Study Guide
Middle School Education: Mathematics
Test Design and Framework
The test design below describes general assessment information. The framework that follows is a detailed outline that explains the knowledge and skills that this test measures.
Test Design
| Format | Computer-based test (CBT) and online-proctored test |
|---|---|
| Number of Questions | 80 multiple-choice questions |
| Time* | 2 hours, 30 minutes |
| Passing Score | 220 |
Test Framework
| Content Domain | Range of Competencies | Approximate Percentage of Test Score | |
|---|---|---|---|
| I. | Number and Operations | 0001–0002 | 19% |
| II. | Algebra and Functions | 0003–0006 | 36% |
| III. | Measurement and Geometry | 0007–0009 | 27% |
| IV. | Statistics and Probability | 0010–0011 | 18% |
Domain I–Number and Operations
Competency 0001–Understand numbers.
For example:
- Analyze the relationships between the subsets of the real numbers.
- Understand the role of place value in any number system.
- Analyze the use of estimation in a variety of situations.
- Translate between different representations of numbers.
- Apply number-theory concepts (e.g., divisibility rules, prime factorization, greatest common factors) in problem-solving situations.
Competency 0002–Understand operations.
For example:
- Analyze relational and operational properties (e.g., multiplication and division of fractions).
- Analyze a variety of conventional and alternative algorithms.
- Solve a variety of real-life and mathematical problems involving integers, fractions, and decimals, including exponents.
- Solve a variety of real-life and mathematical problems involving ratios, proportions, unit rates, and percents.
Domain II–Algebra and Functions
Competency 0003–Understand patterns, relations, and functions.
For example:
- Analyze patterns and relationships.
- Analyze the properties of relations and functions in multiple representations (e.g., tables, graphs, equations, words).
- Analyze direct and inverse proportional relationships.
- Determine the effects of transformations on the graph of a function or relation.
Competency 0004–Understand algebraic techniques and applications.
For example:
- Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor).
- Solve linear and nonlinear equations and inequalities.
- Create algebraic expressions or equations that describe numbers or relationships.
Competency 0005–Understand linear relations and applications.
For example:
- Analyze the relationship between a linear equation or inequality and its representations.
- Solve systems of linear inequalities or equations with a variety of methods.
- Interpret the meaning of the slope and the y-intercept in various contexts.
- Analyze a variety of real-life and mathematical problems involving linear equations, systems, and inequalities.
Competency 0006–Understand nonlinear relations and concepts of calculus.
For example:
- Analyze relationships between multiple representations of a nonlinear equation (e.g., quadratic, polynomial, exponential) or inequality.
- Solve a variety of real-life and mathematical problems involving nonlinear equations and inequalities.
- Demonstrate knowledge of the concepts of limit, continuity, and rate of change as they relate to function behavior.
- Demonstrate knowledge of sequences and series and of recursive definitions.
- Demonstrate knowledge of how concepts of calculus can be used to solve problems in real-life situations.
Domain III–Measurement and Geometry
Competency 0007–Understand measurement principles, procedures, and applications.
For example:
- Reason quantitatively and use units and unit conversions to solve problems.
- Calculate or estimate measures of lengths, areas, and volumes.
- Apply the concepts of similarity, scale factors, and proportional reasoning to solve indirect measurement problems.
- Analyze precision, accuracy, and rounding in measurements and computed quantities.
Competency 0008–Understand Euclidean geometry in two and three dimensions.
For example:
- Analyze properties of points, lines, planes, and angles.
- Use the properties of triangles, quadrilaterals, and other polygons and circles to solve problems.
- Apply principles of similarity and congruence.
- Understand and apply the Pythagorean theorem and its converse.
- Visualize relationships between two-dimensional and three-dimensional figures.
- Analyze geometric arguments using deductive reasoning.
Competency 0009–Understand coordinate and transformational geometry.
For example:
- Analyze two- and three-dimensional figures using coordinate systems.
- Connect algebra and geometry by applying concepts of distance, midpoint, and slope to classify figures and solve problems in the coordinate plane.
- Analyze transformations of figures in the coordinate plane.
- Analyze figures in terms of symmetry and tessellations of the plane.
Domain IV–Statistics and Probability
Competency 0010–Understand principles and techniques of statistics.
For example:
- Analyze the effects of bias and sampling techniques.
- Use appropriate formats for organizing and displaying data.
- Analyze univariate and bivariate data in a variety of representations.
- Make inferences and justify conclusions from data presented in a variety of representations (e.g., scatter plots).
- Analyze the use of measures of central tendency and spread.
Competency 0011–Understand principles of probability and techniques for determining probability.
For example:
- Determine probabilities of simple and compound events.
- Use counting principles (e.g., permutations, combinations) to calculate probabilities and solve problems.
- Use a variety of visual representations to calculate probabilities.
- Demonstrate knowledge of methods for simulating probabilities.