Math problem-solving skills in senior one: 1. The content of "set and function" is cross-complementary, and there are power pairs of functions. Parity and increase and decrease are the most obvious observation images. When the compound function appears, the law of property multiplication is distinguished. To prove it in detail, we must grasp the definition. Exponential function and logarithmic function are reciprocal functions. Cardinality is not a positive number of 1, and 1 increases or decreases on both sides. The domain of the function is easy to find. Denominator cannot be equal to 0, even roots must be non-negative, and zero and negative numbers have no logarithm; The tangent function angle is not straight, and the cotangent function angle is uneven; The real number sets of other functions have intersection in many cases. Two mutually inverse function have that same monotone property; The images are symmetrical with y = x as the symmetry axis; Solve the very regular inverse solution of substitution domain; The domain of inverse function, the domain of original function. The nature of power function is easy to remember, and the index reduces the score; Function properties are exponential, odd mother odd child odd function, odd mother even child even function, even mother non-parity function; In the first quadrant of the image, the function is increased or decreased to see the positive and negative. Second, the trinity of point, line and surface in Solid Geometry is represented by cylindrical billiards. All distances start from points, and all angles are made of lines. Vertical parallelism is the key point, and the concept must be clear in the proof. Line, line, plane, plane, triple cycle. When the whole idea of the equation is solved, it becomes consciousness. Before calculation, it is necessary to prove and draw the removed figure. Auxiliary lines of solid geometry, usually vertical lines and planes. The concept of projection is very important and the key to solving problems. The dihedral angle and volume projection formulas of lines with different planes are vivid. Axioms are naturally three vertical lines, which solve many problems. Three, "Plane Analytic Geometry" directed line segment straight circle, elliptic hyperbolic parabola, parametric equation polar coordinates, the combination of numbers and shapes is called model. Descartes' viewpoint pair, point and ordered real number pair correspond to each other, which opens up a new way of geometry. The two ideas reflect each other and turn into ideas to fight the front line; The undetermined coefficient method is actually the idea of equations. Summarize three types, draw a curve to solve the equation, and give the curve of the equation and the relationship between the curves. Four tools are magic weapons with good coordinate parameters; Plane geometry can not be lost, find the complex number of rotation transformation. Analytic geometry is geometry, smug. The figure is intuitive and detailed, and the number is a number shape. Trigonometric functions Trigonometric functions are functions, and quadrant symbols are marked. Function image unit circle, periodic parity increase and decrease. The same angle relation is very important, and both simplification and proof are needed. At the vertex of the regular hexagon, cut the chord from top to bottom; Write the number 1 in the center to connect the vertex triangles; The sum of squares of a downward triangle, the reciprocal relationship is diagonal, and any function of the vertex is equal to the division of the latter two. The inductive formula is good. When the negative is positive, it becomes larger and smaller, and becomes an acute angle, so it is easy to look up the table. Simplification and proof are indispensable. Semi-integer multiple of two, the odd parity is unchanged, the latter is regarded as an acute angle, and the symbol is judged by the original function. The cosine value of the sum of two angles is converted into a single angle for easy evaluation, and the sine product is subtracted from the cosine product, which distorts the variable angle formula. Sum and difference products must have the same name, and the complementary angle must be renamed. The calculation proves that the angle is the first, pay attention to the name of the structural function, the basic quantity remains unchanged, and it changes from complexity to simplicity. Guided by the principle of reverse order, the product of rising power and falling power and difference. The proof of conditional equality, the idea of equation points out the direction. Universal formula is unusual, rational formula is ahead. The formula is used in the right and wrong direction, and the deformation is used skillfully; 1 add cosine to think cosine, 1 subtract cosine to think sine, power rise angle is halved, and power rise and power drop are a specification; The inverse function of trigonometric function is essentially to find the angle, first to find the value of trigonometric function, and then to determine the range of angle value; Using right triangle, the image is intuitive and easy to rename, and the equation of simple triangle is transformed into the simplest solution set; Note: The formulas of sum-difference multiplication, multiplication and difference are no longer required to be recited. The formulas in this chapter should be memorized by reasoning, and the methods of solving inequalities in inequalities should be strengthened, and the properties of functions should be used. The unreasonable inequality of the opposite side is transformed into a rational inequality. From high order to low order, step-by-step transformation should be equivalent. The mutual transformation between numbers and shapes helps to solve problems. The method of proving inequality is powerful in real number property. Difference is compared with 0, and quotient is compared with 1. Comprehensive method with good direct difficulty analysis and clear thinking. Non-negative common basic expressions, positive difficulties are reduced to absurdity. There are also important inequalities and mathematical induction. Graphic function help, drawing modeling construction method. "Series" is the arithmetic difference between two series and the sum of n items in the general formula. Two finites seek the limit, and four operations are the other way around. The problem of sequence is changeable, and the equation is simplified as a whole calculation. It is difficult to sum series, and it is easy to transform and offset, learn from each other's strengths and calculate the sum formula of split terms. Inductive thinking is very good, just do a procedural thinking: one counts two or three associations, and guessing proves indispensable. There is also mathematical induction, the steps of proof are programmed: first verify and then assume, from k to k plus 1, and the reasoning process must be explained and affirmed in detail by the principle of induction. As soon as the imaginary unit I of the complex number comes out, the number set is extended to the complex number. A complex number and a logarithm, the real and imaginary parts of horizontal and vertical coordinates. Corresponding to a point on the complex plane, the origin is connected with it in the form of an arrow. The axis of the arrow is opposite to the X axis, and the resulting angle is a radial angle. The length of the arrow shaft is a model, and the numbers are often combined. Algebraic geometric triangles, try to transform each other. The essence of algebraic operation is I polynomial operation. The positive integer of I is the second time, and there are four numerical periods. Some important conclusions, cleverly remember the results. The ability of mutual transformation between reality and reality is great, and complex number equals transformation. Solve with equations and pay attention to the whole substitution. Judging the rules of addition parallelogram and subtraction triangle on the geometric operation diagram; Multiplication and division operations, reverse and forward rotation, expansion and contraction of annual module length. In triangular operation, it is necessary to distinguish between radiation angle and mode. It is very convenient to take a square and make a square by using Demofo formula. The radial angle operation is very strange, and the product quotient is used to sum the difference. The four properties are inseparable, equal sum module and * * * yoke, two will not be real numbers, and comparison size is not allowed. Complex numbers are very close to real numbers, so we should pay attention to the essential differences. The two principles of addition and multiplication in permutation and combination and binomial theorem are the laws that run through. What has nothing to do with order is combination, but what needs order is arrangement. Two formulas, two properties, two ideas and methods. Arrange and combine the summary, and the application questions must be transformed. It is common sense to arrange and combine together and choose the back row first. Special elements and positions should be considered first. Don't worry too much, and don't miss too much. Punching is a skill. Arrange combinatorial identities and define proof modeling tests. On binomial theorem, China Yang Hui Triangle. Two properties, two formulas, function assignment transformation.