Massachusetts · MA DESESyllabus
Maths syllabus, dot point by dot point
Every dot point in the Massachusetts Mathssyllabus, with a focused answer for each one. Click any dot point for a worked explainer, past exam questions, and links to related dot points. Written by Claude Opus 4.8, Anthropic's latest AI.
Algebra and Expressions
Module overview →- How do you translate a real-world situation into an equation or inequality and interpret the answer?Create linear, quadratic, and exponential equations and inequalities from a verbal context, solve them, and interpret the solution back in the situation with units.9 min answer →
- How do you read the structure of an algebraic expression and rewrite it to reveal what it means?Interpret the parts of an expression (terms, factors, coefficients) in context, and rewrite expressions in equivalent forms to reveal a quantity such as a y-intercept, a zero, a maximum, or a rate.9 min answer →
- How do you solve linear equations and inequalities, and when does the inequality sign flip?Solve multi-step linear equations and inequalities in one variable, rearrange literal equations for a chosen variable, and represent inequality solutions on a number line.9 min answer →
- How do you add, subtract, and multiply polynomials, and how do you factor them completely?Add, subtract, and multiply polynomials, and factor completely using the greatest common factor, the difference of two squares, and trinomial factoring.9 min answer →
- How do you solve a quadratic equation, and how do you choose between factoring, square roots, and the formula?Solve quadratic equations by factoring with the zero-product property, by taking square roots, and by the quadratic formula, use the discriminant to count real roots, and interpret solutions in context.10 min answer →
- How do you solve a system of equations, and how many solutions can a system have?Solve systems of linear equations by substitution and elimination, recognize systems with one, no, or infinitely many solutions, and find the solution region of a system of inequalities.9 min answer →
Exam Strategy
Module overview →- How do you earn full credit on constructed-response (open-response) questions on the MCAS?Structure a constructed-response answer to earn rubric credit: show the setup and every step, define variables, justify reasoning, and state the answer in context with units.9 min answer →
- How do estimation and checking strategies catch errors and rule out wrong answers on the MCAS?Use estimation to judge whether an answer is reasonable, substitute solutions back to verify, and apply units and benchmarks to catch errors before submitting.9 min answer →
- How do you handle technology-enhanced and multiple-select items on the computer-based MCAS?Approach the computer-based item types: multiple-select (all that apply), drag-and-drop, graphing, and equation-editor entry, with the exact-match scoring and all-or-nothing rules in mind.9 min answer →
- How do you prepare for and handle the no-calculator portion of the Grade 10 Math MCAS?Build the by-hand fluency the calculator-free session demands: integer and fraction arithmetic, factoring, simplifying radicals, and exact answers, and apply efficient mental-math strategies.9 min answer →
- How do you manage time across the two sessions, and what do the four achievement levels mean?Manage time across the two self-paced sessions, prioritize secure points, understand the four next-generation achievement levels, and prepare with released items and practice tests.9 min answer →
- How do you make the most of the reference sheet and the calculator on the Grade 10 Math MCAS?Use the Grade 10 Mathematics Reference Sheet efficiently, know which formulas it does and does not provide, and use the calculator (where allowed) as a check rather than a crutch.9 min answer →
Functions
Module overview →- How do you compare functions given in different forms, and how do you build a function from a description or table?Compare properties of two functions represented in different ways (graph, table, equation, words), and build a function (linear or exponential) to model a relationship from a description or data.9 min answer →
- How do exponential functions model growth and decay, and how do they differ from linear functions?Write and interpret exponential functions for growth and decay, identify the initial value and growth factor, and contrast exponential change (constant ratio) with linear change (constant difference).9 min answer →
- What is function notation, and how do you read the key features of a function from its graph or table?Use and interpret function notation, evaluate functions, identify domain and range, and read key features (intercepts, intervals of increase and decrease, maximum and minimum) from a graph or table.9 min answer →
- How do you find the slope and equation of a line, and what does the rate of change mean in context?Find the slope of a line from two points, write linear equations in slope-intercept and point-slope form, and interpret slope as a constant rate of change in context.9 min answer →
- How do you read the vertex, axis of symmetry, and intercepts of a parabola, and what do the three forms tell you?Graph quadratic functions, find the vertex and axis of symmetry, identify zeros and the y-intercept, and connect standard, factored, and vertex forms to the parabola's features.10 min answer →
- How do changes to a function's equation shift, stretch, or reflect its graph?Describe and apply transformations of functions: vertical and horizontal shifts, reflections, and vertical stretches or compressions, and connect a change in the equation to the change in the graph.9 min answer →
Geometry
Module overview →- How do you find arc length, sector area, and circle measures on the MCAS?Find circumference and area of circles, compute arc length and sector area as fractions of the whole, and apply the central-angle and inscribed-angle relationships.9 min answer →
- What are the rigid motions, and how do they define congruence on the MCAS?Identify and apply rigid motions (translations, reflections, rotations), describe their effect on coordinates, and use them to explain why two figures are congruent.9 min answer →
- How do the distance, midpoint, and slope formulas let you analyze figures on the coordinate plane?Use the distance formula, the midpoint formula, and slope to find lengths and midpoints, classify figures, and verify properties such as parallel and perpendicular sides on the coordinate plane.9 min answer →
- How do the Pythagorean theorem and the trig ratios solve right triangles on the MCAS?Apply the Pythagorean theorem and the sine, cosine, and tangent ratios to find missing sides and angles in right triangles, including in real-world contexts such as angles of elevation.10 min answer →
- What makes two figures similar, and how do dilations and scale factors work on the MCAS?Use dilations and scale factors to establish similarity, set up proportions between corresponding sides of similar figures, and relate the scale factor to changes in perimeter and area.9 min answer →
- How do you find the volume and surface area of solids using the reference sheet formulas?Compute the volume and surface area of prisms, cylinders, cones, spheres, and pyramids using the reference sheet formulas, and solve real-world problems involving capacity and material.9 min answer →
Number and Quantity
Module overview →- How do the laws of exponents let you simplify expressions, and how are zero and negative exponents handled on the MCAS?Apply the product, quotient, and power rules for exponents, interpret zero and negative integer exponents, and simplify expressions with integer exponents without a calculator.9 min answer →
- How do you simplify radicals and rewrite them as rational exponents on the MCAS?Simplify square and cube roots, perform operations with radicals, and convert between radical form and rational-exponent form using the relationship a^(1/n) equals the nth root of a.9 min answer →
- How do you set up and solve proportions, and how do percent change and unit rates appear on the MCAS?Set up and solve proportions, compute and compare unit rates, and apply percent increase, decrease, and percent change to real-world quantities.9 min answer →
- What makes a number rational or irrational, and how do operations on them behave on the Grade 10 MCAS?Classify real numbers as rational or irrational, explain why sums and products of rational and irrational numbers behave as they do, and place numbers on the real number line.9 min answer →
- How do you convert units, use rates, and report answers with appropriate precision on the MCAS?Use unit analysis to convert measurements and rates, choose appropriate units for a quantity, and report answers with a level of accuracy suited to the context.9 min answer →
Statistics and Probability
Module overview →- How do you interpret statistics critically and avoid common data traps on the MCAS?Interpret statistics in context, judge whether a measure or claim is appropriate, recognize misleading displays and biased samples, and reason about how outliers affect summaries.9 min answer →
- How do you use a line of best fit to make predictions, and what does correlation tell you?Fit and interpret a linear model for bivariate data, use the line of best fit to predict and to interpret slope and intercept in context, and distinguish correlation from causation.9 min answer →
- How do you summarize a single data set with center, spread, and shape on the MCAS?Compute and interpret measures of center (mean, median) and spread (range, interquartile range), read box plots and histograms, and describe the shape of a distribution.9 min answer →
- How do you compute probabilities of single and combined events on the MCAS?Compute theoretical and experimental probabilities, apply the addition rule for either-or events and the multiplication rule for independent events, and find complements.9 min answer →
- How do you read a scatterplot and describe the association between two variables on the MCAS?Read scatterplots, describe the form, direction, and strength of an association, identify clusters and outliers, and interpret two-way frequency tables.9 min answer →