1. When sets A and B are known, did you notice the "extreme" situation: or; Did you forget to find a subset of the set?
2. For a finite set m with n elements, the number of subsets, proper subset, nonempty subset and nonempty proper subset is as follows.
3. Inverse laws:,.
4. The negation of "P and Q" is "non-P or non-Q"; The negation of "P or Q" is "non-P and non-Q"
5. The negation of proposition only negates the conclusion; No proposition is that conditions and conclusions are negative.
6. Several important properties of functions:
If a function has everything, then the image of the function is symmetrical about a straight line? Is an even function;
(2) If there are both, then the image of the function is symmetrical about a straight line; Functions and images of functions are symmetrical about a straight line;
③ Function and function image are symmetrical about a straight line; Functions and images of functions are symmetrical about a straight line; The function and the image of the function are symmetrical about the coordinate origin;
(4) If odd function is the increasing function in the interval, then it is also the increasing function in the interval; If an even function is a increasing function on an interval, it is a subtraction function on an interval;
⑤ Shift the image one unit to the left along the X axis to get the image of the function; The image of the function (obtained by translating the image of the function to the right along the X axis;
⑥ Translate the auxiliary image by one unit along the Y axis to obtain the image of function +a; The image of function +a is obtained by translating the auxiliary image down the Y axis by one unit.
7. When finding the analytic expression of the function and the inverse function of the function, is the domain of the function marked?
8. A useful conclusion between a function and its inverse function: the intersection of the original function and the inverse function image is not all on y=x (for example:); It can only be understood as the function value at x+a.
9. If the original function monotonically increases in the interval, there must be an inverse function, and the inverse function also monotonically increases; But functions have inverse functions and are not necessarily monotonous. When judging the parity of a function, have you noticed the necessary and sufficient conditions for whether the domain of the function is symmetric about the origin?
10. Be sure to pay attention to ">; 0 (or
1 1. Do you know the monotone interval of a function? (This function monotonically increases in or; Monotonically decreasing to or) This is a widely used function!
12. Remember that odd function y=f(x) defined on r must pass through the origin.
13. Monotonicity and parity of abstract functions must be solved by the definitions of monotonicity and parity. At the same time, we should understand the important method to prove the equation by using the inequality relation and the monotonicity of the function: f(a)≥b and f(a)≤b? f(a)=b .
14. When solving the logarithmic function problem, did you notice the limitation of real number and base? (The true number is greater than zero, and the cardinal number is greater than zero and not equal to 1) The letter cardinal number needs to be discussed.
15. Have you mastered the formula for changing the cardinal number and its deformation? ( )
16. Do you remember the logarithmic identity? ( )
17. "A quadratic equation with real coefficients has a real number solution" is converted into "".Have you noticed the necessity? If the original question doesn't point out that it is a "quadratic" equation, function or inequality, have you considered the possibility that the coefficient of the quadratic term may be zero? For example, have you discussed how to find the value range of A for everything when A = 2?
18. The important nature of arithmetic progression: if yes, then; Arithmetic
19. Important properties of geometric series: if yes, then; Equal proportion.
20. Have you found that when applying geometric series to find the sum of the first n terms, you need to discuss them in different categories. When?)
2 1. A property of arithmetic progression: Let be the sum of the first n terms of a sequence if and only if it is arithmetic progression.
(a, b are constants), and its tolerance is 2a.
22. Do you know what kind of "dislocation subtraction" method should be used for the summation of series? (If, among them, arithmetic progression and geometric progression are the sum of the top n items)
23. When using the formula for finding the general term of a series, an usually appears in the form of a segment, right? Have you noticed?
24. Do you remember the summation of split terms? (for example)
Superposition method:
Iterative multiplication:
25. When solving the trigonometric problem, did you notice the domain of tangent function and cotangent function? Notice the boundedness of sine and cosine functions? At △ABC, Sina & gt Simbo? A>b, is that right?
Generally speaking, if an absolute value or a square is added to a periodic function, its period will be halved. (For example, all cycles are, but all cycles are,)
27. Is the function a periodic function? (Neither)
28. Do you know the symmetry axis and center of sine curve, cosine curve and tangent curve?
29. Do you know how much 1 equals in a triangle? (
These are collectively called 1 substitutions), and various substitutions of the constant "1" are widely used.
30. In the constant deformation of a triangle, special attention should be paid to various transformations of angles (such as. )
3 1. Do you remember what the requirements of triangulation are? The formula with the least number of items, the least function types, the denominator without trigonometric function, and the value can be found must calculate the value)
32. Do you remember the general method of triangle simplification? (Analyze the differences from three aspects: function name, angle and operation. The common skills are: cutting strings, multiplying the power formula, and transforming with trigonometric formula to generate special angles. Different angles are the same, different names are the same, high order and low order. )
33. Remember some trigonometric functions with special angles?
( )
34. Remember the arc length formula and the sector area formula under the arc system? ( )
35. Auxiliary angle formula: (the quadrant of the angle is determined by the symbols of A and B, and the value of the angle is determined by) plays an important role in finding the maximum value and simplifying.
36. Use the inverse trigonometric function to express the inclination angle of a straight line, the included angle of two vectors, and the angle formed by two straight lines in different planes. , have you noticed their respective range and significance?
(1) The angles formed by straight lines on different planes, angles formed by straight lines and planes, and dihedral angles range from:
② The range of inclination angle, arrival angle and included angle of straight line is:
③ The included angle range of the vector is [0, π].
37. If so, what are the necessary and sufficient conditions?
38. How to find the modulus of a vector? What is the projection in the direction?
39. If the angle with θ is obtuse, then cos θ < 0, right? (The opposite must be eliminated)
40. Do you remember what the translation formula is? This is the most basic method of translating problems. It can also be concluded that if the image with y=f(x) moves |h| units to the left and |k| units to the upward, the translation vector is =(-|h|, |k|).
What is the standard writing format of 4 1. inequality solution set? (generally written as an expression of a set)
42. What is the general idea of solving fractional inequality? (Comprehensive score of transfer project)
43. How to find the absolute value of an inequality with two absolute values? (Double-sided square or classified discussion)
44. When finding the maximum value of a function with important inequalities and variants, have you noticed the conditions when A, B (or A, B are nonnegative) and "equal sign holds"?
45. How to discuss when solving inequalities with parameters? (especially the bottom sum of exponent and logarithm) After discussion, write: To sum up, the solution of the original inequality is ...
46. The general method to solve inequality with parameters is that "the definition of domain is the premise, the increase and decrease of function is the basis, and the classification discussion is the key."
47. The usual solution to the constant inequality problem: the monotonicity of the corresponding function, its main skills are the combination of numbers and shapes, the separation of variables and method of substitution.
48. The two chapters of "Straight Line and Circle" and "Conic Curve" in the textbook reflect that the essence of analytic geometry is to study the geometric properties of figures by algebraic method. (04 Shanghai college entrance examination questions)
49. Several forms of linear equations: point oblique type, oblique truncated type, two-point type, truncated moment type and general type, and their limitations (for example, point oblique type is not suitable for straight lines with non-existent slope, so when setting point oblique or oblique truncated type equations, we should first consider the situation with non-existent slope).
50. When setting the linear equation, the slope of the straight line can generally be set to K. Have you noticed that when the straight line is perpendicular to the X axis, the slope K does not exist? (For example, if a straight line passes through a point and the chord length cut by a circle is 8, find the equation of the straight line where this chord is located. Pay attention to this problem and don't miss the solution of x+3=0. )
5 1. When solving the feasible region of simple linear programming problem, we should pay attention to whether the region represented by inequality is above and below the corresponding line, including the points on the boundary. Judging by special points).
52. For two non-overlapping straight lines, there are
; .
53. The cross-sectional moment of the straight line on the coordinate axis can be positive, negative or 0.
54. The intercept of a straight line on the two coordinate axes is equal, and the linear equation can be understood as, but don't forget that when a=0, the intercept of a straight line y=kx on the two coordinate axes is 0 and equal.
55. There are two ways to deal with the positional relationship between a straight line and a circle: (1) the distance from a point to a straight line; (2) The linear equation and the square equation are simultaneous, and the discrimination method is adopted. Generally speaking, the former is simpler.
56. To deal with the positional relationship between circles, we can use the relationship between the center distance and radius of two circles.
57. In a circle, pay attention to the right triangle composed of radius, half chord length and chord center distance.
58. What is the coordinate formula of fractional points? (The starting point, midpoint, equinox and numerical value should be clear) Did you notice when you solved the problem with the fixed point?
59. Do you know the equation of curve system? Linear system equation? Equation of circle system? The focus of the elliptic system and the asymptote of the hyperbolic system?
60. The cosine equation obtained by the intersection of two circles is obtained by subtracting the quadratic term from the equation of two circles. X0x+y0y=r2 represents the tangent of the point (x0, y0) on the circle x2+y2=r2. If the point (x0, y0) is outside the known circle, what does x0x+y0y=r2 stand for? (Tangent chord)
6 1. Do the three parameters A, B and C in the elliptic equation satisfy a2+b2=c2? What relation should the three parameters in hyperbolic equation satisfy?
62. In the ellipse, pay attention to the right triangle composed of the focus, the center of the circle and the endpoint of the short axis.
63. Remember the focal radius formula of ellipse and hyperbola?
64. In analytic geometry, when studying the positional relationship between two straight lines, it is possible that the two straight lines coincide, while in solid geometry, the two straight lines can generally be understood as non-coincidence.
65. When defining a problem with a conic section, did you notice the order of the numerator and denominator in the definition?
66. When solving a conic curve and a straight line at the same time, it should be noted that the coefficient of the quadratic term in the equation obtained after elimination is zero. Limitations of discriminant (finding intersection, chord length, midpoint, slope, symmetry and existence are all carried out below).
67. The path is the shortest chord in all focus chord of parabola.
68. The parabola y2 = 2px (p >; 0) If the chord parabola of the focus is a (x 1, y 1) and b (x2, y2), then the focal radius formula | ab | = x1+x2+p.
69. If A (X 1, Y 1) and B (X2, Y2) are two endpoints of the chord of the conic C: F (X, Y) = 0, then F(x 1, y 1)=0. When the midpoint and slope of a chord are involved, the point difference method is often used as f (x 1, y 1)-f (x2, y2) = 0 to find the relationship between the midpoint coordinates of chord AB and the slope of chord AB.
70. What is the main method to make the plane angle of dihedral angle? (Definition method, three vertical theorem method, vertical plane method)
7 1. What is the conventional method to find the distance from point to surface? (direct method, volume transformation method, vector method)
72. The key to finding the spherical distance between two points is to find the spherical central angle.
73. Some commonly used conclusions in solid geometry: the height of a regular tetrahedron with a side length of V=.
74. The area projective theorem indicates the projective area and the original area.
75. When using "translation method" to solve the angle formed by straight lines on different planes, it must be noted that the angle obtained after translation is the required angle or the rest angle.
76. For the folding of plane graphics and the unfolding of three-dimensional graphics, we should pay attention to the "invariance" and "invariance" of geometric elements before and after folding and unfolding.
77. When is the projection of the prism vertex on the bottom surface the inner heart, outer center, vertical center and center of gravity of the bottom surface?
78. The laws to solve the permutation and combination problem are: element analysis, position analysis-adjacent problem binding method; Interpolation method for non-adjacent problems: single-line method for multi-line problems; Positioning problem priority method; Classification of multivariate problems; Ordered distribution problem method; Select a question first, and then return; At least the most problems, indirect method.
79. Is the term with the largest coefficient, the maximum coefficient of a term and the maximum binomial coefficient of a term the same concept in the binomial theorem?
80. Can we use "assignment method" and "transformation method" when solving the algebraic sum of the coefficients of binomial expansion, and can we use "general formula method" and "structural analysis method" for specific items?
8 1. Pay attention to some characteristics of binomial (such as; )。
82. What are the applicable conditions of formulas P(A+B)=P(A)+P(B) and P(AB)=P(A)P(B)?
83. Simple random sampling and stratified sampling are similar in that the probability of each individual being drawn is equal.
84.= 0 is a necessary and sufficient condition for the function y=f(x) to have an extreme value at x=x0.
85. Note that the derivative value of a point on the curve is the slope of the tangent. (Geometric meaning of derivative)
86. What are the special solutions to direct questions (multiple choice questions and fill-in-the-blank questions)? (direct method, combination of numbers and shapes, specialization method, reasoning analysis method, exclusion method, verification method, estimation method, etc.). )
87. What are the most basic requirements when answering application questions? (Examining questions, identifying keywords in questions, setting unknowns, listing functional relationships, substituting initial conditions, indicating units, and answering)
88. The common methods for solving trajectory equations are: direct method, undetermined coefficient method, definition method, transfer method (correlation point method), parameter method, etc.
89. Because the college entrance examination is marked by computer, we must try our best to make the handwriting neat and the paper clean, and remember to answer the questions in the designated area.
90. Keeping a good attitude is the key to play the college entrance examination well!