This page covers Arithmetic at the AP / College Prep level, delivered as a formula cheat sheet. The foundation of all mathematics. Four operations, place value, order of operations, and the mental. The material here corresponds to Grades 11–12 courses: AP Calculus AB and AP Calculus BC.
The key formulas for Arithmetic 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: Addition and subtraction, Multiplication and division, Order of operations (PEMDAS), Mental arithmetic, Estimation and rounding.
For each formula, read the conditions carefully. Many errors in Arithmetic 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 arithmetic 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 the order of operations: computing left-to-right without checking precedence. The rule is exponents before multiplication, multiplication before addition — not left-to-right.
Frequently Asked Questions
How is Arithmetic different at the AP / College Prep level compared to earlier levels?
At the AP / College Prep level, Arithmetic builds on Grades 11–12 prerequisites. Students are expected to have completed AP Calculus AB before tackling this material.
Which exams test Arithmetic at this level?
SAT/ACT Math, GRE Quantitative, GMAT Quant.
What is the single most effective way to practise Arithmetic 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.