AMC 12

AMC 12 包含的内容

The four AMC pillars — Algebra, Number Theory, Counting & Probability, and Geometry — plus the precalculus strand (trigonometry, logarithms, complex numbers) that only the AMC 12 tests.

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1. Algebra & Functions

   Sequences, polynomials, exponents, and word problems — the algebraic engine of the early-to-middle contest.

   5 个单元

   • Sequences & Series — Arithmetic, geometric, and recursively defined sequences and their sums.
   • Polynomials & Vieta's Formulas — Roots, coefficients, and the Remainder Theorem tie a polynomial to its factored behavior.
   • Exponents & Radicals — Laws of exponents and radical simplification.
   • Equations, Functions & Word Problems — Linear systems, absolute value, function evaluation, and rate/mixture modeling.
   • Summation Techniques — Closed forms and telescoping tricks for sums of squares, integers, and famous sequences.

2. Number Theory

   Integers up close: divisibility, primes, modular arithmetic, and the structure of the number line.

   4 个单元

   • Divisibility, Remainders & Digits — Counting multiples, divisibility rules, digit sums, and base representations.
   • Primes & Divisor Functions — Prime factorization drives divisor counts, divisor sums, and trailing zeros of factorials.
   • Modular Arithmetic & Cyclicity — Working mod n to find remainders, units digits, and last-two-digit patterns of powers.
   • GCD, LCM & Coprimality — The Euclidean algorithm, totients, and simultaneous congruences (CRT).

3. Counting & Probability

   Systematic counting — combinations, arrangements, distributions — and the probabilities they generate.

   4 个单元

   • Combinations & Binomial Coefficients — Choosing unordered groups, with constraints, and reading coefficients off (x+y)^n.
   • Subsets & Arrangements — The 2^n counting principle and ordered arrangements, including repeated letters.
   • Paths, Grids & Distributions — Lattice paths, grid counts, stars-and-bars distributions, and constrained digit counts.
   • Probability — Dice, coins, and cards via favorable-over-total, complements, and expected value.

4. Geometry

   Euclidean and coordinate geometry: triangles, circles, polygons, and solids.

   4 个单元

   • Triangles — Right, special, equilateral, and similar triangles plus area by base-height and Heron.
   • Circles & Angles — Circumference, area, inscribed angles, chords, and angle relationships.
   • Polygons & Quadrilaterals — Diagonals, interior structure, and areas of regular polygons and trapezoids.
   • Coordinate Geometry & Solids — Distance and area in the plane, and volumes and diagonals of 3-D figures.

5. Precalculus

   Trigonometry, logarithms, and complex numbers — the topics that separate the AMC 12 from the AMC 10.

   3 个单元

   • Trigonometry — Exact values on the unit circle for the core angles.
   • Complex Numbers — Powers of i, arithmetic in the complex plane, and modulus.
   • Logarithms & Exponential Equations — Log laws, change of base, and solving exponential equations.

6. More topics

   Further topics from the exam's official scope.

   42 个单元

   • Fractions
   • Linear Equations
   • Simplifying & Evaluating
   • Perimeter & Area
   • Negative Numbers & Absolute Value
   • Averages
   • Counting Integers in Ranges
   • Composite Figures
   • Geometric Transformations
   • Inequalities
   • Counting Divisors
   • Speed & Travel
   • The Pythagorean Theorem
   • Quadratic Equations
   • Solids & Spatial Reasoning
   • Order of Operations & Powers
   • Digits & Place Value
   • Factors & Multiples
   • Median, Mode & Spread
   • Angles & Polygons
   • Logic Puzzles
   • Unit Conversion
   • Number Patterns
   • Unit Rates
   • Nets, Surface Area & Volume
   • Number Bases
   • Functions & Their Features
   • Linear Functions & Lines
   • Trigonometry
   • Cycles & Repetition
   • Ratios & Sharing
   • Arithmetic in Context
   • Roots & Powers
   • Money Problems
   • Percents
   • Percent Change
   • Smart Calculation
   • Function Transformations
   • Proportional Relationships
   • Counting Shapes
   • Rational & Irrational Numbers
   • Time & Clocks

AMC 12 示例题

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