1. Multiple choice question: This big question is a small question of *** 12, with 5 points for each small question. Only one of the four options given in each small question meets the requirements of the topic.
(1) known set a = {x | x2-x-2 < 0}, b = {x |-1< X< 1}, then
(1) AB? (B)BA(C)A=B？ (D)A∩B=？
Propositional intention This topic mainly investigates the relationship between the solution of a quadratic inequality and the set, which is a simple problem.
Analytic A = (- 1, 2), so BA, so B.
(2) Complex number z =? What is the plural of * * * yoke?
(1) (2) (3)? (D)？
Proposition intention This topic mainly investigates the division operation of complex numbers and the concept of * * * yoke complex numbers, which is a simple problem.
Analysis? =? =? ,∴? What is the plural of * * * yoke? , so choose D.
(3) In a scatter plot of a set of sample data (x 1, y 1), (x2, y2), (xn, yn)(n≥2, x 1, x2, ..., xn is not completely equal), if all sample points (,yi, xn are not completely equal),
(1)-1? (B)0？ (C) 12？ 1
The problem of propositional intention mainly examines the correlation coefficient of samples, which is a simple problem.
This sample data is from perfect positive correlation, so its correlation coefficient is 1, so D is selected.
(4) setting? ,? Is it oval? :? = 1(? >? > 0 left and right focus),? For a straight line? A little, △? Is it the bottom corner? Isosceles triangle, and then what? The eccentricity of is
....？
Propositional intention This topic mainly examines the nature of ellipses and the idea of combining numbers and shapes.
Analysis ∵△? Is it the bottom corner? Isosceles triangle,
∴? ,? ,∴? =? ,∴? ,∴? =? , so choose C.
(5) The vertices A( 1, 1) and B( 1, 3) of the regular triangle ABC are known, and the vertex C is in the first quadrant. If the point (x, y) is within △ABC, then? The value range of is
(A)( 1-3，2)(B)(0，2)？
(C)(3- 1，2)(D)(0， 1+3)
Propositional intention This topic mainly investigates the solution of simple linear programming, which is a simple problem.
Analysis topic knowledge C( 1+? 2) Make a straight line? :? Translate a straight line? , have image knowledge, straight line? After point b, =2, when passing through c,? =? ,∴? The value range is (1-3,2), so a is selected.
(6) If the program block diagram on the right is executed, enter a positive integer? (? ≥2) and real numbers? ,? ,…,? , output? ,? , then
. ? +? For what? ,? ,…,? total
. ? For what? ,? ,…,? arithmetic mean value
. ? And then what? What are they? ,? ,…,? The maximum and minimum values in.
. ? And then what? What are they? ,? ,…,? Minimum quantity and maximum quantity
Propositional intention This topic mainly investigates the significance of block diagram representation algorithm, and it is a simple topic.
The algorithm of block diagram analysis is to find the maximum and minimum values of n numbers. And then what? What are they? ,? ,…,? The largest number and the smallest number, so choose C.
2 1 Century Education Network (7) As shown in the figure, the side length of a small square on the grid is 1, and the thick line draws three views of a certain geometry, then the volume of the geometry is
.6? .9. 12. 18
Proposition intention This topic mainly examines the three views and volume calculation of simple geometry, and is a simple topic.
According to the three-view analysis, its corresponding geometric shape is a triangular pyramid, its bottom side is 6, the height here is 3, and the height of the pyramid is 3, so what is its volume? =9, so choose B.
(8) If the radius of the circle cut by the spherical surface of the ball O on the plane α is 1 and the distance from the center of the ball O to the plane α is 2, then the volume of the ball is?
(A)6π？ (B)43π(C)46π？ 63π
Propositional intention
analyse
(9) known? & gt0,? , straight line? =? And then what? =? Is it a function? What about two adjacent symmetry axes of an image? =
(1) π4? (B)π3(C)π2(D)3π4
Propositional intention This topic mainly examines the images and properties of trigonometric functions, which belongs to a mid-range topic.
The analysis depends on the topic. =? ,∴? = 1,∴? =? (? ),
∴? =? (? ),∵? ,∴? =? , so choose a.
(10) equilateral hyperbola? The center of is at the origin and the focus is at? On the axis? With parabola? Where is the alignment? 、? Two o'clock? =? And then what? The actual axis length of is
. ? ..4? .8
Propositional Intention This topic mainly examines the positional relationship between parabola directrix, straight line and hyperbola, and is a simple topic.
From the problem analysis, the directrix of parabola is:? Let the equilateral hyperbolic equation be:? , will it? Substitute into equilateral hyperbolic equation? =? ,∵? =? ,∴? =? , the solution? =2,
∴? The real axis length of is 4, so c.
(1 1) When 0
(A)(0，22)？ (B)(22， 1)(C)( 1，2)？ (d) Article 2, paragraph 2
Propositional intention This topic mainly investigates the images and properties of exponential function and logarithmic function and the idea of combining numbers with shapes, which belongs to a mid-range topic.
From the images of exponential function and logarithmic function, we can know the analysis. , the solution? , so choose a.
(12) series {? } Are you satisfied? , then {? The sum of the first 60 items of {is
(1) 3690? (2) 3660? (C) 1845(D) 1830
Propositional intention This topic mainly examines the ability to flexibly use the knowledge of sequence to solve the problem of sequence, which is a difficult problem.
Analysis method 1 has problems.
= 1,①? =3②? =5③=7,? =9,
= 1 1,? = 13,? = 15,? = 17,? = 19,? ,
……
∴ ②-① Get？ =2, ③+②? =8, the same? =2,? =24,? =2,? =40,…,
∴? ,? ,? ,,, is a list containing all the items 2,? ,? ,? … is the arithmetic progression with the first term of 8 and the tolerance of 16.
∴{? What is the sum of the first 60 items of {? = 1830.
Law 2 can prove that:
2. Fill in the blanks: This big question has four small questions, each with 5 points.
(13) curve? The tangent equation of point (1, 1) is _ _ _ _ _ _ _
Propositional intention This topic mainly investigates the geometric meaning of derivatives and linear equations, and is a simple topic.
Analysis? If the tangent slope is 4, the tangent equation is? .
(14) geometric series? The sum of the first n terms of {is Sn. If S3+3S2=0,? Is it fair? =_______
Propositional intention This topic mainly examines the n terms and formulas of geometric series, which is a simple problem.
When is the analysis? = 1,? =? ,? =? , from S3+3S2=0? ,? =0,∴? =0 and {? } is a contradiction in geometric series, so? ≠ 1, from S3+3S2=0? ,? , the solution? =-2.
( 15)? Known vector? ,? What is the included angle? And |? |= 1,|? |=? , then |? |=? .
Propositional intention. This problem mainly investigates the quantitative product of plane vectors and its algorithm, which is a simple problem.
Analyze ∵|? |=? , square? , that is? , solution |? |=? Or? (shed)
(16) Setting function? =(x+ 1)2+sinxx2+ 1 The maximum value is m, and the minimum value is m, then m+m = _ _ _
Propositional intention is a difficult problem, which mainly investigates the parity, maximum, transformation and reduction of functions.
Analysis? =? ,
Settings? =? =? And then what? This is a strange function,
∵? The maximum value is m, and the minimum value is? ,∴? The maximum value of is M- 1, and the minimum value is? - 1,
∴? ,? =2.
Third, problem solving: the idea of solving problems should be clearly written, explaining the process or calculus steps.
(17) (The full mark of this little question is 12) Do you know? ,? ,? What are they? Three inner corners? ,? ,? Opposite to? .
(1) Q? ;
(2) What if? =2,? What is the area of? , beg? ,? .
Proposition intention This topic mainly investigates the application of sine and cosine theorem, which is a simple topic.
Analysis (ⅰ) by? And sine theorem
Because? , so? ,
Again? , so? .
(2) area? =? =? , so? =4,
And then what? So what? =8, solution? =2.
18. (The full mark of this small question is 12) A flower shop buys several roses from the farm every day at the price of one 5 yuan, and then sells them at the price of 10 yuan. If it is not sold out that day, the remaining roses will be disposed of as garbage.
(1) If a flower shop buys 17 roses a day, find the analytic function of the profit y (unit: yuan) and the demand n (unit: branches, n∈N) of that day. ?
(2) Flower shop records 100 days? The daily demand of roses (unit: branches) is summarized in the following table:
Daily demand number141516171819 20
Frequency10 201616151310.
(1) Suppose the flower shop buys 17 roses every day during this 100 day, then what about this 100 day? Average daily profit (unit: yuan);
(2) If the flower shop buys 17 roses a day, the frequency of each demand recorded on 100 day is taken as the probability of each demand, and the probability that the profit of that day is not lower than that of 75 yuan is obtained.
The problem of propositional intention is relatively simple, which mainly investigates the probability of finding the average value of samples with a given sample frequency and finding the sum of mutually exclusive events with frequency as the probability.
Analysis (1) Daily needs? When, profit? =85;
The demand of the day? When, profit? ,
∴? About what? What is the analytical formula of? ;
(2) (1) In this 100 day, the daily profit of 100 day is 55 yuan, the daily profit of 20 days is 65 yuan, the daily profit of 16 day is 75 yuan, and the daily profit of 54 days is 85 yuan, so the average profit of this100 day is.
=76.4;
(2) The profit is not lower than that of 75 yuan, and only the demand on that day is not lower than 16, then the probability that the profit on that day is not lower than that of 75 yuan is
(19) (the full mark of this small question is 12) as shown in the figure, triangular prism? The middle and side edges are perpendicular to the bottom surface, ∠ ACB = 90, AC=BC= 12AA 1, and d is the midpoint of edge AA 1.
(1)? Proof: plane? Aircraft
(ii) Aircraft? Divide this prism into two parts and find the volume ratio of these two parts.
Propositional intention This topic mainly examines the determination and properties of vertical lines, lines and planes in space and the volume calculation of geometry, and examines the spatial imagination and logical reasoning ability. This is a simple topic.
Analysis (1) Understanding BC⊥ from the title? ,BC⊥AC？ ,∴? Face? And ∵ face? ,∴? ,
Know it from the title? ,∴? =? , that is? ,
Again? ,? ∴? Face? ∵ face? ,
∴ face Face? ;
(2) Set up pyramids? What is the volume of? ,? = 1, which is derived from the meaning of the question. =? =? ,
By prism? Volume? = 1,
∴? = 1: 1, ∴ plane? Divide this prism into two parts, and the volume ratio is 1: 1.
(20) (The full score of this small question is 12) Set a parabola? :? (? What is the point of > 0)? , alignment is? ,? For what? The last point is called? As the center, a circle with a radius? Turn it in Yu? ,? It’s two o’clock.
(1) What if? ,? What is the area of? , beg? The value and circle? Equation of;
(2) What if? ,? ,? Three point one line? Up, straight line? With what? Parallel, and then what? With what? There is only one thing in common. What is the origin of coordinates? ,? The ratio of distance.
Proposition Intention This topic mainly examines the basic knowledge such as the equation of circle, the definition of parabola, the positional relationship between straight line and parabola, the distance formula from point to straight line, the parallelism between straight line and straight line, and examines the idea of combining numbers with shapes and the ability to solve operations.
Analytical alignment? Yu? The focus of the axis is e, and the radius f of the circle is? ,
Then |FE|=? ,? =? , e is the midpoint of BD,
(Ⅰ)? ∵? ,∴? =? ，|BD|=？ ,
Let a (? ,? ), defined by parabola, |FA|=? ,
∵? What is the area of? ,∴? =? =? =? , the solution? =2,
∴F(0, 1),FA|=？ The equation of circle f is:
(Ⅱ)? 1∶ analysis? ,? ,? Three point one line? Go ahead. ∴? Is it a circle? The diameter of? ,
According to the definition of parabola? ,∴? ,∴? What is the slope of? Or-? ,
∴ Straight line? The equation is:? , ∴ lineages? Distance? =? ,
Set a straight line? The equation is:? , body double? Have to? ,
∵? With what? There is only one thing in common. ∴? =? ,∴? ,
∴ Straight line? The equation is:? , ∴ lineages? Distance? =? ,
∴ Where is the origin of coordinates? ,? The ratio of distances is 3.
Analysis 2 is set by symmetry? And then what?
Point? About the point? Symmetry:
Have to: straight line?
Tangent point?
straight line
Where is the origin of coordinates? What is the ratio of distance? .
(2 1) (the full mark of this small question is 12) Let the function f(x)=? ex-ax-2
(i) Find the monotone interval of f(x)
(ii) if a= 1, k is an integer, and when x >; 0，(x-k)？ f？ (x)+x+ 1 & gt； 0, find the maximum value of k.
Please answer any of questions 22, 23 and 24. If you do too much, score according to the first question. Please write down the question number clearly when you answer.
22.？ (The full mark of this small question is 10) Elective course 4- 1: Selected lectures on geometry.
As shown in the figure, D and E are the midpoint of AB and AC on the edge of △ABC, and the straight line d E intersects the circumscribed circle of △ABC and F and G. If CF∨AB, it is proved that:
(Ⅰ)? CD = BC
(ⅱ)△BCD∽△GBD。
Propositional intention This question mainly examines the basic knowledge such as the judgment of straight line parallelism and triangle similarity, and is a short answer.
Analysis (1)? ∫d, e is the midpoint of AB and AC, ∴DE∥BC,
∫CF∨AB，？ ∴BCFD is a parallelogram,
∴CF=BD=AD？ The connection AF and ∴ADCF are parallelograms,
∴CD=AF，
∫CF∨AB，？ ∴BC=AF？ ∴cd=bc；
(Ⅱ)? ∵FG∥BC,∴GB=CF，
According to (I), BD=CF, ∴GB=BD,
∫∠DGB =∠EFC =∠DBC，？ ∴△BCD∽△GBD.
23.？ (Full score for this small question 10) Elective course 4-4: Coordinate System and Parameter Equation.
Known curve? What is the parametric equation of? (? Is a parameter), with the coordinate origin as the pole. The positive semi-axis of the shaft is the polar axis to establish the polar coordinate system, curve? What is the polar coordinate equation? =2, the vertices of the square ABCD are all there? , while A, B, C and D are arranged in counterclockwise order, and the polar coordinate of point A is (2,? ).
(i) Find the rectangular coordinates of points A, B, C and D;
(Ⅱ) Let p be? Is there a problem? The value range of.
Proposition intention This question examines parameter equations and polar coordinates, which is an easy question type.
Analysis (Ⅰ) From what is known and available? ,? ,
,? ,
Namely A( 1,? )，B(-？ ， 1)，C(―― 1，―? )，D(？ ,- 1),
(2) Settings? , manufacturing? =? ,
then what =? =? ,
∵? ,∴? The value range of is.
24. (The full mark of this small question is 10) Elective course 4-5: Selected lectures on inequality.
Known function? =? .
(i) When? If, find the solution set of inequality ≥3;
(Ⅱ)? What if? ≤? Does the solution set of contain? , beg? The value range of.
Propositional intention This topic mainly investigates the solution of inequality with absolute value, which is a simple problem.
Analysis (Ⅰ) When? What time? =? ,
What time? When ≤2, it is determined by? ≥3? , the solution? ≤ 1;
When 2
What time? When ≥3, by? ≥3? ≥3, solution? ≥8,
∴? The solution set of ≥3 is {? |? ≤ 1 or? ≥8};
(Ⅱ)≤? ,
What time? ∈,? =? =2,
∴? , conditional? And then what? , that is? ,
So it meets the requirements? The value range of is.