AIME 7+ Topics (These topics will get you to 7+ on the AIME) 
Topic 
Additional Practice and Reference 
 Word Problems.
 Traditional word problems  Mixture, Work, or Rate, Time, and Distance.

 Problems in Elementary Mathematics  Lidsky (Algebra.6)

 Linear and nonlinear systems of equations.
 Equation solving, using symmetry, knowledge of basic identities, factorization, ... .

 A Problem Book in Algebra  Krechmar (Chapter 1)

 Logarithms and Exponents.
 Basic rules and definition, base change, in combination with equation solving and algebraic identities.

 A Problem Book in Algebra  Krechmar (Chapter 1)
 Problems in Elementary Mathematics  Lidsky (Algebra.4)

 Quadratics, Cubics, Polynomials and Vieta's Formulas.
 Quadratics, Cubics and higher polynomial problems involving roots, coefficients, and Vieta's formulas.

 Problems in Higher Algebra  Faddeev (Chapter 5.3)

 Complex Numbers (Basic).
 Basic complex number questions.

 Problems in Higher Algebra  Faddeev (Chapter 1.1 and 1.2)

 Arithmetic and Geometric Sequences and Series (Basic).
 Basic sequences and series questions generally involving arithmetic and geometric progressions and combinations.

 Chapter 7  A Problem Book in Algebra  Krechmar

 Combinatorial Counting (Basic).
 Basic combinatorial counting questions and the Binomial Theorem.

 Counting, 2nd Edition  Meng, Guan (2013)

 Triangle Geometry (Basic).
 Application of the most common theorems  Pythagorean, Similar Triangles, Angle Bisector Theorem, Area, Stewart's Theorem, Cevians, Medians, ... .

 Problems in Elementary Mathematics  Lidsky (Geometry A)

 Triangle Geometry (Mass Point).
 Application of all the techniques  Cevians (Medians, Altitudes, Bisectors,) Transversals, Splitting, ratios and in combination with elementary triangle theorems.


 Number Theory (Elementary).
 Modular Arithmetic, LCM, GCD, Primes, Base Arithmetic, Integer Algebra, ...

 Elementary Number Theory: A Problem Oriented Approach  Roberts
/ 
 Number Theory (Divisors).
 Application of the most common theorems  Number of Divisors, Sum of Divisors, Product of Divisors, "Revese" problems in each of these areas.

 Elementary Number Theory: A Problem Oriented Approach  Roberts

 Probability.
 Conditional, unconditional, geometric, and elementary combinatorial probabiility questions occur regularly, but not every year.

 Challenging Mathematics Problems with Elementary Solutions I  Yaglom
