Massachusetts Grade 10 Mathematics MCAS (DESE): the five conceptual categories, the two computer-based sessions and calculator policy, the reference sheet, the four achievement levels, and how to study after Question 2

The Grade 10 Mathematics MCAS is the high school mathematics test in the Massachusetts Comprehensive Assessment System, administered by the Massachusetts Department of Elementary and Secondary Education (DESE). It is built directly from the high school standards in the 2017 Massachusetts Curriculum Framework for Mathematics. This page is the index for the whole subject: it explains the five conceptual categories, the two computer-based sessions with their calculator policy, the item types, the reference sheet, the four achievement levels, and, importantly, what changed after the November 2024 ballot vote. The topic pages below carry the worked MCAS-style questions across the online item types.

What the test is, and what changed in 2024

For three decades the Grade 10 MCAS in English Language Arts and Mathematics, plus one high school Science and Technology/Engineering test, formed the state's Competency Determination: the set of exams a student had to pass to earn a high school diploma. In November 2024 voters approved ballot Question 2, which repealed the law tying the diploma to those test scores. Under DESE guidance issued on 11 December 2024, a student now earns the Competency Determination by completing district-certified coursework that meets the state academic standards, not by reaching a passing MCAS score.

This is the single most important fact for a current Grade 10 student to understand correctly:

• The Grade 10 Mathematics MCAS is still administered to nearly all students. Participation is required by state and federal law, and Question 2 did not change that.
• A passing score is no longer required to graduate. The test is no longer a graduation gate.
• The results still matter: they feed the state's school and district accountability system and give families a measure of how a student is performing against the standards.

So the test is real, it still counts for accountability, and doing well still signals readiness, but failing it no longer blocks a diploma. This page treats the Grade 10 Mathematics MCAS as what it now is: a meaningful measure of high school mathematics, worth preparing for, that is no longer an exit exam.

The five conceptual categories

The 2017 framework organizes the high school mathematics standards into five conceptual categories, and the Grade 10 test draws on all five. It assesses standards that overlap the Model Algebra I and Model Geometry courses, or the Model Mathematics I and Model Mathematics II courses for schools on the integrated pathway, so it is a survey of foundational high school mathematics rather than a single-course exam.

The topic pages on this site follow these five categories, plus a sixth set of pages on exam strategy.

The two sessions and the calculator policy

The Grade 10 Mathematics test is computer-based for nearly all students; a paper-based form is offered only as an approved accommodation. It is made up of two separate test sessions. Each session contains a mix of question types, and the test is largely self-paced within DESE's session time targets.

The calculator policy depends on the session. One portion of the test is taken without a calculator, to check the fluency a student should have by hand, and the remaining portion allows a calculator (the one built into the online platform, or an approved handheld). Because the no-calculator portion exists, you cannot rely on a calculator for arithmetic, factoring, fraction work, or simplifying a radical. A Grade 10 Mathematics Reference Sheet is available to every student throughout the test.

The item types

On the computer-based test the Grade 10 Mathematics questions come in several formats:

• Selected-response questions, which on the test are multiple-choice (one correct option) and multiple-select (choose all that apply from several options). Multiple-select is unforgiving: you usually earn the point only when every correct option is chosen and no incorrect one is.
• Technology-enhanced items, such as dragging values into a table, plotting points or a line or a parabola on a grid, or typing an expression or equation into the online equation editor. Many of these are scored by exact match, so a sign slip simply costs the point.
• Short-answer questions, which ask for a brief numeric or symbolic answer.
• Constructed-response (open-response) questions, which are worth more points and require you to show or explain your work. These are scored with a rubric that awards partial credit for a correct method and clear reasoning, so a bare answer with no work loses most of the available points.

The achievement levels

Raw points are converted to a scale score, and DESE reports the result in one of four achievement levels, from highest to lowest:

• Exceeding Expectations
• Meeting Expectations
• Partially Meeting Expectations
• Not Meeting Expectations

Meeting Expectations is the benchmark that signals a student is on track for the next grade and for college and career readiness. The raw-to-scale conversion is set by DESE for each administration to keep the standard consistent across forms, so you should not assume a fixed number of raw points maps to a particular level.

The reference sheet

Every student is given a Grade 10 Mathematics Reference Sheet, and a copy appears at the end of the released test items document. It provides:

• Area formulas: triangle $A = \frac{1}{2}bh$, rectangle $A = bh$, parallelogram $A = bh$, trapezoid $A = \frac{1}{2}(b_1 + b_2)h$, and circle $A = \pi r^2$, plus the circumference $C = 2\pi r$ and the approximation $\pi \approx 3.14$.
• Volume formulas: rectangular prism $V = Bh$ (or $lwh$), cylinder $V = \pi r^2 h$, sphere $V = \frac{4}{3}\pi r^3$, cone $V = \frac{1}{3}\pi r^2 h$, and pyramid $V = \frac{1}{3}Bh$, with total surface area formulas alongside.
• Right-triangle tools: the Pythagorean theorem $a^2 + b^2 = c^2$, the special right triangle ratios, and the trigonometric ratios $\sin, \cos, \tan$.
• A few algebra and finance formulas: the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, simple interest, and distance equals rate times time.

The sheet is a support, not a substitute for understanding. Many essentials are not on it: the slope formula, the laws of exponents and logarithms, the line forms (slope-intercept and point-slope), vertex form, and every statistics formula must be carried in memory. Knowing which formula fits a problem is the skill the test rewards.

How to study the Grade 10 Mathematics MCAS

1. Build no-calculator fluency. A whole session is taken without a calculator. Practice integer and fraction arithmetic, factoring, simplifying radicals, and evaluating expressions by hand until they are automatic.
2. Write like a rubric scorer on constructed response. Show the setup, every step, and a sentence of interpretation in context. A correct answer with no work loses most of the open-response points; correct method with a small slip still earns partial credit.
3. Know the reference sheet and its gaps. Practice with it in front of you so you know exactly what it gives. Memorize the slope formula, the exponent and logarithm rules, the line forms, and the statistics formulas, which are not on it.
4. Practice the online item types. Multiple-select, drag-and-drop, graphing, and equation-editor entry behave differently from paper multiple choice. The DESE practice tests on the MCAS Resource Center let you rehearse the exact interface.
5. Connect the five categories. Functions reappear in geometry through coordinate methods; the quadratic formula links algebra and functions; ratios connect number, geometry, and statistics. Seeing the through-lines makes each topic an extension rather than a fresh start.

The categories, topic by topic

Each topic below has its own answer page with worked MCAS-style questions, plus an overview guide and a quiz for each module.

Number and Quantity.

• The real number system and rational versus irrational, properties of exponents, radicals and rational exponents, units, quantities, and precision, ratios, rates, and proportional reasoning.

Algebra and expressions.

• Interpreting and rewriting expressions, polynomial operations and factoring, linear equations and inequalities, systems of equations and inequalities, solving quadratic equations, creating equations from context.

Functions.

• Function notation and key features, linear functions and rate of change, quadratic functions and their graphs, exponential functions and growth, comparing and building functions, transformations of functions.

Geometry.

• Congruence and rigid motions, similarity and dilations, right triangle trigonometry, circles, angles, and arcs, coordinate geometry, volume and surface area.

Statistics and probability.

• One-variable data and distributions, two-variable data and scatterplots, linear regression and correlation, probability rules and models, interpreting data and avoiding traps.

Exam strategy.

• Using the reference sheet and the calculator, the no-calculator session, answering constructed-response questions, technology-enhanced and multiple-select items, estimation and checking your work, time management and the achievement levels.

For the official materials

DESE publishes the Grade 10 Mathematics released items, the scoring guides and sample student work, the Grade 10 Mathematics Reference Sheet, and the test design documentation on its Massachusetts Comprehensive Assessment System pages, and computer-based practice tests are on the MCAS Resource Center. For the current rules on graduation and the Competency Determination after Question 2, the authoritative source is DESE's own guidance and regulations. Always study from the current released items, because the question style, the item types, and the standards are specific to the Massachusetts MCAS.