# Middle School Mathematics (0069)

## Topics Covered

In each of the content categories, the test will assess an examinee's ability to use appropriate mathematical language and representations of mathematical concepts, to connect mathematical concepts to one another and to real-world situations, and to integrate mathematical concepts to solve problems. Because the assessments were designed to measure the ability to integrate knowledge of mathematics, answering any question may involve more than one competency and may involve competencies from more than one content category. Representative descriptions of topics covered in each category are provided below.

Current section: I. Arithmetic and Basic Algebra

### IV.a. Data, Probability, and Statistical Concepts

1. Organize data into a presentation that is appropriate for solving a problem (e.g., construct a histogram and use it in the estimation of probabilities)
1. Read and analyze data presented in various forms (e.g., tables, charts, graphs, line, bar, histogram, circle, double line, double bar, scatterplot, stem plot, line plot, box plot); draw conclusions from data
1. Solve probability problems involving finite sample spaces by actually counting outcomes; solve probability problems by using counting techniques; solve probability problems involving independent and dependent events; solve problems by using geometric probability
1. Solve problems involving average, including arithmetic mean and weighted average; find and interpret common measures of central tendency (i.e., mean, sample mean, median, mode) and know which is the most meaningful to use in a given situation; find and interpret common measures of dispersion (e.g., range, spread of data, standard deviation, outliers)

### IV.b. Discrete Mathematics

1. Use and interpret statements that contain logical connectives (and, or, if—then) as well as logical quantifiers (some, all, none)
1. Solve problems involving the union and intersection of sets, subsets, and disjoint sets
1. Solve basic counting problems involving permutations and combinations without necessarily knowing formulas; use Pascal's triangle to solve problems
1. Solve problems that involve simple sequences or number patterns (e.g., triangular numbers or other geometric numbers); find rules for number patterns
1. Use and interpret matrices as tools for displaying data
1. Draw conclusions from information contained in simple diagrams, flowcharts, paths, circuits, networks, or algorithms
1. Explore patterns in order to make conjectures, predictions, or generalizations