# Study Guide

## Test Design and Test Objectives

Field 99: Adult Education: Mathematics

### Test Overview

Format | Computer-based test (CBT) |
---|---|

Number of Questions | 60 selected-response questions |

Time | 1 hour and 30 minutes (does not include 15-minute CBT tutorial) |

Passing Score | 240 |

### Test Objectives

Subareas | Range of Objectives | Approximate Test Proportions | |
---|---|---|---|

I | Number Sense and Algebraic Thinking | 1–2 | 50% |

II | Geometry & Measurement and Data Analysis, Statistics & Probability | 3–4 | 50% |

#### Subarea I–Number Sense and Algebraic Thinking

##### Objective 0001: Demonstrate knowledge of number properties and number operations, and apply quantitative reasoning and problem-solving skills.

For example:- Demonstrate understanding of the place value system and the relative magnitude of numbers (e.g., using the number line, real-world applications).
- Interpret and solve computational and real-world mathematical problems involving number operations (addition, subtraction, multiplication, and division) with positive and negative integers (whole numbers), fractions, decimals, and percentages.
- Demonstrate understanding of the principles of basic number theory (e.g., prime factorization, greatest common factor, least common multiple).
- Identify equivalent ways of representing integers, fractions, decimals, and percentages, including the use of exponents and scientific notation.
- Apply quantitative reasoning skills to estimate solutions and evaluate the validity of information in a variety of computational and real-world situations.
- Apply ratio concepts and proportional reasoning to solve computational and real-world mathematical problems.
- Apply inductive and deductive reasoning to analyze patterns and draw conclusions.
- Identify appropriate information, resources, strategies, and tools to solve computational and real-world mathematical problems.

##### Objective 0002: Demonstrate knowledge of fundamental principles and applications of algebra to model and solve problems.

For example:- Find the value of an unknown in a given equation.
- Recognize the structure of, manipulate, and simplify polynomials.
- Solve systems of linear equations or inequalities involving real-world situations using a variety of methods.
- Recognize and apply the concept of a function, use function notation, and analyze functions using different representations (e.g., algebraic, graphic, numeric tables, verbal descriptions).
- Construct, graph, and interpret linear and quadratic functions that model real-world relationships.
- Identify appropriate information, resources, strategies, and tools to solve algebraic and real-world mathematical problems.

#### Subarea II–Geometry & Measurement and Data Analysis, Statistics & Probability

##### Objective 0003: Demonstrate knowledge of fundamental principles and applications of geometry and measurement.

For example:- Identify lines (e.g., parallel, perpendicular) and angles (e.g., right, acute, obtuse), and classify shapes according to their lines and angles.
- Demonstrate knowledge of how to construct geometric figures on the coordinate plane.
- Demonstrate knowledge of properties of geometric figures, and describe the relationships between them (e.g., angle measures, congruence, similarity).
- Model and solve real-world problems involving concepts of perimeter, circumference, area, surface area, and volume of two- and three-dimensional geometric figures.
- Model and solve real-world problems involving angles, triangles, quadrilaterals, polygons, and circles.
- Model and solve real-world mathematical problems involving right triangles and the Pythagorean theorem.
- Identify appropriate information, resources, strategies, and tools to solve geometric, measurement, and real-world mathematical problems.

##### Objective 0004: Demonstrate knowledge of fundamental principles and applications of data analysis, statistics, and probability.

For example:- Demonstrate knowledge of appropriate techniques for collecting representative categorical and quantitative data while avoiding bias (e.g., surveys, sampling a population) and techniques for displaying data and data distributions (e.g., histograms, scatter plots, bar graphs).
- Apply concepts related to measures of central tendency (e.g., mean, median, mode) and variability (e.g., range, standard deviation) to interpret data in a variety of formats (e.g., text, graphs, tables).
- Demonstrate knowledge of concepts related to how statistics are used to draw inferences, make predictions, and justify conclusions.
- Apply fundamental properties of probability to estimate the outcomes of real-world events.
- Identify appropriate information, resources, strategies, and tools to solve computational and real-world mathematical problems involving data, statistics, and probability.