Test Information Guide

Overview and Test Objectives
Field 63: Mathematics

Test Overview

Table outlining the test format, number of questions, time, and passing score.
Format Computer-based test (CBT); 100 multiple-choice questions, 2 open-response items
Number of Items by Subarea
  • Subarea I: 12–14 multiple-choice questions
  • Subarea II: 36–38 multiple-choice questions
  • Subarea III: 24–26 multiple-choice questions
  • Subarea IV: 24–26 multiple-choice questions
  • Subarea V: 2 open-response items
Time 4 hours (does not include 15-minute CBT tutorial)
Passing Score 240

The Massachusetts Tests for Educator Licensure (MTEL) are designed to measure a candidate's knowledge of the subject matter contained in the test objectives for each field. The MTEL are aligned with the Massachusetts educator licensure regulations and, as applicable, with the standards in the Massachusetts curriculum frameworks.

The test objectives specify the content to be covered on the test and are organized by major content subareas. The chart below shows the approximate percentage of the total test score derived from each of the subareas.

The test assesses a candidate's proficiency and depth of understanding of the subject at the level required for a baccalaureate major according to Massachusetts standards. Candidates are typically nearing completion of or have completed their undergraduate work when they take the test.

Pie chart of approximate test weighting.

Sub area I 10%, Sub area II 30%, Sub area III 20%, Sub area IV 20%, and Sub area V 20%.

Test Objectives

Table outlining test content and subject weighting by sub area and objective.
Subareas Range of Objectives Approximate Test Weighting
Multiple-Choice
I Number Sense and Operations 01–03 10%
II Relations, Functions, and Algebra 03–08 30%
III Geometry and Measurement 09–12 20%
IV Probability, Statistics, Calculus, and Discrete Mathematics 13–17 20%
80%
Open-Response*
V Integration of Knowledge and Understanding 18–19 20%

*The open-response items may relate to topics covered in any of the subareas.

Subarea I–Number Sense and Operations

Objective 0001: Apply knowledge of the properties and structure of the real number system.

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Objective 0002: Apply knowledge of the properties and structure of the complex number system and linear algebra.

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Subarea II–Relations, Functions, and Algebra

Objective 0003: Analyze and apply algebraic techniques to expressions, equations, and inequalities.

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Objective 0004: Apply the principles and properties of relations and functions.

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Objective 0005: Apply the principles and properties of linear, absolute value, and quadratic relations and functions.

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Objective 0006: Apply the principles and properties of exponential and logarithmic relations and functions.

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Objective 0007: Apply the principles and properties of polynomial, radical, and rational relations and functions.

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Objective 0008: Apply the principles and properties of trigonometric functions and identities.

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Subarea III–Geometry and Measurement

Objective 0009: Apply the principles, concepts, and procedures related to units and measurement.

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Objective 0010: Apply the axiomatic structure of Euclidean geometry.

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Objective 0011: Apply the principles and properties of Euclidean geometry to solve problems involving two- and three-dimensional objects.

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Objective 0012: Apply the principles and properties of coordinate and transformational geometry and the characteristics of non-Euclidean geometries.

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Subarea IV–Probability, Statistics, Calculus, and Discrete Mathematics

Objective 0013: Apply the principles, properties, and techniques of probability.

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Objective 0014: Apply the principles and concepts of descriptive statistics to the problem-solving process.

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Objective 0015: Apply principles and techniques of limits, continuity, and differential calculus.

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Objective 0016: Apply principles and techniques of integral calculus.

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Objective 0017: Apply the properties and techniques of discrete mathematics.

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Subarea V–Integration of Knowledge and Understanding

Objective 0018: Prepare an organized, developed analysis on a topic integrating knowledge from at least two of the following: number sense and operations; relations, functions, and algebra; geometry and measurement; probability, statistics, calculus, and discrete mathematics.

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Objective 0019: Prepare an organized, developed analysis on a topic integrating knowledge from at least two of the following: number sense and operations; relations, functions, and algebra; geometry and measurement; probability, statistics, calculus, and discrete mathematics.

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