AIME Study Guide 2026
Everything you need to pass the AIME exam in one place: the exam format, every topic to study, real practice questions with explanations, flashcards, and full-length practice tests. Free, no sign-up needed.
📋 AIME Exam Format at a Glance
45
Questions
180 min
Time Limit
60.00%
Passing Score
📚 AIME Topics to Study (22)
Inequalities and Optimization · 7 cardsInequalities and Optimization · 7 cardsInequalities and Optimization · 7 cardsAlgebra · 6 cardsAlgebra · 6 cardsAlgebra · 6 cardsGeometry · 6 cardsGeometry · 6 cardsGeometry · 6 cardsPolynomials and Functions · 6 cardsPolynomials and Functions · 6 cardsPolynomials and Functions · 6 cardsSequences and Series · 6 cardsSequences and Series · 6 cardsSequences and Series · 6 cardsTrigonometry and Complex Numbers · 6 cardsTrigonometry and Complex Numbers · 6 cardsTrigonometry and Complex Numbers · 6 cardsCombinatorics · 5 cardsMathematical Reasoning · 5 cardsNumber Theory · 5 cardsProblem-Solving Strategies · 5 cards
✍️ Sample AIME Questions & Answers
1. In the Fibonacci sequence 1,1,2,3,5,8,13,…, what is the 9th term?
✓ 34
Continuing: 1,1,2,3,5,8,13,21,34; the 9th term is 34.
2. If a + b = 5 and ab = 3, what is a^3 + b^3?
✓ 80
Using the identity a^3+b^3=(a+b)^3-3ab(a+b)=125-45=80.
3. The roots of 3x^2 - 5x + 1 = 0 are r and s. Find r^2 + s^2.
✓ 19/9
r+s=5/3, rs=1/3; r^2+s^2=(r+s)^2-2rs=25/9-2/3=25/9-6/9=19/9.
4. Find the 10th term of the arithmetic sequence 3, 7, 11, 15, …
✓ 39
a_n=3+(n-1)×4; a_10=3+36=39.
5. What is the sum of all positive integers less than 50 that are divisible by 7?
✓ 168
The integers are 7, 14, 21, 28, 35, and 42. Their sum is 7+14+21+28+35+42= 147.
6. For positive reals x and y with x + y = 1, what is the minimum value of 1/x + 1/y?
✓ 4
1/x + 1/y = (x+y)/(xy) = 1/(xy) ≥ 4 since xy ≤ (x+y)²/4 = 1/4, with equality when x = y = 1/2.
🎯 Free AIME Practice Tests
Inequalities and Optimization · 7 questionsInequalities and Optimization · 7 questionsInequalities and Optimization · 7 questionsGeometry · 6 questionsAlgebra · 6 questionsGeometry · 6 questionsAlgebra · 6 questionsTrigonometry and Complex Numbers · 6 questionsAlgebra · 6 questionsGeometry · 6 questions
📖 AIME Guides & Articles
- AIME Exam Guide: Prep, Format & Practice Tests 2026
- AIME Cut Off Scores and Exam Tips to Qualify
- AIME Math Skills: Careers and Job Market Advantages
- AIME Training Programs: How to Prepare for the American Invitational Mathematics Examination
- AIME Exam Prep: Study Guide, Problem Types, and How to Actually Get Better
- AIME Math: Subject Knowledge You Need to Pass
- AIME Exam Eligibility Guide
- AIME Practice Test PDF (Free Printable 2026)
Your AIME Study Path
1. Learn with Flashcards → 2. Drill Practice Tests → 3. Take the Full Exam Simulation