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Competition Mathematics · AMC 12

See the structure before the computation takes over.

AMC 12 Preparation asks students to coordinate a broader high-school mathematics toolkit, sustain longer chains of reasoning, and recognize the structural shortcut that makes a difficult problem manageable.

16 sessions
1 hr 45 min each
Once weekly* school year
$300* per month

*Summer terms meet twice weekly and complete the same 16-session course in eight weeks. Summer tuition is $600 per month.

Course fit

For students ready to reason across the full high-school mathematical landscape.

This workshop is designed for students who

  • are comfortable with high-school algebra and geometry and want problems that demand greater abstraction
  • want to coordinate functions, trigonometry, geometry, number theory, and combinatorics without chapter labels
  • can sustain multi-step reasoning while continuing to search for a cleaner structural approach
  • want to extend competition mathematics beyond AMC 10 without reducing preparation to timed repetition

The workshop spine

Ideas become useful when labels disappear.

The exact topic map may change as the curriculum develops. The 16-session learning progression remains consistent across the AMC family.

  1. 01Learn the tool

    Build a useful idea or representation before applying it.

  2. 02Focus the problem

    Work through carefully selected problems that isolate the idea.

  3. 03Remove the label

    Meet unfamiliar mixed problems without being told which tool to use.

  4. 04Add the clock

    Practice judgment, selection, and recovery under competition conditions.

  5. 05Integrate

    Compare approaches and carry the strongest habits into the next cycle.

Representative problem domains

A connected field, not four isolated chapters.

01

Advanced algebra & functions

Polynomials, rational expressions, sequences, complex numbers, and functional structure

02

Combinatorics & probability

Advanced counting, recursive structure, probability, and careful case partitioning

03

Geometry & trigonometry

Euclidean and coordinate geometry, circles, transformations, and trigonometric relationships

04

Number theory

Divisibility, congruence, integer equations, prime structure, and constructive arguments

These domains describe the intended range, not a fixed weekly syllabus. Problems increasingly combine ideas and require students to decide what matters.

Problem-solving habits

Productive struggle has a method.

  1. 01Begin

    Translate the question and test a small example.

  2. 02Organize

    Draw, tabulate, classify, or split into cases.

  3. 03Notice

    Look for symmetry, invariants, and hidden constraints.

  4. 04Recover

    Recognize a dead end and change representation.

  5. 05Compare

    Study why one solution is clearer or more efficient.

Most of the work happens together.

The course is primarily an in-class mathematical workshop. Outside work remains light or optional so discussion, experimentation, and solution comparison stay central.

Competition pathway

A platform for competition mathematics beyond AMC 12.

AMC 12 is the culminating level in the current Provident Scholars AMC pathway. The goal is a more mature, transferable approach to unfamiliar mathematics—not a guaranteed score or advancement outcome.

See the complete program pathway