Master Reference Sheet

Algebra 1 · Axiom Academy

FORMULA SHEET Master Reference Sheet: Algebra 1 Complete compilation of formulas, properties, and procedures — from order of operations through quadratics, sequences, and statistics. M ultiplication & D ivision (left to right) A ddition & S ubtraction (left to right) Simplify both sides (distribute, combine like terms) Move variable terms to one side Move constant terms to the other side Divide or multiply to isolate the variable Given slope & y -intercept → slope-intercept Given point & slope → point-slope Given two points → find slope first, then point-slope Graphing: quick visual, approximate answers Substitution: one equation already solved for a variable Elimination: coefficients are opposites or easily made so One solution: lines intersect (different slopes) No solution: parallel lines (same slope, different intercepts) Infinite solutions: same line (equivalent equations) Large number: move decimal left, positive exponent Small number: move decimal right, negative exponent Multiplying: multiply a -values, add exponents Dividing: divide a -values, subtract exponents a : initial value ( y -intercept) Always factor out the GCF first Count terms: 2 terms: difference of squares? 3 terms: trinomial (ac-method or trial & error) Check whether factors can be factored further Quadratic Functions and Equations Factoring: if easily factorable Square roots: if in the form (x - h)^2 = k Completing the square: to convert to vertex form Quadratic formula: always works

This is the written version of the interactive lesson above. See the full Algebra 1 course.