Problems 1-20: speed and fundamentals
Basic Operations, Order of Operations, Distributive Property, Compare Fractions/Decimals, Multiplication Shortcuts, Squaring Numbers, Conversions, GCD/LCM, Percent Problems, Mean/Median/Mode, Sums of Integers, Remainders, Consumer Math, and Number Theory.
Problems 21-40: algebra, geometry, and patterns
Powers, Substitution, Word Problems, Inverses, Absolute Value, Ratio/Proportion, Square/Cube Roots, Sets, Base Conversions, Solve Equations, Systems of Equations, Repeating Decimals, More Remainders, Perimeter/Area, Sequences, and Quadratic/Cubic.
Problems 41-60: advanced algebra and geometry
Laws of Exponents, Right Triangles, Coordinate Geometry, Regular Polygons, Inequalities, Geometry Theorems, Direct/Inverse Variation, Sequences and Series, Complex Numbers, Logs and Log Equations, Factorials/Permutations/Combinations, Probability/Odds, Conics, Binomial Theorem, Base Operations, Roots of Equations, and Polygonal Numbers.
Problems 61-70: upper-level contest topics
Volume/Surface Area, Greatest Integer, Remainder Theorem, Trigonometry, Determinants, Matrices, Vectors, Composite Functions, Bases with Decimals/Fractions, and Polar/Rectangular Coordinates.
Problems 71-80: advanced functions and calculus
Function Domains/Ranges, Modular Arithmetic, Limits, Derivatives, Slopes of Tangent Lines, Asymptotes, Critical Values, Max/Min Problems, Definite Integration, and Inverse Functions.
Examples
- Problems 1-20 lean on fast arithmetic, like 48 x 25 or 35^2.
- Problems 21-40 add algebra and patterns, like powers, roots, and repeating decimals.
- Problems 71-80 include calculus-style questions, like limits and derivatives.
References
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