The best way to cover class 11 portion is simply start with NCERT and just one reference book for each subject.
Mathematics - RD Sharma
Physics - Concepts of Physics HV Verma
Chemistry - Just NCERT
Since, you just want to invest one month and you want to brush up the concepts, these books are enough.
I hope this helps.
Dear Aspirant ,
If you want to revise Class 11 portion in 1 month , then you should try to make your notes so that you can use in that month . It should include all the formulas , all the important questions . You can also buy Careers360 JEE Crash Course which includes both Class 11 and Class 12 syllabus .