This page covers Algebra 1 at the High School Introductory level, delivered as a formula cheat sheet. Linear equations, systems, polynomials, and quadratics. The gateway course to advanced mathematics —. The material here corresponds to Grades 9–10 courses: Algebra 1 and Geometry.
The key formulas for Algebra 1 at the High School Introductory 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: Linear equations and inequalities, Systems of equations, Polynomials, Quadratic equations, Functions and graphing.
For each formula, read the conditions carefully. Many errors in Algebra 1 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
Solve for x: 4(x − 3) = 2x + 6
4x − 12 = 2x + 6 (distribute). 2x = 18 (subtract 2x, add 12). x = 9.
Distributing incorrectly across subtraction: 3(x − 2) ≠ 3x − 2. The 3 multiplies both terms inside the parentheses: 3x − 6.
Frequently Asked Questions
How is Algebra 1 different at the HS Intro level compared to earlier levels?
At the High School Introductory level, Algebra 1 builds on Grades 9–10 prerequisites. Students are expected to have completed Algebra 1 before tackling this material.
Which exams test Algebra 1 at this level?
SAT Math (heavy weighting), ACT Math, Common Core Algebra.
What is the single most effective way to practise Algebra 1 for HS Intro students?
The most effective practice at the High School Introductory 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.