Senior one:

Set and function

Content intersection and complement set, and power exponential pair function. 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.

trigonometric function

Trigonometric functions are functions, and quadrant symbols are labeled. 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;

The numb 1 records that triangle connecte the vertices in the center; The sum of the squares of the downward triangle, the reciprocal relationship is diagonal,

Any function of a vertex is equal to the division of the last two. The inductive formula is good, negative is positive and then big and small,

It is easy to look up the table when it becomes a tax corner, and it is essential to simplify the proof. Half of the integer multiple of two, odd complementary pairs remain unchanged,

The latter is regarded as an acute angle, and the sign is judged as the original function. The cosine of the sum of two angles is converted into a single angle, which is convenient for evaluation.

Cosine product minus sine product, angular deformation 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 of cosine, 1 subtract cosine to think of sine, power-on angle is halved, and power-on and power-off is a norm;

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;

sequence

Arithmetic ratio two series, the sum of n terms 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, but it is skillful to eliminate dislocation and transform.

Learn from each other's strong points and calculate the sum formula of split terms. Inductive thinking is very good, just do a program to think about it:

Counting two and seeing three associations, guessing proves indispensable. There is also mathematical induction to prove that the steps are programmed:

First verify and then assume, from k to k plus 1, the reasoning process must be detailed and affirmed by the principle of induction.

Senior two:

inequality

The solution to inequality is to use the properties of functions. 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.

Equation of straight line and circle

conic section