Praxis Algebra I (5162) Study Guide

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Algebra Praxis Study Guide

There are several states that require aspiring Algebra I teachers to pass the Praxis Algebra I (5162) as part of the teacher certification process. On test day, candidates will have to answer 60 questions in 150 minutes (2.5 hours). There will be both selected-response and numeric-entry questions on the exam. Test takers can use an Algebra Praxis study guide to help them get familiar with not only the format of the test, but also the content. The Praxis Algebra I exam tests candidates' knowledge of many different algebraic concepts, including equations and inequalities, functions, numbers, and probability. Explore our Praxis 5162 study guide below to learn about the content that will be examined.

Algebra I Praxis Study Guide (5162)
Principles of Algebra38% (~23 questions)
Functions30% (~18 questions)
Number and Quantity; Probability and Statistics32% (~19 questions)
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Principles of Algebra

Candidates need to be prepared to demonstrate their knowledge of foundational concepts in algebra, such as an understanding of algebraic expressions and skills in reasoning.

Algebraic Expressions, Polynomials, Equations, and Inequalities

In order to solve algebraic problems, test takers need to know how to write algebraic expressions and manipulate the expressions as needed. For example, test takers should know how to rewrite quadratic expressions in a way that allows them to find the maxima or factor the expression.

Questions will also examine test takers' ability to solve mathematical operations involving polynomials. Candidates should be prepared to solve and graph equations or inequalities. They may also need to rearrange equations as needed to solve for a specific variable.

Reasoning and Techniques for Solving Equations and Inequalities

Building on their knowledge of equations and inequalities, test takers will have to demonstrate their understanding of the various methods used to solve these problems. They should be able to solve problems that consist of one or two equations or inequalities.

Specific techniques that will be evaluated include:

  • Completing the square
  • Graphing equations
  • Factoring equations
  • Estimating solutions of functions

To complete some of these strategies, test takers will have to be familiar with concepts such as x- and y-axis, the elimination method, intersection, and scalar multiples.

Rate of Change

Questions about the rate of change aim to examine candidates' understanding of equations and graphs. For example, if given a nonlinear equation on a graph or written out symbolically, test takers should be able to identify the rate of change.

On a graph, test takers should also be able to explain how the slope represents the rate of change and be familiar with how to identify the intercepts of the line. When working with a linear function, test takers should be able to predict the rate of change using a graph.

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Test takers will be evaluated on their understanding of functions. They will need to be able to explain what functions represent and how they can be expressed.

Function Concept, Notation, and Behavior

Candidates need to know what a function is and how two functions relate to each other. This means understanding the terms of domain and range and knowing how to find the domain and range using the function's rule. They need to know what function notation is and be able to use function notation when solving problems.

Test takers will also have to create tables and graphs based on the functions' relationship. They should be able to explain the relationship between quantities and describe the function, such as if the function is even.

Functions as Models

Ultimately, test takers should understand that functions serve as models for the relationship between different quantities. They need to be able to find new functions from old ones, including the inverse function (if one exists).

Examinees must have knowledge of linear, exponential, and quadratic models. This means knowing how to identify the equations for each type of model and solving problems with the appropriate model. They need to be able to solve problems given a graph or an equation.

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Number and Quantity; Probability and Statistics

The exam will also evaluate test takers' understanding of different types of numbers, including units and data analysis. Candidates should also be familiar with concepts in probability.

Radicals, Exponents, Rational, and Irrational Numbers

Test takers should be prepared to solve problems involving radicals, exponents, and rational and irrational numbers. They need to have knowledge of the properties of exponents and radicals and be able to write numbers using scientific notation. They also need a general understanding of magnitude for small and large numbers.

Questions may also ask about the principles of using rational and irrational numbers. For example, test takers should know that if they add a rational number and an irrational number, then the answer is going to be an irrational number.

Units and Data

Test takers must know how to use the correct units of measurement for problems. This includes being able to evaluate their solutions for reasonability.

Candidates will also have to analyze data that contains one or two variables. They should be familiar with a wide range of methods for representing data, including:

  • Box plots
  • Scatter plots
  • Time series
  • Normal distributions
  • Histograms

They also need to be able to calculate the appropriate statistics for the type of data they are presented with, such as determining the mean or standard deviation of data sets.

Linear Regression and Probabilities

Given a data set, test takers should also be able to identify a function that fits the data. Using this function, they should be able to solve problems and find the residuals and linear correlation coefficient, as well as the slope and intercepts. They will need to be familiar with terms such as causation and correlation.

Test takers will also need to be prepared to answer some questions about probability. They may need to demonstrate their skills in determining the probability of either simple or compound events.

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