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So you have got a year?!!

That is a good start. And a demanding one. All good starts are demanding by birth-right. They ask you to do more in the subsequent days. This article is mainly targeted at class 12 pass-outs who are targeting I.S.I. 2012 (or those 12th graders who are able to devote some serious time to mathematics).
Target to solve 100 problems a day (no less). You DO NOT HAVE 365 DAYS. Actually it's about 360 days (counting 2012 to be a leap year and assuming I.S.I. entrance to be held in first week of May). So really we are looking at some 36000 problems in the coming year and trust me that is sufficient to get you there.
Wake up at 5 in the morning. Do about 5 hrs of mathematics. In the afternoon devote 2-3 hours. Same in the evening. That is sufficient for 100 problems a day. That is sufficient as far as time management is concerned.
The books you need to solve->

1. TMH IIT Math and M.L. Khanna IIT Math books make about 20000 problems together. They are important because they are comprehensive.
2. I.S.I. 10+2 Test of Mathematics has about 1500 problems (along with Test Papers)
3. Excursion in Mathematics + Challenges and Thrills in Pre college mathematics together have about 2000 problems.
4. Algebra - Hall and Knight (or better Barnard Child), Complex Numbers from A to Z, (2000 problems)
5. Trigonometry - Loney (about 1000 problems)
6. Coordinate Geometry - Loney (about 1000 problems)
7. Calculus - A combined effort of Apostle, Maron, Piscunov, Tarasov (about 4000 problems)
8. Mathematical Circles, Combinatorics by Brualdi, Selected Problems by yaglom, Problem Solving Strategies by Arthur Engel, IMO compendium, Functional Equation by Venkatchala, Inequalities of Little Mathematical Library and Venkatchala, Number Theory by Burton or Zuckermann should account for the rest 4000-5000 problems.

Note that some problems will need superb intellectual effort, some will ask for tidy computation. So the key is to distribute all kinds of problems in a day. Try about 20 challenging problems per day. Rest 80 should be normal (or subnormal) stuff.

All the best and keep working!

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