E T S Praxis Series

Middle School Mathematics (0069)

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Topics Covered

In each of the content categories, the test will assess an examinee's ability to use appropriate mathematical language and representations of mathematical concepts, to connect mathematical concepts to one another and to real-world situations, and to integrate mathematical concepts to solve problems. Because the assessments were designed to measure the ability to integrate knowledge of mathematics, answering any question may involve more than one competency and may involve competencies from more than one content category. Representative descriptions of topics covered in each category are provided below.

Current section: I. Arithmetic and Basic Algebra

III. Functions and Their Graphs

  1. Understand function notation for functions of one variable and be able to work with the algebraic definition of a function (i.e., for every x there is one y)
  1. Identify whether a graph in the plane is the graph of a function; given a set of conditions, decide if they determine a function
  1. Given a graph, for example, a line, a parabola, a step, absolute value, or simple exponential, select an equation that best represents the graph; given an equation, show an understanding of the relationship between the equation and its graph
  1. Determine the graphical properties and sketch a graph of a linear, step, absolute-value, quadratic, or exponential function
  1. Demonstrate an understanding of a physical situation or a verbal description of a situation and develop a model of it, such as a chart, graph, equation, story, or table
  1. Determine whether a particular mathematical model, such as an equation, can be used to describe two seemingly different situations. For example, given two different word problems, determine whether a particular equation can represent the relationship between the variables in the problems
  1. Find the domain (x-values) and range (y-values) of a function without necessarily knowing the definitions; recognize certain properties of graphs (e.g., slope, intercepts, intervals of increase or decrease, axis of symmetry)
  1. Translate verbal expressions and relationships into algebraic expressions or equations; provide and interpret geometric representations of numeric and algebraic concepts