I set, simple logic, reasoning and proof

1, the elements in the set are deterministic, different and out of order.

2. When describing the set, we must pay attention to the representative elements, and distinguish whether it is a point set or a number set.

3. Whether to ignore the situation when analyzing subsets or proper subset (or application conditions).

4. When solving the set problem, we should pay attention to the classified discussion. Don't forget to use the number axis or venn diagram to solve, and pay attention to whether the endpoint values are equal.

5. The four propositions and their relations are mutually negative, and the propositions are the same as true and false. How to judge the truth of compound proposition?

6. "No proposition" and "No proposition" are two different concepts. The negation of the proposition is "non-P", which negates the conclusion of the proposition. No proposition denies the condition and conclusion of the original proposition "If P is Q" at the same time.

7. What is the negation of full name proposition and proper name proposition? If the full name proposition is true, it is necessary to prove that all conditional conclusions are true. As long as there are counterexamples, the full name proposition can be judged to be false. A special proposition can be judged as true as long as it finds a condition that makes the conclusion valid, and it can be judged as false only if it proves that all the conditions can't make the conclusion valid.

8. The concept and judgment of necessary and sufficient conditions (definition method, setting method). The judgment of the necessary and sufficient relationship can be transformed into a proposition to judge its negation, or it can be based on counterexamples or the particularity of the problem.

9. When judging the necessary and sufficient relationship of conditions, we should make clear the difference between sufficient conditions and necessary conditions, and consider the problem comprehensively and accurately, so that there can be more than one sufficient condition or necessary condition for the conclusion to be established.

10. What are the forms of reasoning? What are the common proof methods? Have you mastered the requirements of each proof method?

Second, functions, derivatives and inequalities

1 1. Do you understand the concepts of mapping and function? In the mapping, have you noticed the arbitrariness of the elements in A and the uniqueness of the corresponding elements in B?

12, three elements of function and three types of questions. Note that the definition domain and value domain are non-empty number sets; Definition domain and value domain should be written in the form of set or interval.

13. Did you pay attention to the principle of "domain priority" when solving function problems?

14, is the domain marked when finding the analytical expression of the function? When judging the parity of a function, we should first check whether the domain of the function is symmetrical about the origin.

15. When judging the monotonicity of a function (finding monotone interval), do you want to find the domain first? Whether or not the symbols ""and "or" were mistakenly added between monotonous intervals.

16. What is the method to judge the monotonicity of a function? (definition, image, derivation). The judgment of monotonicity of composite function follows the principle of "increasing the same while reducing the differences". Have you mastered the method of finding the parameter range of known function monotonicity?

17, pay special attention to the reversal of monotonicity and parity of functions (compare sizes, solve inequalities, and find parameter ranges).

18, remember the following conclusion?

① If the function f (x) satisfies f (a+x)= f (a-x) or f (x)= f (2a-x), then the image of the function f (x) is symmetrical about x=a;

② If the function f (x) satisfies f (a+x)=-f (a-x) or f (x)=-f (2a-x), then the image of the function f (x) is symmetrical about the point (a, 0);

③ If the function f (x) satisfies f (x+T)= -f (x) or f (x+T)=, the period of the function f (x) is 2t.

19. What is the relationship between parity, symmetry and periodicity of a function? (knowing that two of them can ask for the third)

20. The relationship between the zero point of the function, the root of the equation and the abscissa of the intersection of the function image and the X axis. How to judge whether the function y=f (x) has zero in a given interval (a, b)? What does it have to do with a function having zero?

22. Have you mastered the relationship and application of the three "secondary"? We should use "two viewpoints" when finding the maximum value of quadratic function: look at the opening direction; Second, look at the relative position relationship between the symmetry axis and a given interval. The range of parameters can be transformed into the distribution of roots.

23. Special reminder: the two roots of quadratic equation ax2+bx+c=0 are inequality AX2+BX+C >; 0(& lt； 0) The endpoint value of the solution set is also the abscissa of the intersection of the image of the quadratic function y=ax2+bx+c and the X axis.

24. Are you ready for the tool of "combination of numbers and shapes" to study function problems?

25. What are the transformations of function images? (translation, expansion, symmetry)

26. Have you mastered the image and monotonous interval of the function? How to use it to find the maximum value of a function? What is the relationship between finding the maximum value of a function with inequality?

27. Don't forget the "main parameter transposition" of the problem of constant establishment, pay attention to verifying whether the equal sign is established, and pay attention to the method of separating parameters.

28. What problems should be paid attention to when solving fractional inequalities? (The denominator cannot be divided, and it is usually solved by general division. )

29. What problems should be paid attention to in solving exponential inequality and logarithmic inequality? (homology is solved by monotonicity. Note that the base is not 1, and the true value of logarithm is greater than 0)

30. The inequality | ax+b | c (<; Have you mastered the solution of c)? (Geometric meaning, zero division method, mirror image method)

3 1, we can use inequalities | a +b| | a |+| b |, | a +b| | a- c |+| c-b | | to solve (prove) some simple problems.

32. When using the basic inequality to find the maximum value, it is easy to ignore the conditions for its use. (One positive, two fixed, three phases, etc. )

33. Important inequalities refer to those inequalities. What is the chain of inequality derived from them?

34. Have you mastered the basic method of inequality proof? (Comparison, synthesis, analysis, reduction to absurdity, mathematical induction, monotonicity)

35. Pay attention to the common problems of linear programming. Is the geometric meaning of Z considered in the objective function of linear programming?

36. Do you remember the definition of derivative? What is its geometric and physical significance?

37. Have the derivative formulas of common functions and the derivative rules of sum, difference, product and quotient and the derivative rules of composite functions been recited?

38. What problems can be solved by using derivatives? What are the specific steps? (tangent, monotonicity, extreme value, maximum value)

39. What is the relationship between monotonicity of function and the sign of derivative function? (Sufficient condition) What is the relationship between the extreme point and the point where the derivative function value is 0? (Necessary condition)

40. Are you familiar with the image of cubic function y = ax3+bx2+cx+d (a 0)? How about monotonicity? What is its center of symmetry?

4 1. Can you draw an overview of the function according to its monotonicity and extreme value? How to find the extreme value (maximum value) of a known function in the dynamic interval with the help of the image of the function?

42. Given the number of function zeros, the number of intersection points of two function images, and the positional relationship between the two function images, how to find the parameter range?

Third, trigonometric functions.

43. Are there any misunderstandings about the concepts of quarter angle, acute angle, angle less than 900, negative angle and congruent corner? Are the angle system and the arc system mixed?

44. Have you remembered the two definitions of trigonometric function? (ratio definition, directed line segment definition)

45. Are you skilled in solving trigonometric inequalities with trigonometric function lines and images?

46. When calculating the value of trigonometric function, did you consider the value range of X? Are you used to solving problems with images or monotonicity?

47. Have you learned the trigonometric transformation formula by heart? (triangle relation of the same angle, inductive formula, trigonometric function of sum and difference of two angles, double angle formula)

48. When finding the known angle of trigonometric function, we should pay attention to the selection of trigonometric function and the mining of angle range.

49. In the process of triangle transformation, we should pay attention to the problems of "angle splitting, angle splicing" and chord cutting.

50. How to find the monotone interval, symmetry axis (center) and period of the function y = Asin(ωx +φ)? (pay attention to the positive and negative of a and ω when finding the monotone interval; Pay attention to the sign of ω when calculating the period)

5 1. Are you familiar with the five-point drawing? How to make an image of function y = Asin(ωx +φ)? How to determine the analytic expression of a function from an image? (The key is to determine a, ω and φ)

52. Have you mastered the transformation of y = sinx → y = Asin(ωx +φ)? How about the other way around?

53. Find the range of Y-function = sinx +cosx+ sinxcosx, and pay attention when changing elements.

54. When solving the triangle problem, the sine and cosine theorems should be applied to transform the corner points in time.

Fourth, sequence, mathematical induction.

55. Use the definition of arithmetic and geometric series: (1) Pay attention to the conditions.

56. When calculating the sum of the first n terms of geometric series, we should pay attention to two situations: q = 1 and q≠ 1.

57. How many methods are there to find the general term of series? (Formula, recurrence relation, proof of inductive conjecture). How many common methods are there for summation of series? (formula, dislocation subtraction, split term cancellation)

58. When it is known that Sn is looking for an, are n= 1 and n≠ 1 considered?

59. How to solve the problem of monotonicity and maximum value in series?

60. When applying mathematical induction, we should pay attention to the complete steps (two steps and three conclusions); Second, in the process from n = k to n = k+ 1, we should first use inductive hypothesis, and then flexibly use other methods such as comparison and analysis.

6 1, have you noticed the combination of series with functions, equations and inequalities?

Five, plane vector, analytic geometry

62. Remember the range of the inclination angle of the straight line. What is the relationship between the slope of a straight line and the inclination angle?

63. What is the direction vector of a straight line? What is the relationship between the direction vector of a straight line and its slope?

64. There are several forms of linear equations. What are their limitations? Have you noticed the usage of the form x = my+n?

65. Is intercept a distance? What does "equal intercept" mean?

66. What are the necessary and sufficient conditions for two straight lines A1X+B1Y+C1= 0 and A2x+B2y+C2=0 to be parallel and vertical respectively?

67. Remember the distance formula from a point to a straight line and the distance formula between two parallel lines.

68. How many symmetries are there in analytic geometry? How to solve (axial symmetry, central symmetry) respectively?

69. What are the general steps to solve the curve equation? What is the difference between finding the equation of a curve and finding the trajectory of a curve? What are the common methods to find the trajectory?

70. How to determine the positional relationship between a straight line and a circle (geometric method, algebraic method)? How to judge the positional relationship between straight line and conic curve?

7 1. Do you remember the relationship between A, B, C and E in the conic equation?

72. Have you noticed the application of the definition of conic in solving problems? Pay attention to the right triangle composed of radius inside the circle, chord center distance and half chord length; Characteristic triangle and focus triangle in ellipse and hyperbola.

Remember the common conclusions in circles, ellipses, hyperbolas and parabolas.

74. It is easy to ignore the condition that the distance | PF |≥c-a from the point p on the hyperbola to the corresponding focus f.

75. Remember the common problems in analytic geometry? (positional relationship, chord length, symmetry, midpoint chord, fixed point, alignment, fixed value, etc.). )

76. Remember the common problem-solving methods in analytic geometry (such as setting without seeking, point difference method, etc.). ). When using the point difference method to find the linear equation of the string, we should pay attention to the test.

77. In the calculation of straight lines and conic curves, the equation in the form of Ax2+Bx+C = 0 is often obtained by simultaneous elimination of quadratic curve equation and straight line equation. In the following calculation, two problems must be considered: ① the relationship between a and 0; (2) Have you ever thought about the relationship between the discriminant △ and 0?

78. Have you noticed the application of plane geometry knowledge in solving analytic geometry problems? How to mine implicit conditions in plane geometry? Have you noticed the application of vectors in analytic geometry?

79. Mathematical thinking methods commonly used in analytic geometry: method of substitution thought, equation thought, holism thought, etc. Will they be considered when solving problems?

Six, solid geometry

80. Space graphics should pay attention to two problems: first, correctly identify the positional relationship of points, lines and surfaces of space elements according to space graphics; Second, pay attention to changing the perspective, correctly judge the position, shape and quantitative relationship of spatial graphics, and find ideas or methods to solve problems.

Although solid geometry is the continuation and development of plane geometry, not all the conclusions of plane geometry can be unconditionally extended to solid geometry.

82. Are you skilled in making three views from geometric figures (or straight views) and restoring geometric figures (or drawing corresponding straight views) from three views? Have you noticed the virtual reality of lines?

83. In solid geometry, the relationship between parallelism and verticality can be transformed into: line ‖ line ‖ face ‖ face, line ⊥ line ⊥ face ⊥ face. What is the basis of these changes?

84. What is the range of angles formed by straight lines on different planes? What is the range of line and plane angle? What is the range of dihedral angle?

85. The key to finding the angle of a line is to find the projection of a straight line on the plane.

86. What are the methods of making the plane angle of dihedral angle? (Use the definition, the method of three vertical lines, and the vertical plane of the side that constitutes the dihedral angle). Have you mastered these methods?

87. Solid geometry problem solving is divided into three parts: homework, proof and calculation. Do you only pay attention to work and calculation, but ignore the link of proof?

88. Can you find the direction vector of a straight line and the normal vector of a plane? How to find the angle formed by straight lines on different planes, the included angle between lines and planes, and the dihedral angle by vector method?

89. When studying angles with vectors, did you find the relationship between vector included angle and graphic angle?

90. To solve solid geometry problems with the coordinates of space vectors, it is necessary to establish a reasonable coordinate system and a right-handed rectangular coordinate system, correctly write the coordinates of the required points, and pay attention to the transformation of vector expressions and graphic expressions.

9 1, do you remember the following conclusion:

① If ∠AOB=∠AOC, the projection of point A on the plane BOC is on the bisector of ∠BOC.

(2) Given that the angles formed by the diagonal of a cuboid and the three sides passing through the same vertex are respectively, there is cos2α+cos2β+cos2γ = 2.

The diameter of the circumscribed sphere of a cube or cuboid is equal to the length of its diagonal.

Seven, permutation, combination, binomial theorem, probability statistics

92. What is the key to choosing two principles? (classification or step by step)

93. Have you remembered the formula for calculating the number of permutations and combinations? Have you noticed their situation?

94. What is the nature of the combination number? How is it reflected in Yang Hui Triangle?

95. Do you know the difference and connection between permutation and combination? Have you mastered the common methods to solve the problem of permutation and combination? Don't forget to "reasonably classify, choose the back row first" when solving the comprehensive questions!

96. There are direct methods and indirect methods to solve the problem of permutation application. For combined application problems with additional conditions, we must pay attention to the classification of "including" and "not including", "at most" and "at least" or start from the opposite side!

The general term of binomial expansion is generally used to find the specific term of binomial expansion.

98. What are the main applications of binomial theorem?

99. Is there a difference between binomial theorem (a+b)n and (b+a)n expansion? Is the theorem inverse familiar?

100. Can the combination method be used to solve the problem of finding the coefficient of a specific term in binomial (or polynomial) expansion?

10 1, binomial coefficient and binomial coefficient are two different concepts. Assignment method is often used to solve the coefficient problem! Are you familiar with the method of finding the term with the largest coefficient (or the term with the largest absolute value of coefficient) in the expansion? Be sure to pay attention to solving the deformation of skills!

102, binomial coefficient sum of binomial expansion terms, binomial coefficient sum of odd terms, binomial coefficient sum of even terms, and binomial coefficient sum of odd (even) terms can you distinguish them? What about the coefficient sum of their terms?

103. Have you mastered all four common probability types? Have you noticed the premise of each probability application?

104. Can geometric quantities be correctly selected when calculating probability with geometric probability? (Line length, area, geometric volume)

105. The common thinking methods to solve the probability of random events are: be good at decomposing complex problems when thinking positively, and learn to use the method of reverse thinking when solving some problems. Have you noticed that there are two ways to solve the probability of "most" and "least" events: classification and indirect.

106, probability application questions Do you have the habit of writing "answers"? Are the steps to solve the problem complete? Can you write down all the steps to solve the allocation table problem? Have you completed the steps of finding the expectation and variance?

107, remember three commonly used distributions. What are the expectation and variance formulas of binomial distribution?

108. What are the properties of the normal density curve? Will you use its symmetry to find the probability?

109. What are the sampling methods? What is the connection and difference between them?

How many methods are there to estimate the population with samples? What is it?

1 1 1. How many statistical charts are there? Does the histogram of frequency distribution have the same meaning as the vertical axis in the bar graph? Can you correctly apply various statistical charts?

1 12. What are the numerical characteristics of the sample? Can you use them correctly to estimate the population?

1 13. What is the relationship between variables? Can you use the least square method to find the linear regression equation and make a prediction?

What is the basic idea of independence test? How to judge the possibility of the relationship between two variables according to the value of K2?

Eight, preliminary algorithm, complex number

1 15, can you correctly distinguish and use various block diagrams? (Start-stop box, input-output box, processing box, judgment box)

1 16. Can you correctly understand and use various algorithm statements? Are you familiar with the relationship between assignment statements and sequences?

1 17. Can we correctly judge the number of cycles in the cycle structure?

1 18, can you understand the given program block diagram and program? Can you give a correct calculation result? Can you correctly judge the missing condition?

Are you familiar with the relationship between complex numbers and real numbers? Remember the conditions in the definitions of real number, imaginary number and pure imaginary number?

120, the size of complex number cannot be compared. Remember the definition of complex equation and use it to solve complex problems.

12 1, remember the geometric meaning of complex numbers. Remember, on the complex plane, there is a one-to-one relationship among complex numbers, points and vectors.

122, can you skillfully add, subtract, multiply and divide complex numbers and Divison operations? This is a common question in the college entrance examination!

Nine, the basic method

123, is there any special way to answer multiple-choice questions? (estimation method, special value method, feature analysis method, intuitive selection method, reverse verification method)

124, when answering open-ended questions, thoroughly understand the new information in the questions, which is the premise of accurate problem solving.

125, when solving the multi-parameter problem, the key is to extract the parameter variables properly and try to get rid of the trouble of the parameter variables. Among them, the separation, concentration, elimination, substitution and anti-customer-oriented strategies of parameter variables seem to be the general methods to solve this kind of problems.

126. The classification discussion should be "neither heavy nor leaking, with a clear-cut stand", and finally make a summary.

127, when doing application problems, the units after operation should be accurate, and don't forget the "answer" and the range of variables; When you fill in the answers to the application questions in the blanks, you should write down the unit.

128, substitution idea, reverse idea, from special to general idea, equation group idea, whole idea, etc. Will you consider it when you solve the problem?

129. In solving problems, if you want to apply important conclusions that are not in the textbook, you should give simple proofs in the process of solving problems.