This page covers Arithmetic at the High School Advanced 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 10–12 courses: Algebra 2 and Trigonometry.
The key formulas for Arithmetic at the High School Advanced 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 high school advanced 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 HS Advanced level compared to earlier levels?
At the High School Advanced level, Arithmetic builds on Grades 10–12 prerequisites. Students are expected to have completed Algebra 2 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 HS Advanced students?
The most effective practice at the High School Advanced 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.