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Mathematics Competencies Tested on the Praxis Core

The Praxis Core Mathematics test covers four major skill areas with each skill area addressing a number of sub-skills. An outline showing these skill areas and their major sub-skills is shown below.

Subarea I: Number and Quantity

• Ratios and Proportional Relationships

• Understand ratio concepts and use ratio reasoning to solve problems

• Analyze proportional relationships and use them to solve real-world and mathematical problems

• The Real Number System

• Apply understanding of multiplication and division to divide fractions by fractions

• Compute fluently with multi-digit numbers and find common factors and multiples

• Apply understanding of operations with fractions to add, subtract, multiply, and divide rational numbers

• Know that there are numbers that are not rational, and approximate them by rational numbers

• Work with radicals and integer exponents

• Quantities

• Reason quantitatively and use units to solve problems

Subarea II: Algebra and Functions

• Seeing Structure in Expressions

• Apply understanding of arithmetic to solve algebraic expressions

• Solve real-life and mathematical problems using numerical and algebraic expressions

• Use properties of operations to generate equivalent expressions

• Reasoning with Equations and Inequalities

• Understand the connections between proportional relationships, lines, and linear equations

• Understand solving equations as a process of reasoning and explain the reasoning

• Reason about and solve one-variable equations and inequalities

• Solve equations and inequalities in one variable

• Analyze and solve linear equations and pairs of simultaneous linear equations

• Represent and solve equations and inequalities graphically

• Functions

• Interpreting Functions

• Building Functions

Subarea III: Geometry

• Congruence and Similarity

• Draw, construct, and describe geometrical figures and describe the relationships between them

• Experiment with transformations in the plane

• Right Triangles

• Understand and apply the Pythagorean theorem

• Circles

• Understand and apply theorems about circles

• Geometric Measurement and Dimension

• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume

• Explain volume formulas and use them to solve problems

• Modeling with Geometry

• Apply geometric concepts in modeling situations

Subarea IV: Statistics and Probability

• Basic Statistics and Probability

• Develop understanding of statistical variability

• Summarize and describe distributions

• Use random sampling to draw inferences about a population

• Investigate chance processes and develop, use, and evaluate probability models

• Investigate patterns of association in bivariate data

• Interpret Categorical and Quantitative Data

• Summarize, represent, and interpret data on a single count or measurement variable

• Interpret linear models

• Make Inferences and Justify Conclusions

• Understand and evaluate random processes underlying statistical experiments

• Use Probability to Make Decisions

• Use probability to evaluate outcomes of decisions

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