# Study Guide

## Test Design and Test ObjectivesField 99: Adult Education: Mathematics

### Test Overview

Format Computer-based test (CBT) 60 selected-response questions 1 hour and 30 minutes (does not include 15-minute CBT tutorial) 240 ### Test Objectives

Table outlining test content and subject weighting by sub area and objective
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.