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 Contents Mathematics Number Concepts and Computation Skills Word Problems Involving Integers, Fractions, or Decimals Interpret Information from a Graph, Table, or Chart Graph Numbers or Number Relationships One- and Two-Variable Equations Word Problems Involving One and Two Variables Algebraic Expressions Problems Involving Geometric Figures Apply Reasoning Skills Data, Statistics, and Probability Practice Math Tests Main Menu Exit Student Demo Buy Now for \$39.95 and begin using the entire course in less than two minutes

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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