Mathematics Competencies Tested on the PAPA
The math test covers seven major skill areas with each skill area addressing one or more subskills. An outline showing these skill areas and their major subskills is shown below.
0005 Understand Numbers and the Number System
 demonstrating knowledge of real numbers and number operations
 demonstrating fluency in computation, including operations on decimals, percents, fractions, and exponents
 using number sense and different number representations (e.g., scientific notation) to solve mathematical and realworld problems
 demonstrating knowledge of place value and the relative magnitude of numbers
0006 Apply Principles of Algebra to Expressions and Equations
 analyzing and extending a variety of patterns
 using the concepts of variable, equality, and equation to generate, interpret, and evaluate algebraic expressions based on verbal descriptions
 manipulating algebraic expressions and solving equations using a variety of techniques (e.g., performing operations, simplifying, factoring)
 applying algebraic principles to represent and solve word problems involving fractions, ratios, proportions, and percents
0007 Apply Principles of Algebra to Linear and Nonlinear Functions
 translating between different representations (e.g., tables, verbal descriptions, equations, graphs) of linear and nonlinear functions
 relating the characteristics of a linear equation (e.g., slope, intercepts) to its graph
 selecting a linear equation that best models a realworld situation, and interpreting the slope and intercepts in the context of the problem
 selecting a nonlinear function that best models a realworld situation
 solving linear equations, systems of linear equations, and inequalities algebraically and graphically
0008 Understand Measurement Concepts and Geometry Principles
 estimating and calculating measurements using metric, customary, and nonstandard units, unit conversions, and dimensional analysis in realworld situations
 applying formulas to calculate perimeter, circumference, length, area, surface area, volume, and angles for two and threedimensional figures in mathematical and realworld situations
 estimating and calculating measurements indirectly using the Pythagorean theorem, ratios, proportions, and the principles of similarity and congruence
 determining how the characteristics of geometric figures (e.g., area, volume) are affected by changes in their dimensions
 solving a variety of measurement problems (e.g., time, temperature, rates of change)
 analyzing polygons using attributes of sides, angles, and parallel and perpendicular lines
 applying geometric transformations (e.g., translations, reflections, rotations) to geometric figures and using the concepts of symmetry, similarity, and congruence to solve problems
 using coordinate geometry and algebraic methods (e.g., Pythagorean theorem) to analyze geometric figures and solve problems
0009 Demonstrate Knowledge of Data, Statistics, and Probability
 using measures of central tendency (e.g., mean, median) and spread (e.g., range) to draw conclusions and make predictions from data
 selecting appropriate ways to display data and statistical information (e.g., tables, circle graphs, histograms)
 analyzing and drawing inferences from data presented in different formats (e.g., frequency distributions, percentiles, graphs)
 calculating probabilities for simple, compound, independent, dependent, and conditional events described in various ways (e.g., word problems, tree diagrams, Venn diagrams)
 demonstrating knowledge of counting principles and combinations and permutations
0010 Understand Problem Solving, Reasoning, and Mathematical Communication
 solving problems using a variety of methods (e.g., estimation, drawing a picture, working backward, using manipulatives)
 using mathematical reasoning to evaluate arguments (e.g., distinguishing between inductive and deductive reasoning, using counterexamples, evaluating informal proofs) and determining the reasonableness of solutions to problems (e.g., estimation)
 translating between verbal descriptions and mathematical language, notation, and symbols (e.g., function notation, set notation, order relations)
 identifying connections between mathematical concepts, other academic disciplines, and technology
