The first part is set, mapping, function, derivative and calculus set mapping concept elements, relational operation between sets: intersection, union, complement axis, venn diagram, function image property certainty, mutual difference and disorder definition. The ternary image method defines the parity, periodic symmetry and monotonicity of the range property of the corresponding relationship. The defined field is symmetric about the origin, and odd function→ f (0) = is defined at x = 0. 2. Prove monotonicity: difference (quotient) and derivative method; 3. Monotonicity of compound function, basic inequality, boundedness of Nike function, trigonometric function, combination of numbers and shapes, derivative, power function, logarithmic function, trigonometric function, basic elementary function, abstract function, compound function assignment method, dichotomy of typical function and equation, mirror image method, application of distributed zero function of quadratic and cubic equation roots, establishment of function model, and expression of conceptual derivative of basic elementary function. Method of substitution found the relationship between the geometric meaning of analytic piecewise function and the positive and negative monotonicity of monotonicity derivative of physical meaning. Pay attention to the optimization problems in life. The period of monotonicity evaluation domain of application function is t, and odd function→ f (t) = f () = f (0). Monotonicity of compound function = 0: the property of cubic function increasing with different decreasing, the image and application of linear function, quadratic function and inverse proportional function, the property and application of translation transformation, symmetry transformation, folding transformation and expansion transformation, the image and its maximum transformation, the second part, the concept of trigonometric function and plane vector angle, the definition of trigonometric function at any angle, the relationship between trigonometric function and the same angle, the arc length formula of trigonometric function arc system, The relationship between the trigonometric function line of the sector area formula and the trigonometric function with the same angle induces the deformation and inversion of the formulas of formulas of trigonometric functions, angle and difference angle, as well as the substitution and simplification of "1", and the image definition domain of evaluating and proving the trigonometric function (constant deformation). The symmetry axis (except tangent function) passes through the highest point (or lowest point) of the function image and is a straight line perpendicular to the X axis, and the center of symmetry is sine and cosine function. The symmetric center of the tangent function is (0,0) (k ∈ z). Sinx function y = Sinx = cosine function y = Cosx tangent function y = tanxy = asin (wx+j)+b ① Images can be obtained by translating and stretching sine curves, but it should be noted that translating first and then stretching is different from translating first. (2) The image can also be drawn with five points; (3) Find the monotone interval by whole substitution (pay attention to the symbol of W); ④ Minimum positive period t =；; ⑤ Symmetry axis X =, and symmetry center is (,b)(k∈Z). The basic theorem of linear operation of plane vector concept geometric meaning The addition, subtraction, multiplication and division of coordinates represent the geometric meaning of scalar product. * * * line and vertical * * * line (parallel) vertical distance image ∨? =l？ x 1y2-x2y 1=0⊥？ =0? X 1x2+Y 1Y2 = 0 Discussion on the number of solutions of trigonometric cosine theorem area sine theorem Practical application S△ = ah = absinc = (where p =) The projection in the direction is ||||| cosq = \ o (a, \ s \ up5 (→ b, \ s \). Up5(.Up5(→ symmetry || = included angle formula Part III Sequence and inequality concept sequence represent arithmetic progression's analogy analysis methods with geometric progression: an = f (n) general term formula, mirror method, list method, recursive formula, arithmetic progression general term formula, summation formula, property judgment, an = a1+(n-/kloc-). Dan = a1qn-1an+am = AP+aranam = product of the first n terms of APAR and Sn = the first n terms (an > 0) TN = common recursive types and methods: geometric series {an+} construction of arithmetic progression ① an+1-an = = pan+q4pan+1an = an-an+1= 35kan+1= pan+qn geometric progression an≠0, Q ≠ 0sn = formula method: apply arithmetic, sum formula of the first n terms of geometric progression, sum in groups, add in reverse order, add in cracks, add in dislocation, common sum methods, properties of inequalities, simple linear programming inequalities, basic inequalities: ≤ sequence is a special function, objective function is a linear function: z = ax+byz =: construction slope z =: geometric meaning construction of distance application problem. Product value, and minimum application: one positive and two definite, three phases equal ≤≤≤≤≤The fourth part analyzes the equation position relationship between geometric dip angle and slope straight line. The change of dip angle coincides with the change of slope, and they intersect in parallel and vertically: a1b2-a2b1≠ 01a2+b x0) Two-point formula: y = kx+b = intercept. The distance from the intersection of two straight lines to the straight line: d =, the distance between parallel lines: d = the equation of circle; General equation of circle; The positional relationship between a straight line and a circle; The position of two circles. Or the solution of D < R curve and equation trajectory equation: direct method, definition method, correlation point method, definition of conic curve ellipse hyperbola parabola and standard equation property range, symmetry, vertex, focus, major axis (real axis), minor axis (imaginary axis), asymptote (hyperbola), directrix (parabola only) and symmetrical point B (2a-x/kloc-) Y)-Symmetry of points (A and B curves F (2A-X, 2B-Y2) about straight line AX+BY+C = 0 Part V: The position of solid geometric points and points in line space, line and plane; The point on the straight line is outside the straight line and inside the plane; The point outside the plane intersects the line outside the plane; Have nothing in common; There is only one thing in common; Points on the line intersect with the plane in parallel; Have nothing in common; Have nothing in common. Point straight line is out of plane, straight line is parallel in plane, intersecting in plane, parallel in plane, vertical relation is transformed into each other, straight line is transformed into each other, parallel line, parallel line, vertical line, vertical plane, vertical space geometry, cylindrical prism, regular prism, cuboid, cube frustum, frustum, pyramid, spherical triangular pyramid, tetrahedron, regular tetrahedron, side surface area, and two between surface areas. The plane formed by the volume length of the three views and the angular straight line of the space with the same height and width: (0,90) Range: [0,90] Range: [0, 180] Distance from point to surface Distance between straight line and plane Distance between parallel planes Transform the distance of space Part VI Statistics and Probability Statistics Random sampling lottery random number table method Simple random sampling system sampling stratified sampling * * Same features: sampling. Use samples to estimate the frequency distribution of population samples, estimate the frequency distribution table and frequency distribution histogram of population density curve, and estimate the correlation between population mode, median, mean variance and standard deviation variables. Linear correlation scatter plot regression binary linear contingency table (2×2) Basic properties of independent analysis probability The geometric probability of mutually exclusive events's classical probability of opposing events is calculated by random simulation method, and the probability p (a+b) = p (a)+p (b). Conclusion It is proved directly that the comprehensive analysis method is proved indirectly through causal reasoning and causal reasoning. Mathematical inductive reasoning proves that reasoning and proof are sufficient and unnecessary conditions, necessary and insufficient conditions, and the necessary and sufficient conditions are compound propositions or: púq and: pùq are not:? P guess the original proposition: if p is the inverse proposition of q: if q is p, no proposition: if? p？ Q inverse proposition: if? q？ P Mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit. Mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit, mutual benefit and mutual benefit.