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I. Collections and Functions

The content sub-orthogonal complements the set, also has the power to refer to the function. The nature of odd and even and increase or decrease, the most obvious observation image.

The compound function appears, the property multiplication rule is identified, if you want to prove it in detail, you must also grasp that definition.

Exponential and logarithmic functions, each of which is an inverse function. Base not 1 positive number, 12 sides increase or decrease the change.

The function defines the domain as a good request. The denominator cannot be equal to 0, the even-time root is nonnegative, 0 and negative numbers are no logarithm;

Tangent function angle is not straight, cotangent function angle is uneven;

The two reciprocal functions are the same, the monotone properties are all the same, the images are symmetrical and the y=x are symmetrical axes;

The solution is very regular, the inverse of the definition of the field of the inverse function, the definition of the domain, the original function of the range.

The properties of power function are easy to remember, indexation is about fractions, function properties look at exponent, odd mother Chizzichi function,

Odd mother and even function, even mother non-singular even function; in the first quadrant of the image, the function increases or decreases.

Second, "Trigonometric functions"

Trigonometric functions are function, quadrant notation coordinates.

function Image unit circle, periodic odd or even increase and decrease now. The relationship between the same angle is very important and the simplification proves that it is necessary.

The hexagonal vertices are cut from top to bottom chord, the center is numbered 1, and the vertex triangle is connected;

The downward triangular sum of squares, the reciprocal relationship is diagonal, vertex any function, equal to the following two eradication.

Induction formula is good, negative positive after the small, into a tax angle to look at the table, simplified proof of the indispensable.

The second half of the integer multiples, the odd constant, the latter as a sharp angle, the symbol of the original function of the sentence.

The cosine of the two angles is transformed into a single angle, the cosine product minus the sine product, and the change of the angular deformation.

And the difference of the product must have the same name, mutual residual angle variable names.

The calculation proves that the angle first, pay attention to the structure function name, keep the basic quantity unchanged, bondholders toward the simple change.

Reverse principle for guidance, ascending reduction and difference product. The conditional equation proves that the equation thought refers to Lu Ming.

The universal formula is not general, and the rational type is first. Formula and inverse use, the use of deformation and skillfully used;

1 cosine to think of cosine, 1 cosine to think of sine, power up a corner half, ascending descending it for fan;

The inverse function of trigonometric functions, in essence, is to seek the angle, first, the trigonometric value, and then the range of the angle value;

Using right triangle, the image is intuitive and good for changing the name, simple triangle equation, into the simplest solution set;

Third, "Inequality"

The way of solving inequalities, using the properties of functions. The irrational inequalities are referred to as rational inequalities.

The higher times toward the lower generation, the step-by-step conversion to be equivalent. The conversion between the numbers is a great help to the solution.

The real nature of the method of proving inequality is very powerful. The difference between the 0 and the size of the quotient and 1 compete.

The direct difficulty analysis is good, the thought clear synthesis method. Non-negative commonly used basic formula, the front is difficult to disprove the method.

There are also important inequalities, as well as mathematical induction methods. Graphical functions to help with drawing modeling constructs.

Iv. "series"

Equal and inferior than two series, the general formula N and. Two limited limit, arithmetic order change.

The series problem is more changeable, the equation is returned to the whole calculation, the sequence sum is more difficult, the dislocation phase elimination skillfully transforms.

Gaussian method, splitting sum formula calculation. Inductive thought is very good, make a program good thinking:

A second look at the three associations, guess the proof can not be less. There are also mathematical induction methods to prove the procedure:

First of all, verify and then assume that from K to K plus 1, the inference process must be detailed, inductive principle to affirm.

V. "Plural"

The imaginary unit I out, the number set expands to the plural. A plural pair of numbers, horizontal ordinate real imaginary part.

Corresponds to a point on a complex plane, and the origin is connected to it as an arrow. The shaft and the x-axis are positive, which is the radial angle.

The length of the shaft is a mold, often the number of shapes to combine. Algebraic geometry triangular, mutual transformation try.

The essence of algebraic operation has I polynomial operation. I the positive whole number of times mu, four numerical period now.

Some important conclusions, to memorize skillfully used results. The ability of virtual reality is large, the plural is equal to transform.

Using the solution of the equation, pay attention to the whole substitution technique. On the geometric chart, the addition parallelogram,

Subtraction Triangle Law, multiplication division of the operation, reverse direction to do the rotation, stretching the whole year modulus length.

The triangular operation must distinguish the angular and the modal. The Li formula is very convenient.

The angular operation is peculiar, and the difference is caused by the accumulation of quotient. Four properties are not, equal and modulo and conjugate,

Two would not be for real numbers, the comparison size is not advisable. Complex numbers are very close and must be noted for essential differences.

Vi. permutation, combination, two-term theorem

Two principles of addition multiplication, which runs through the constant law. The order-Independent is the combination, the requirement ordered is the arrangement.

Two formulas two natures, two kinds of thought and method. The combination of permutations and application problems must be transformed.

It is common sense to choose the back row before the arrangement is combined. Special elements and positions, first of all pay attention to more considerations.

Not heavy does not leak much thinking, bundle intervening spaces is the skill. Permutation combinatorial identities, define proof modeling test.

About Hi Shang theorem, China Yang Hui Triangle. Two properties two formula, function assignment transformation.

Seven, "Three-dimensional geometry"

Point line face Trinity, column cone billiard as representative. Distance from the point of departure, the angle is the line into.

Vertical parallelism is the focus, proving that the concept must be clarified. The line line and surface, three pairs between the cycle now.

The whole of the equation thought, and the consciousness dynamic cutting. Before calculating, it is necessary to prove that the drawing is drawn.

Three-dimensional geometric auxiliary lines, commonly used perpendicular and planar. The concept of projective is very important for solving problems.

Dihedral angle straight line, volume projective formula live. Axiom Nature three perpendicular, solves the problem a large area.

Eight, "Plane analytic geometry"

There are straight line circles, elliptic hyperbolic parabolic lines, parametric equation polar coordinates, and number-form combination called model.

Descartes ' point of view is that the point and ordered real number pairs, both of which correspond, create a new way of geometry.

The two kinds of ideas reflect, the thought of the former array, the determination of the undetermined coefficient method, is actually the thought of the equation group.

Three types of synthesis, draw a curve to find the equation, give the equation composition line, the Curve position Relationship Award.

Four Tools is a magic weapon, the coordinate thought parameter is good, the plane geometry cannot lose, the rotation transforms the complex number to beg.

Analytic geometry is geometric, and learning not to live. The graphic is intuitive, and mathematics is a mathematical form.