Three methods, which are approximate Lie symmetry method, approximate Noether symmetry method and approximate Mei symmetry method, are adopted to study the first order approximate symmetries and approximate conserved quantities of a typical perturbed mechanical system. Six identical first order approximate symmetries and approximate conserved quantities of the typical perturbed mechanical system are obtained by approximate Lie symmetry method and approximate Noether symmetry method, but only five of them can be obtained by approximate Mei symmetry method.