Praxis Algebra I study guide
Praxis Algebra I · Work through your exam, one topic at a time.
Praxis Algebra I (5165) is a Praxis Subject Assessment from ETS, the same organisation behind the Praxis Core and other teacher-certification tests. Candidates take it to demonstrate subject knowledge in algebra for educator licensure; whether you need it, and the score you must reach, are set by your state rather than by ETS, so check your state's requirements before you register. The Praxis Algebra I study guide has 6 sections and about 2,198 words.
01Algebraic Expressions and Operations
This domain tests whether you can move fluently between verbal descriptions, expressions, and simplified or factored forms. Items typically ask you to simplify polynomial, radical, or rational expressions, apply exponent rules, evaluate an expression for given values, or write an expression that models a context such as perimeter, area, cost, or consecutive integers.
345 words, about 2 min02Linear Equations and Inequalities
Questions here ask you to solve multi-step equations and inequalities, work with slope and the three standard forms of a line, decide whether lines are parallel or perpendicular, and translate real contexts (rate plus fixed fee, break-even points, ticket sales) into a linear model. Core rules Slope between two points: m = (y₂ − y₁)/(x₂ − x₁).
381 words, about 2 min03Functions and Their Graphs
This domain tests function concepts rather than isolated equation solving: identifying functions, evaluating function notation, describing domain and range, reading key features from a graph, and applying transformations. Expect items that give a graph or table and ask for intercepts, intervals of increase or decrease, or average rate of change.
371 words, about 2 min04Systems of Equations and Inequalities
Items here ask you to solve two-variable systems by substitution, elimination, or graphing, classify a system by its number of solutions, and graph the solution set of a system of linear inequalities. Context problems involving mixtures, ticket revenue, or break-even analysis are common.
376 words, about 2 min05Quadratic Functions and Equations
This domain covers solving quadratic equations by factoring, completing the square, and the quadratic formula; interpreting the discriminant; and analyzing parabolas - vertex, axis of symmetry, intercepts, and maximum or minimum values in applied settings such as projectile height or area optimization. Core rules Standard form y = ax² + bx + c with a ≠ 0; vertex form y = a(x − h)² + k with vertex (h, k).
371 words, about 2 min06Exponential Functions and Data Modeling
This strand tests exponential growth and decay models, geometric sequences, and the statistics of fitting a model to data: scatter plots, lines and curves of best fit, correlation, and residuals. Expect percent-change contexts such as population, depreciation, and compound interest, plus items asking you to choose between a linear and an exponential model.
354 words, about 2 min