The perfect score is 150. Examination time 120 minutes.
Precautions:
1. Before answering questions, be sure to fill in your name and admission ticket number at the designated position on the answer sheet.
2. When answering multiple-choice questions, the answer label of the corresponding question on the answer sheet must be blacked out with 2B pencil. If you need to change it, clean it with an eraser, and then choose to apply other answer labels.
3. When answering multiple-choice questions, you must write the answer in the position specified in the answer sheet with a 0.5mm black pen.
All questions must be answered on the answer sheet, and the answers on the test paper are invalid.
5. After the exam, return the test paper and the answer sheet together.
Reference formula:
If events A and B are mutually exclusive, then P(A+B)=P(A)+P(B).
If events A and B are independent of each other, then p (a b) = p (a) p (b).
If the probability of event A occurring in one trial is p, then the probability of event A occurring exactly k times in n independent repeated trials.
pn(K)= kmPk( 1 P)n-K
The volume of a sphere with radius r V= πR3.
1. Multiple-choice question: This topic is entitled *** 10, with 5 points for each question and 50 points for each question. Only one of the four options given in each small question meets the requirements of the topic.
(1) Complex number 1+ =
(A) 1+2i(B) 1-2i(C)- 1(D)3
Standard answer a
Problem analysis 1+ = 1+
The concept and operation of complex number in college entrance examination.
Error-prone to remind calculation errors.
The concept and calculation of complex numbers are simple questions. As long as the candidates are careful, they will not make mistakes.
(2) If it is an integer, then "all are even numbers" is "even numbers".
(a) Sufficient and unnecessary conditions (b) Necessary and insufficient conditions.
(3) Necessary and sufficient conditions (4) It is neither sufficient nor necessary.
Standard answer a
The test questions are analyzed evenly and fully; Even number means even number or even number means even number is not necessary, so choose a.
College entrance examination sites use number theory knowledge and then judge one by one according to the concept of necessary and sufficient conditions.
Error-prone reminder is that even numbers are even numbers or odd numbers.
Subject network preparation tips are even and easy to obtain; Give an example when you deny the necessary and sufficient conditions.
(3) the positional relationship between the circle O 1 and the circle O2 is
(a) separate (b) intersect (c) circumscribe (d) inscribe
Standard answer b
So, test analysis
The general equation and standard equation of the college entrance examination circle and the positional relationship between the two circles
Error-prone reminder intersection
The general equation and the standard equation of the circle are interactive, which tells us that we must master every knowledge point comprehensively.
(4) Assuming that the maximum value of the function y= is m and the minimum value is m, the value of is
(A) (B) (C) (D)
Standard answer c
If and only if the above formula is equal, the maximum value is the minimum value.
Mean value theorem of college entrance examination sites
Correct selection of error-prone reminders
In the preparation teaching of subject network, we should attach great importance to the deformation of mean value theorem and strengthen training.
(5) Assuming that random variables obey normal distribution N(3, a2), then =
(A) (B) (C) (D)
Standard answer d
The test analysis obeys the normal distribution N(3, a2), then the curve is symmetrical.
Significance and main properties of normal distribution of college entrance examination sites.
Properties of error-prone prompt normal distribution: curves about symmetry
According to the nature of normal distribution, the preparation tips of subject network are several knowledge points. Although this question only examines the concept, the error rate is quite high because the candidates do not pay attention to mastering every knowledge point comprehensively. This question tells us that we must master every knowledge point comprehensively.
(6) If the function defined on satisfies: For any existence, the following statement must be correct.
(a) for odd function (b) for even function (c) for odd function (d) for even function.
(8) suppose that the asymptote of hyperbola (A > 0, B > 0) is eccentric, and the hyperbolic equation is
(A) - = 1 (B)
(C) (D)
Standard answer c
Test analysis, so
Geometric properties of hyperbola in college entrance examination sites
Error-prone reminder elimination parameter
Geometric Properties of Conic Curves Required for College Entrance Examination.
(9) As shown in Figure (9), there are four small balls in the big ball with volume V, and the spherical surface of each small ball is larger than the center of the big ball and has only one intersection with the spherical surface of the big ball. The centers of the four small balls are the four vertices of a square with the center of the big ball as the center. V 1 is the volume of the intersection of small balls (the shaded part in the figure), and V2 is black in the inner and outer figures of the big ball.
(A)V 1= (B) V2=
(C)V 1 >V2 v 1 & lt； V2
Standard answer d
Let the radius of the big ball be, and the radius of the small ball be according to the meaning of the question, so this is the truth.
Volume formula and overall thinking of college entrance examination ball
Error-prone Tips and the Essence of Inequality
The combination of numbers and shapes is a sharp weapon to solve problems in college entrance examination, so we should grasp it well.
The range of (10) function f(x)= () is
(A) (B) (C) (D)
Standard answer b
If the test questions are analyzed by the special value method, then f(x)= cancel a,
So that the contradiction at that time eliminated C and D.
Trigonometric function and function range of college entrance examination sites
Error-prone reminders are not easy to solve problems with function values.
Tips for preparing for the exam in the subject network strengthen the special method-eliminating the method to solve the training of multiple-choice questions, save precious time and improve the accuracy.
2. Fill in the blanks: This big question has 6 small questions, each with 4 points and * * * 24 points. Fill in the answers in the corresponding places on the answer sheet.
(1 1) let the set U = {1, 2,3,4,5}, A = {2 2,4}, B = {3 3,4,5}, C = {3 3,4},
rule
Standard answer {2,5}
Test analysis,
Setting and Operation of College Entrance Examination Website
The concept of error-prone reminder complement
The preparation tips of the subject network should express the set, which is generally not wrong.
(12) Given the function f(x)= (when x 0), the points are continuous at x=0, then.
Model answer
The analysis of test questions is continuous at x=0.
That's why.
Concept and limit operation of continuous test sites in college entrance examination
Error-prone prompt
The function of preparing for the exam in the subject network constantly solves the problem of less knowledge points. Although this question only examines the concept, the error rate is quite high because the candidates do not pay attention to mastering every knowledge point comprehensively. This question tells us that we must master every knowledge point comprehensively.
(13) known (A >；; 0), then.
Standard answer 3
Test analysis
Calculation of index and logarithm of college entrance examination sites
Error-prone prompt
Tips for preparing for the exam in subject network strengthen the training of computing ability, the accuracy and speed of training.
(14) Let be the sum of the top n items in arithmetic progression {},,, then.
Standard answer -72
Test analysis,
Sum formula of arithmetic sequence in college entrance examination and application of arithmetic progression property.
Error-prone hints on the nature of arithmetic series
It is not difficult to prepare for the exam, but be careful not to lose points because of calculation errors.
(15) The line intersects the circle at points A and B, and the midpoint of the chord AB is (0, 1), then the equation of the line is.
Model answer
The analysis of the test questions is based on the center of the circle, the slope of the straight line is, the midpoint of the chord AB is, and the slope is, so it is obtained from the point inclination.
The positional relationship between straight line and circle in the center of college entrance examination
Error-prone prompt
Tips for preparing for the exam on the subject network Pay attention to the geometric properties of the circle.
(16) If someone has four kinds of light bulbs (each color has enough light bulbs), install them at six points, A, B, C, A 1, B 1 and C 1, as shown in the drawing (16).
Standard answer 2 16
Problem analysis is the bottom * * *,,
, according to the principle of classification and counting, according to the principle of classification and counting step by step.
The concept of arrangement and combination of test sites in college entrance examination can be used to solve some practical problems.
Error-prone reminder to master some basic methods of arrangement and combination, and analyze the problems from special circumstances to avoid mistakes.
Basic problem-solving methods of arranging and combining preparation tips of subject network
Third, the solution: this big question is ***6 small questions, with a score of ***76. The solution should be written in words, proof process or calculus steps.
(17) (the full score of this small question is 13, (1) small question 6, (2) small question 7).
Let the opposite sides of internal angles a, b and c be a, b, c, A= and c=3b, respectively. Find:
The value of (i); (ii) the value of cotb+cotc.
Standard answer solution: (1) Obtained by cosine theorem
= Therefore
(2) Solution 1: = =
From the sine theorem and the conclusion of (I)
therefore
Solution 2: The conclusion of cosine theorem and (i) is as follows.
=
therefore
In the same way.
therefore
The junior high school entrance examination mainly examines the basic knowledge such as cosine theorem, basic formula of trigonometric function, trigonometric identity transformation, and reasoning and operation ability. The simplification of trigonometric functions usually adopts the inverse operation of power decreasing, tangent chord and angle difference formula.
Error-prone prompts that positive cotangent is transformed into positive remainder.
Trigonometric function is an easy question in the college entrance examination, and it is the basis for us to get marks. .
(18) (The full score of this small question is 13, (1) small question 5, (2) small question 8. )
Party A, Party B and Party C play table tennis according to the following rules: the first game is played by Party A and Party B, then each game is played by the winner of the previous game, and the loser of the previous game says goodbye. According to this rule, the game will continue until one side wins two games in a row or plays six games. Assuming that the probability of winning or losing each game is zero, the winning or losing of each game is independent of each other. Q: (I) hit. (ii) A breakdown of the number of games played when the game is stopped and the expected e 。
Standard answer: order means that A, B and C win K games respectively.
(1) According to the probability formula that independent events occur at the same time and mutually exclusive events occurs at least once, the probability that the game has not stopped after three games is
All possible values of (ii) are 2, 3, 4, 5, 6 and.
Therefore, there is an allocation list.
2
three
four
five
six
P
Therefore (the Bureau)
This topic mainly examines the concepts and calculation of simultaneous independent events, mutually exclusive events, distribution table and mathematical expectation, and examines the ability to analyze and solve practical problems.
Error-prone reminders stop when you win two games in a row or play six games.
The exam preparation subject network suggests paying attention to probability application questions, and there must be probability application questions in the test questions in recent years.
(19) (The full score of this small question is 13, (1) small question 6, (2) small question 7. )
As shown in figure (19), B=, AC=, D, E are on AB and AC respectively.
，DE=3。 Now fold it into a straight dihedral angle along DE and find:
(i) the distance between AD and BC;
(ii) The size of dihedral angle A-EC-B (expressed by inverse trigonometric function).
Standard answer solution 1:
(i) In the answer (19), in the figure 1, because, BE∑BC. Because b = 90, AD⊥DE.
In fig. 2 (19), since A-DE-B is a straight dihedral angle, the bottom surfaces of AD⊥DE and AD⊥ DBCE are taken from.
There are also AD⊥DB. and DB⊥BC, so DB is the common perpendicular of straight lines AD and BC.
Find the length of DB. In the answer (19) diagram 1, it is from.
We also know that DE=3, so
because
If the spatial rectangular coordinate system is established in the positive direction of Y axis and Z axis, then D (0 0,0,0), A (0 0,0,4), E (0 0,3,0) will be the extension lines of DF⊥ce and cross CE.
In f, connect AF.
So set
, and (1)
And by (2)
At the same time (1) and (2)
Because, therefore, because, it is the plane angle of dihedral angle A-EC-B. Because there are reasons.
Therefore, the size of dihedral angle A-EC-B is
The college entrance examination center mainly examines the knowledge of straight lines, the positional relationship between straight lines and planes, the distance between straight lines on different planes, the ability of spatial imagination and thinking, and the ability to solve solid geometry problems by comprehensive method or vector method.
Error-prone prompt
It is suggested that the parallel, vertical and dihedral angles in solid geometry are the key points in the examination.
(20) (Full score for this small question 13. (1) The short question is 5. (2) The short question is 8. )
Set letters
(i) used to represent the sum respectively;
(2) When bc takes the minimum value, find the monotone interval of the function g(x)=.
Standard answer: (1) Because
And because the curve passes through the point (0,), so
The tangent of the curve is perpendicular to the axis, so.
(2) Derived from (1)
So when the minimum value is obtained. At this time, there is
therefore
So make, solve
while
while
while
Thus, the monotonic decreasing range of the function is (-∞, -2) and (2,+∞); The interval of monotonically increasing is (-2,2).
This topic mainly examines the concept and calculation of derivative, using derivative to study monotonicity of function, using monotonicity to find the maximum value and the properties of inequality.
Error-prone reminder cannot find the minimum value.
The application of the properties of derivative research function in the compilation of subject network has been a frequent test site since the use of new textbooks in 2003.
(2 1) (The full score of this small question is 12, (1) small question 5, (2) small question 7. )
If there are two points on the plane of graph (2 1) and sum, the moving point satisfies:
(1) Find the trajectory equation of a point:
(ii) If
By solving the equation, the coordinates of point P are
The college entrance examination center mainly examines the basic knowledge, basic methods and the ability to analyze and solve problems, such as the equation and geometric properties of the ellipse.
Error-prone reminders cannot associate conditions with.
Tips for preparing for the exam in subject network attach importance to the teaching and training of geometric meaning of analytic geometric conditions.
(22) (This small question is full 12, (1) small question 5, (2) small question 7. )
Let all positive number series {an} satisfy.
(i) If you find a3 and a4, guess the value of a2cos (without proof);
(2) Remember that n≥2 holds, and find the value of a2 and the general formula of the sequence {bn}.
Standard answer: (a) the reason
Therefore, the general term of conjecture is
Summarize all landowners
Know from the title
The inequality is 22k+ 1