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

I. Arithmetic and Basic Algebra

  1. Add, subtract, multiply, and divide rational numbers expressed in various forms; apply the order of operations; identify the properties of the basic operations on the standard number systems (e.g., closure, commutativity, associativity, distributivity); identify an inverse and the additive and multiplicative inverses of a number; use numbers in a way that is most appropriate in the context of a problem
  1. Order any finite set of real numbers and recognize equivalent forms of a number; classify a number as rational, irrational, real, or complex; estimate values of expressions involving decimals, exponents, and radicals; find powers and roots
  1. Given newly defined operations on a number system, determine whether the closure, commutative, associative, or distributive properties hold
  1. Demonstrate an understanding of concepts associated with counting numbers (e.g., prime or composite, even or odd, factors, multiples, divisibility)
  1. Interpret and apply the concepts of ratio, proportion, and percent in appropriate situations
  1. Recognize the reasonableness of results within the context of a given problem; using estimation, test the reasonableness of results
  1. Work with algebraic expressions, formulas, and equations; add, subtract, and multiply polynomials; divide polynomials; add, subtract, multiply, and divide algebraic fractions; perform standard algebraic operations involving complex numbers, radicals, and exponents, including fractional and negative exponents
  1. Determine the equations of lines, given sufficient information; recognize and use the basic forms of the equation for a straight line
  1. Solve and graph linear equations and inequalities in one or two variables; solve and graph systems of linear equations and inequalities in two variables; solve and graph nonlinear algebraic equations; solve equations and inequalities involving absolute values
  1. Solve problems that involve quadratic equations, using a variety of methods (e.g., graphing, formula, calculator)