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Mathematics (201)
 
Number and Quantity
 
Algebra and Functions
 
Geometry
 
Statistics and Probability
 
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Mathematics Competencies Tested on the GACE

The math 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

  • See 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

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

    • Experiment with transformations in the plane

  • Similarity, Right Triangles, and Trigonometry

    • 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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