Mike is good at math.

此题应为:Mike is (doing) (well) (in) math.
你所说的“Mike is do well in English”从语法上来讲是不对的,因为be动词is后必须要跟现在分词,也就是doing,而不是do.也可以用一般现在时,如果改成Mike does well in English就是对的.
第二句“Mike as good as English”,没有be动词或行为动词做谓语,语法上有错误,而且意思也不通,一般“as...as...”是指和...一样,比如as tall as Tom(和汤姆一样高).
此题是考查“擅长,精通……”的用法,一般有以下几种表述：
be good at sth.
do well in sth.
be skilled in sth.
be expert in sth.