American Invitational Mathematics Examination, AIME

American Invitational Mathematics Examination, AIME Page contains practice problems from Number Theory, Algebra, Combinatorics, Geometry and Statistics.

American Invitational Mathematics Examinations, AIME

The students among the top 5% of the candidates who took the AMC 12, are invited to take the AIME. Cracking this Examination leads the students to the United States of America Mathematics Olympiad (USAMO).

Access the Past papers, mock tests, solutions, sequential hints and training resource for AIME I & II.

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What is AIME and How to prepare for it  

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  • Take a Mock Test for AIME I & II.
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Mock Tests, Past Problems- Solutions with Hints

Solutions of selected Problems from American Mathematics Invitational Examinations I & II.

AIME I – Topic-wise Past Problems

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    2015 – Problem 4 – Area of Equilateral Triangle

    2015- Problem 11- Perimeter of Triangle

    2015- Problem 13- Trigonometry

    2012- Problem 8- Solids

    2012- Problem 13- Circles and Triangles

    2008- Problem 2- Squares and Triangles

    2008 – Problem 5 – Cones and Circle

    2001 – Problem 7 – Incenter and Triangle

    1999 – Problem 2 – A Parallelogram and a line 

    1999 – Problem 4 – Squares and Triangles

    1997 – Problem 11 – Trigonometry and Greatest Integers

    1995 – Problem 7 – Trigonometry and Positive Integers

    1994 – Problem 10 – Right angled Triangle

    1994 – Problem 12 – Length and Inequalities

     

     

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    2012- Problem 9- Logarithm and Equations 

    2012- Problem 14- Complex numbers

    2009- Problem 2- Complex numbers

    2008- Problem 1- Percentage

    2008- Problem 3- Logic and speed

    2008- Problem 4- Equations and Integers

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    2015- Problem 1- Number Series

    2015- Problem 3- Cube of Positive Integers

    2015- Problem 10- Theory of Equations

    2012 – Problem 5 – Arrangement of Digits

    2010 – Problem 1 –  Probability of Divisors

    2000 – Problem 1 – Least Positive Integer Problem

    1999 – Problem 1 – Smallest Prime problem

    1999 – Problem 3 – Perfect Square Problem

    1999 – Problem 9 – Function of Complex Numbers

    1997 – Problem 1 – Odd & Even Integers

    1997 – Problem 3 – Two & Three Digit Numbers

    1995 – Problem 6 – Problem on Positive Integers

    1995 – Problem 8 – GCD & Ordered Pair

    1994 – Problem 13 – Complex roots and equations

    1984- Problem 12- Function and Equation

     

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    2012- Problem 3- Arrangements

    2010- Problem 4- Probability

    2009- Problem 9- Combinations

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    AIME II – Topic-wise Past Problems

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      2007:  Problem 23: Area of Pinwheel

       2008: Problem 23: Area of triangle and square

      2008: Problem 25: Area of Circle

      2009: Problem 25: Total Surface Area of a Cube

       2010: Problem 23: Circles and Semi-circles

       2011: Problem 20: Area of Trapezoid

       2011: Problem 25: Area of square and circle

      2012: Problem 24: Area of Star and Circle

       2012: Problem 25: Area of Triangle and Square

       2013: Problem 24: Area of square and pentagon

      2013: Problem 25: Rolling Ball Problem 

       2014: Problem 14: Area of Trapezium

      2014: Problem 20: Circles and rectangles

       2014: Problem 25: Circumference of a semicircle

       2015: Problem 21: Hexagon and Triangle

       2015: Problem 25: Area of square

       2016: Problem 25: Radius of semicircle

       2017: Problem 25: Area of circle

       2018: Poblem 20: Area of Triangle

       2018: Problem 24: Area of cross section of cube

       2019: Problem 2: Area of Rectangle

      2019: Problem 24: Menalaus Theorem

       

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      2011: Problem 13: Planes and Distance

      2009: Problem 23: Quadratic Equation

      2008: Problem 1: Percentage

      2008: Problem 4: Equations and Integers

       2010: Problem 2: Ratio and Proportion

      2010: Problem 21: Linear Equation

      2013: Problem 5: Mean and median calculation

       2013: Problem 15: Powers of numbers

      2014: Problem 24: Median

       2018: Problem 6: Time and Distance

       

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      2006: Problem 22: Largest and smallest numbers 

      2006:  Problem 25: Prime numbers

      2010: Problem 21: Page number counting

       2011: Problem 24: Parity

      2013: Problem 13: Representation of numbers in base 10

      2013: Problem 15: Powers of numbers

       2014: Problem 8: Test of Divisibility

       2014: Problem 21: Divisibility

      2014: Problem 23: Numbers

       2016: Problem 5: Divisibility

       2016: Problem 20: Least common multiple

       2016: Problem 24: Divisibility rule

       2017: Problem 7: Divisibility

      1985: Problem 13: GCD and Sequence

      1984: Problem 12: Function and Symmetry

       

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       2008: Problem 14: Arrangements

       2009: Problem 13: Probability of an event

       2010: Problem 24: Probability

       2012: Problem 10: Permutation and basic counting

       2018: Problem 11: Probability

      2018: Problem 19: Sign Pyramid

       2019: Problem 25: Stick and Dot Method

       

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       2008- Problem 3: Logic and Speed

       

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