Inequality and function, trigonometric function and solution triangle, 3 solid geometry, 4 series, 5 permutation and combination and probability, 6 derivative. Combining inequality with function, this paper examines the establishment of definition domain, value domain and constant. Trigonometric function and solving triangle, investigate the mutual transformation of figure, period and angle, value domain and definition domain. Proof of vertical parallel relationship among solid geometry, line, line surface and surface. There are three commonly used methods to solve dihedral angle, namely, the method of co-edge perpendicularity, the method of projected area ratio and the method of normal vector application, so we should master the spatial rectangular coordinate system flexibly. The summation of sequence, arithmetic difference, geometric series and the solution of general terms all need to use some classical methods flexibly, such as adding split terms, superposition and elimination.