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Your guide to a higher score on the Praxis IIr: Mathematics Content Knowledge Test (0061) Why CliffsTestPrep Guides? Go with the name you know and trust Get the information you need-fast! Written by test-prep specialists About the contents: Introduction Overview of the exam How to use this book Proven study strategies and test-taking tips Part I: Subject Review Focused review of all exam topics: arithmetic and basic algebra, geometry, trigonometry, analytic geometry, functions and their graphs, calculus, probability and statistics, discrete mathematics, linear algebra, computer science, and mathematical reasoning and modeling Reviews cover basic terminology and principles, relevant laws, formulas, theorems, algorithms, and more Part II: 3 Full-Length Practice Examinations Like the actual exam, each practice exam includes 50 multiple-choice questions Complete with answers and explanations for all questions Test Prep-Essentials from the Experts at CliffsNotesr

E. D. McCune, Ph.D., is Regents professor in the Department of Mathematics and Statistics at Stephen F. Austin State University in Texas.

Sandra Luna McCune, Ph.D., is Regents professor and mathematics specialist in the Department of Elementary Education at Stephen F. Austin State University in Texas. Regents professor is the highest honor the university is empowered to bestow upon a faculty member. The Drs. McCune reside in Nacogdoches, Texas.

Introduction.

General Description.

Calculator Requirements.

Format of the Test.

The Role of the Mathematics CK in Teacher Certification.

Questions Commonly Asked About the Mathematics CK.

How to Use This CliffsTestPrep Book.

How to Prepare for the Day of the Test.

Test-Taking Strategies for the Mathematics CK.

Graphing Calculators and the Mathematics CK.

PART I: SUBJECT AREA REVIEWS.

Review for the Praxis Mathematics: Content Knowledge (0061).

Notation, Definitions, and Formulas.

Notation.

Definitions.

Discrete Mathematics.

Formulas.

Algebra and Number Theory.

The Real and Complex Number Systems.

Rules to Compute By.

Order of Operations.

Properties of Number Systems.

Properties of the Counting Numbers.

Ratio, Proportion, Percent, and Average.

Algebraic Expressions, Formulas, and Equations.

Special Products.

Simplifying Polynomials.

Factoring Polynomials.

Rules for Radicals.

Rules for Exponents.

Steps for Solving One-Variable Linear Equations.

Steps for Solving a Quadratic Equation by Factoring.

Steps for Solving a Quadratic Equation by Completing the Square.

Steps for Solving a Quadratic Equation by Using the Quadratic Formula.

Systems of Equations and Inequalities.

Steps for Solving a System of Two Linear Equations by Substitution.

Steps for Solving a System of Two Linear Equations by Elimination (That Is, by Addition).

Steps for Solving a System of Two Linear Equations by Using the Trace Feature.

Steps for Graphing a Two-Variable Linear Inequality.

Geometric Interpretations of Algebraic Principles.

Algebraic Representations of Lines, Planes, Conic Sections, and Spheres.

Algebraic Representation of a Line.

Algebraic Representation of Conic Sections.

Formulas Used in Two- and Three-Dimensional Coordinate Systems.

Measurement.

Unit Analysis.

Precision, Accuracy, and Approximate Error.

Informal Approximation Concepts.

Geometry.

Relationships Involving Geometric Figures.

Relationships among Quadrilaterals.

Problems Involving Properties of Plane Figures.

Problems Involving Properties of Circles.

The Pythagorean Theorem.

Perimeter, Area, and Volume.

Geometric Transformations.

Trigonometry.

The Six Basic Trigonometric Functions.

The Law of Sines and the Law of Cosines.

Special Angle Formulas and Identities.

Trigonometric Equations and Inequalities.

Rectangular and Polar Coordinate Systems.

Functions.

Representation of Functions.

Modeling with Functions.

Properties of a Function.

Problems Involving Functions.

Composition and Inverses of Functions.

Functions of Two Variables.

Calculus.

Limits.

Derivatives.

Continuity.

Analyzing the Behavior of a Function.

The Mean Value Theorem and the Fundamental Theorem of Calculus.

Integration as a Limiting Sum.

Approximation of Derivatives and Integrals.

Differentiation and Integration Techniques.

Differentiation Formulas.

Integration Formulas.

Limits of Sequences and Series.

Properties of Limits of Sequences.

Properties of Convergent Series.

Data Analysis and Statistics.

Organizing Data.

Measures of Central Tendency and Dispersions.

Regression.

Normal Distributions.

Informal Inference.

Types of Studies.

Characteristics of Well-Designed Studies.

Probability.

Sample Spaces and Probability Distributions.

Conditional Probability and Independent and Dependent Events.

Expected Value.

Empirical Probability.

Matrix Algebra.

Vectors and Matrices.

Operations with Matrices.

Solving Systems of Linear Equations.

Determinants.

Representation of Geometric Transformations.

Discrete Mathematics.

Counting Techniques.

Recursive Functions.

Equivalence Relations.

Arithmetic and Geometric Sequences and Series.

Discrete and Continuous Representations.

Modeling and Solving Problems.

PART II: 3 FULL-LENGTH PRACTICE TESTS.

Mathematics: Content Knowledge Practice Test 1.

Mathematics: Content Knowledge Practice Test 1 Answer Key.

Answer Explanations for Practice Test 1.

Mathematics: Content Knowledge Practice Test 2.

Mathematics: Content Knowledge Practice Test 2 Answer Key.

Answer Explanations for Practice Test 2.

Mathematics: Content Knowledge Practice Test 3.

Mathematics: Content Knowledge Practice Test 3 Answer Key.

Answer Explanations for Practice Test 3.Simplifying Radicals.

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