participate in a new skill training.
(i) Find out the probability of selecting exactly 1 employee who has participated in skills training;
(2) After this training, the number of employees who have not participated in any skills training is a random variable, and x is found.
Distribution list and mathematical expectation.
Analysis (1) The probability of selecting exactly 1 employee who has participated in other skills training.
(II) The possible values of the random variable x are: 0, 1, 2, 3.
The ∴ distribution list of random variable x is
X 0 1 2 3
P
∴X's mathematical expectation.
19. (Text) The three views (the front is perpendicular to the plane) and the front view of a polyhedron are shown in the figure, where m and n are the midpoint of A 1B and B 1C 1 respectively.
(1) Calculate the volume of polyhedron;
(2) verify the ‖ plane;
(3) If this point is the midpoint of AB, verify the AM plane.
Analysis (1) As shown in the right figure, in the orthographic diagram of this polyhedron, AA 1⊥ plane ABC, and AC⊥BC, AC=BC=CC 1=, so;
(2) Lian, from the rectangular nature: AB 1 intersects with A 1B at point M, at △AB 1C 1, from the midline nature, MN//AC 1, and from the plane ACC1.
(3) In the rectangle,,, so, so, because the plane plane,, so the plane, so, that is, again, so the plane is the AM plane.
(Theory) It is known that, ⊥ plane,, are the moving points on,, respectively.
(1) proves that no matter what value is taken, there is always a plane ⊥ plane;
(2) If the dihedral angle between planes is, the value of is.
Analyze (1)∵⊥ plane, ∴ plane, then ∴⊥ plane, then in the middle, and ∴∴? respectively.
(2) Take the point, ∵⊥ plane, ∴⊥ plane as shown in the figure and ∴ in the middle as the origin, and establish a spatial rectangular coordinate system. In the middle, in the middle, again, and then.
∵,∴,∵,∴,
Say it again,
Let it be the normal vector of a plane, then, because, therefore, because =(0, 1, 0), so, because it is the normal vector of a plane, and the dihedral angle between planes is,, or (irrelevant, abandon), so when planes are formed,
20. Known functions have extreme values.
(i) The numerical range to be obtained;
(ii) If the extreme value is obtained and the constant remains unchanged at this time, the range of the value is obtained.
Analysis (Ⅰ) ∫∴, in order to have extreme value, the equation has two real number solutions, so △ =, ∴.
(ii) Get the extreme value at ∴. ∴.
∴∵∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴∴875
∴, that is ∴ or, that is, the value range is.
2 1. Any point of a known ellipse whose right focus is f, its upper vertex is a and p is C 1. The circle C2 whose center is on the Y axis and the straight line with slope are tangent to point B, AF‖.
(1) Equation for finding eccentricity of circle and ellipse.
(2) Let p be the tangents PE and PG of circle C2. If the minimum value is 0, find the equation of ellipse.
Analysis (1) The circle C2 with the center on the Y axis and the straight line with the slope of 1 are tangent to point B, so the center is on the straight line passing through B and perpendicular to it, and the center is on the Y axis, so the center C2 (0 0,3).
The distance from the center of the circle to the straight line, so the C2 equation of the circle is:, AF‖, so there is, that is, the eccentricity of the ellipse is;
(2) Settings
In, the geometric properties of an ellipse are:
, so there is, because, so,
So the equation of the ellipse is.
22. (Liberal Arts) (1) If the series is a subsequence of the series, try to judge the size relationship between sum;
(2) In the sequence, it is known that it is a arithmetic progression with non-zero tolerance, a5=6.
Dangqi
(2) if there are natural numbers.
Form geometric series. It is proved that when a3 is an integer, a3 must be a positive divisor of 12.
Analysis (1);
② ① Because, therefore,
,;
(2) because, that is
Because it must be a positive divisor of 12.
(science) a known sequence.
(i) When;
(ii) If the generic term of the sequence is found;
(iii) It is proved that there are terms in the sequence that satisfy ≤3.
Analysis (1);
When? Therefore.
㈡.
∴ conjecture exists for any positive integer l (that is, week)
4) A series of periods.
Let's prove it by mathematical induction.
(i) Established;
(ii) Assuming that it was established at that time.
,
,,
,。
According to (i) and (ii).
It can also be proved.
(III) Assume that for all n, the series is the first term.
Arithmetic progression with an error of -3, so there is a large enough one.
N, so that this contradicts the hypothesis, ∴ the hypothesis does not hold, ∴ in the sequence, one term satisfies ≤3.