SOF IMO study plan

SOF IMO · Give each week a clear focus.

8 weeks · About 6 hours per week

Week 1

Mathematical reasoning and logical ability

Diagnose current strengths by solving 25 mixed IMO-style problems under timed conditions and logging error types (algebra, combinatorics, geometry, number theory, logic).
Classify each logged error as conceptual, procedural, or careless, and rank the three weakest sub-areas.
Build a personal formula and theorem sheet covering core algebraic identities, inequalities, and modular arithmetic facts.
Establish a weekly 6-hour schedule with two problem sessions and one review session.

A written diagnostic report listing error categories, ranked weak sub-areas, and a one-page theorem sheet.

Week 2

Solve 30 number-theory problems emphasizing divisibility, modular arithmetic, and prime factorization.
Apply the pigeonhole principle and parity arguments to at least 10 combinatorial-logic problems.
Write full proofs for 8 selected problems, checking each step for logical gaps.
Review and correct all errors from week 1's diagnostic.

A proof portfolio of 8 complete written solutions with self-assessed correctness notes.

Week 3

Solve 25 algebra and inequality problems, including AM-GM, Cauchy-Schwarz, and substitution techniques.
Practice constructing counterexamples to test the validity of conjectures.
Complete 10 logic puzzles involving truth-tellers, knights-and-knaves, and deductive elimination.
Time 15 problems at competition pace and record completion rates.

A timed log of 15 solved problems with accuracy rate and average time per problem.

Week 4

Solve 20 combinatorics problems covering counting, permutations, and inclusion-exclusion.
Develop a checklist for distinguishing counting over- and under-counting errors.
Complete a full 4-hour mock IMO paper under exam conditions.
Analyze mock results and identify recurring reasoning weaknesses.

A scored 4-hour mock exam with a written error analysis of every missed problem.

Week 5

Solve 20 geometry problems emphasizing angle chasing, similar triangles, and circle properties.
Practice drawing accurate diagrams and annotating them with known equalities.
Integrate geometry with algebraic methods by solving 5 coordinate or trigonometric geometry problems.
Review week 4 errors and re-solve them without hints.

A geometry solution set of 10 fully annotated proofs with diagrams.

Week 6

Solve 15 multi-step problems that combine two or more domains (e.g., number theory with combinatorics).
Practice writing rigorous induction proofs for at least 6 problems.
Complete 10 problems requiring construction of a general argument from special cases.
Refine the theorem sheet with newly learned lemmas.

A combined-domain problem set of 15 solutions with induction proofs included.

Week 7

Complete two 4.5-hour mock IMO papers on separate days under strict timing.
Score each mock using official-style marking and record domain-wise performance.
Re-solve all incorrect problems from both mocks and write corrected proofs.
Identify the two highest-frequency error types across mocks.

Two scored mock papers plus a corrected-solutions document for every missed problem.

Week 8

Consolidate all notes into a final one-page quick-reference sheet.
Solve 20 rapid-fire problems from the weakest sub-areas to build speed and confidence.
Complete one final 4-hour mock and compare results with week 7.
Set a post-exam improvement plan based on final performance data.

A final performance summary comparing mock scores across weeks 4, 7, and 8 with a written improvement plan.

Week 2: Complete the diagnostic report and proof portfolio of 8 solutions; verify all week 1 errors are corrected.

Week 4: Achieve at least 50% on the first full 4-hour mock IMO paper with a written error analysis.

Week 6: Demonstrate the ability to solve combined-domain problems with at least 70% accuracy on the 15-problem set.

Week 8: Show measurable improvement over week 7 mock scores and submit the final performance summary.