Mathematics Competencies Tested on the PAPA
The math test covers seven major skill areas with each skill area addressing one or more sub-skills. An outline showing these skill areas and their major sub-skills 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 real-world 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 real-world situation, and interpreting the slope and intercepts in the context of the problem
- selecting a nonlinear function that best models a real-world 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 real-world situations
- applying formulas to calculate perimeter, circumference, length, area, surface area, volume, and angles for two- and three-dimensional figures in mathematical and real-world 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
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