AMC 10

AMC 10 包含的内容

A ladder through the four AMC 10 pillars — Algebra, Number Theory, Counting & Probability, and Geometry. Each unit moves from a core skill to the clever twists that show up in the 25-problem, 75-minute contest. (Trigonometry, logarithms, and complex numbers are AMC 12 additions — see the AMC 12 course.)

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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. More topics

   Further topics from the exam's official scope.

   44 个单元

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

AMC 10 示例题

仅供阅读。其余题目需登录后使用；每个孩子的第一轮练习免费。