This page covers Discrete Mathematics at the AP / College Prep level, delivered as a formula cheat sheet. Logic, set theory, graph theory, combinatorics, and proof techniques. The mathematical spine of comp. The material here corresponds to Grades 11–12 courses: AP Calculus AB and AP Calculus BC.
The key formulas for Discrete Mathematics at the AP / College Prep level are organised below. Each formula is accompanied by a note on when it applies and what common variations exist.
The skills covered by these formulas are: Logic and proof techniques, Set theory, Graph theory, Combinatorics, Algorithms and complexity.
For each formula, read the conditions carefully. Many errors in Discrete Mathematics come from applying a formula outside its domain of validity — using a geometric formula that assumes a right angle when the angle is not specified, or applying a probability rule that requires independence when the events are dependent.
Use this sheet as a revision tool after you have worked through problems — not as a first introduction to the material. A formula you have derived or used is one you will remember; a formula you have only read is one you will forget under exam pressure.
Worked Example
A standard discrete math problem at the ap college prep level.
Work through step by step: identify what is given, what is asked, apply the relevant technique, and check your answer against the original conditions.
Confusing inclusive OR (at least one of A or B) with exclusive OR (exactly one of A or B) — they are different in formal logic and produce different truth tables.
Frequently Asked Questions
How is Discrete Mathematics different at the AP / College Prep level compared to earlier levels?
At the AP / College Prep level, Discrete Mathematics builds on Grades 11–12 prerequisites. Students are expected to have completed AP Calculus AB before tackling this material.
Which exams test Discrete Mathematics at this level?
CS foundational courses, GRE Computer Science, Software engineering interviews.
What is the single most effective way to practise Discrete Mathematics for AP / College Prep students?
The most effective practice at the AP / College Prep level is deliberate work on novel problem setups — not repeated drilling of the same template. Attempt problems before looking at solutions, and review errors by identifying the specific step where the reasoning broke down.