1.？ Parity of function
(1) If f(x) is an even function, then f (x) = f (-x)? ;
(2) If f(x) is odd function and 0 is within its domain, then? F(0)=0 (can be used to find parameters);
(3) The parity of the judgment function can be defined in equivalent form: f (x) f (-x) = 0 or? (f(x)≠0)；
(4) If the analytic formula of a given function is complex, it should be simplified first, and then its parity should be judged;
(5) odd function has the same monotonicity in the symmetric monotone interval; Even functions have opposite monotonicity in symmetric monotone interval;
2.？ Some problems about compound function
Solving the domain of (1) composite function: if known? The domain of is [a, b], and the domain of its composite function f[g(x)] can be solved by the inequality a≤g(x)≤b; If the domain of f[g(x)] is known as [a, b], what is it? When the domain of f(x) is equivalent to x∈[a, b], find the range of g(x) (i.e.? The domain of f(x)); When learning functions, we must pay attention to the principle of domain priority.
(2) The monotonicity of the composite function is determined by "the same increase but different decrease";
3. Function image (or symmetry of equation curve)
(1) Prove the symmetry of the function image, that is, prove that the symmetry point of any point on the image about the symmetry center (symmetry axis) is still on the image;
(2) Prove the symmetry of the image C 1 and C2, that is, prove that the symmetry point of any point on C 1 about the symmetry center (symmetry axis) is still on C2, and vice versa;
(3) curve C 1: f (x, y) = 0, and the equation of symmetry curve C2 about y=x+a(y=-x+a) is f (y-a, x+a) = 0 (or f (-y+a,-x+a) =
(4) Curve C 1:f(x, y)=0 The C2 equation of the symmetrical curve about point (a, b) is: f (2a-x, 2b-y) = 0;
(5) If the function y=f(x) is constant to x∈R, and f (a+x) = f (a-x), then the image y=f(x) is symmetrical about the straight line x=a;
(6) The image of functions y = f (x-a) and y = f (b-x) and the straight line x=? Symmetry;
4. The periodicity of the function
(1)y=f(x) for x∈R, f(x? +a)=f(x-a)？ Or f (x-2a? )=f(x)？ (a>0) is a constant, then y=f(x) is a periodic function with a period of 2a;
(2) If y=f(x) is an even function, and its image is symmetrical about the straight line x=a, then f(x) is a periodic function with a period of 2 ~ a;
(3) If y=f(x) odd function, and its image is symmetrical about the straight line x=a, then f(x) is a periodic function with a period of 4 ~ a;
(4) If y=f(x) is symmetric about points (a, 0) and (b, 0), then the period of f(x) is 2? The periodic function of;
(5) If the image of y=f(x) is symmetrical (a ≠ b) about the straight lines x = a and x = b, then the period of the function y = f (x) is 2? The periodic function of;
(6) When y=f(x) equals x∈R, f(x+a)=-f (x) (or f(x+a)=, then the period of y = f (x) is 2? The periodic function of;
For other knowledge points, we should also summarize them separately. We can summarize the knowledge points according to the course catalogue (or chapter unit), such as the catalogue method.
Basic knowledge articles
One? Set and simple logic
(1) assembly
Simple logic
Two? Function concept and basic elementary function
(A) the concept and nature of function
(b) functional images
(3) Exponential function and logarithmic function
(D) Power function
(5) Functions and equations
(VI) Functional model and its application
(7) Inverse function
Three? Derivative and its application
(A) the concept and application of derivative
(B) the application of derivatives in function research
(3) definite integral
Four? Trigonometric function, identity transformation and triangle solution
(A) the concept of trigonometric function
(2) Images and properties of trigonometric functions
(3) trigonometric identity transformation
(4) Solving triangles
Five? plane vector
plane vector
Six? plural
plural
Seven? Order, limit
(A) the concept of sequence
(2) arithmetic progression and geometric progression
(3) Comprehensive application of sequences
(4) Limit
Eight? inequality
(A) inequality and the essence of inequality
(2) Unary quadratic inequality and fractional inequality
(c) Binary linear inequalities and simple linear programming
Basic inequality
Nine lines, nine planes, simple geometry and space vectors.
(a) spatial geometry
(2) the positional relationship between points, lines and surfaces
(3) The concept and operation of space vector
(D) the application of space vector
Ten? Lines and circles
linear equation
(2) Equation of circle
(3) The positional relationship between straight lines and circles, and between circles.
Eleven? Conical section
(1) ellipse
(2) hyperbola
(3) Parabola
(D) the unified definition of conic section
(5) The positional relationship between straight line and conic curve.
(6) Curves and equations
Twelve? Reasoning and proof
Reasoning and proof
Thirteen? algorithm
algorithm
Fourteen? statistics
statistics
Fifteen? Probabilistic preliminary
Probabilistic preliminary
Sixteen? Probability; possibility
Probability; possibility
Seventeen? Binomial theorem
(1) permutation and combination
(2) binomial theorem
Eighteen? Special lecture on geometric proof
Special lecture on geometric proof
Nineteen? Matrix sum transformation
Matrix sum transformation
Twenty? Coordinate system and parametric equation
Coordinate system and parametric equation
Twenty one? inequality
Selected inequality
In addition, you can also add some topics appropriately to consolidate the knowledge points you have learned:
Comprehensive monograph
(A) set and common logical language view
(B) Analysis of the function of the test center and the prospect of the college entrance examination.
(3) The application of derivatives;
(4) Analysis of trigonometric function test sites and the prospect of college entrance examination.
(5) On intersection and union in constant inequality problems.
(6) The application of function thought in sequence.
(7) Learning "Three-dimensional Geometry Proposition of College Entrance Examination"
(8) Analyze the analysis of geometry test sites and the prospect of college entrance examination.
(9) Analysis of test sites of counting principle and prospect of college entrance examination.
(10) Probability of College Entrance Examination and Analysis of Future Test Sites.
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Of course, you are a student with a hard mathematical foundation and have a good grasp of some knowledge points. The college entrance examination is coming, so we can spend less time summarizing the knowledge we have mastered and more time sorting out our weak links!
I believe that through systematic study and induction, your mathematics will improve steadily! I wish you a smooth college entrance examination!