Mathematics Competencies Tested on the GACE
The math test covers four major skill areas with each skill area addressing a number of subskills. An outline showing these skill areas and their major subskills 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 realworld and mathematical problems
 The Real Number System
 Apply understanding of multiplication and division to divide fractions by fractions
 Compute fluently with multidigit 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 reallife 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 onevariable 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 reallife 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
