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Mathematics II

Massachusetts Mathematics II Curriculum

Video lessons and practice for every Mathematics II topic. Aligned to the Massachusetts Mathematics Curriculum Framework for high school students.

Massachusetts Mathematics II Curriculum | StudyPugHelp

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CC.HSN.Q.A.1

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

CC.HSN.Q.A.3

Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

CC.HSA.SSE.A.1

Interpret expressions that represent a quantity in terms of its context.

CC.HSA.SSE.B.3

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

CC.HSA.APR.A.1

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

CC.HSA.APR.B.3

Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

CC.HSA.CED.A.1

Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

CC.HSA.CED.A.2

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

CC.HSA.REI.C.7

Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

CC.HSF.IF.C.9

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

CC.HSF.BF.B.3

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

CC.HSF.LE.A.3

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.

CC.HSF.LE.A.4

For exponential models, express as a logarithm the solution to ab^ct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

CC.HSF.IF.A.3

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

CC.HSF.BF.A.2

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

CC.HSN.RN.A.1

Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

CC.HSN.RN.B.3

Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

CC.HSF.TF.A.1

Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

CC.HSF.TF.A.2

Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

CC.HSF.TF.A.3

Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π–x, π+x, and 2π–x in terms of their values for x, where x is any real number.

CC.HSF.TF.B.5

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

CC.HSF.TF.C.8

Prove the Pythagorean identity sin^2(θ) + cos^2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

CC.HSG.SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor.

CC.HSG.SRT.A.2

Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

CC.HSG.SRT.B.5

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

CC.HSG.SRT.C.6

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

CC.HSG.SRT.C.7

Explain and use the relationship between the sine and cosine of complementary angles.

CC.HSG.C.A.1

Prove that all circles are similar.

CC.HSG.C.A.2

Identify and describe relationships among inscribed angles, radii, and chords.

CC.HSG.C.A.3

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

CC.HSG.C.A.4

Construct a tangent line from a point outside a given circle to the circle.

CC.HSG.C.B.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

CC.HSG.GPE.A.1

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

CC.HSG.GPE.A.2

Derive the equation of a parabola given a focus and directrix.

CC.HSG.GPE.B.5

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.

CC.HSG.GPE.B.6

Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

CC.HSG.GPE.B.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

CC.HSG.GMD.A.1

Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

CC.HSG.GMD.A.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

CC.HSG.GMD.B.4

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

CC.HSG.MG.A.1

Use geometric shapes, their measures, and their properties to describe objects.

CC.HSG.MG.A.2

Apply concepts of density based on area and volume in modeling situations.

CC.HSS.ID.B.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

CC.HSS.CP.A.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").

CC.HSS.CP.A.2

Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

CC.HSS.CP.A.3

Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

CC.HSS.CP.A.5

Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.

CC.HSS.CP.B.7

Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

CC.HSS.CP.B.9

Use permutations and combinations to compute probabilities of compound events and solve problems.

Massachusetts Mathematics II: Full Course Overview

Mathematics II is a pivotal high school course in Massachusetts that deepens students' understanding of algebra, geometry, functions, and probability. Aligned to the Massachusetts Mathematics Curriculum Framework, this course prepares students for advanced mathematics and directly supports performance on the Grade 10 MCAS assessment.

Algebra and Functions

Students in Massachusetts Mathematics II extend their algebraic reasoning to work with quadratic and exponential expressions. Key topics include:

  • Interpreting and rewriting expressions, including rational exponents and radicals
  • Creating and solving quadratic equations and systems involving linear and quadratic equations
  • Analyzing function transformations — shifts, stretches, and reflections
  • Writing arithmetic and geometric sequences recursively and explicitly
  • Exploring exponential growth and comparing it to linear and polynomial growth
  • Finding inverse functions and expressing exponential solutions using logarithms

Geometry and Trigonometry

The geometry strand of Massachusetts Mathematics II covers similarity, right triangle trigonometry, circles, and coordinate geometry. Students will:

  • Use similarity transformations and the AA criterion to prove triangles similar
  • Apply trigonometric ratios (sine, cosine, tangent) and the Pythagorean Theorem to solve applied problems
  • Prove theorems about triangles and use congruence and similarity in geometric proofs
  • Explore circle theorems including inscribed angles, chords, and tangent lines
  • Derive equations of circles and parabolas using the Pythagorean Theorem and coordinate methods
  • Use coordinates to prove geometric theorems, find distances, and compute perimeters and areas

Trigonometric Functions

Massachusetts Mathematics II introduces the unit circle and radian measure, extending trigonometry beyond right triangles. Students learn to:

  • Understand radian measure and the unit circle definition of sine, cosine, and tangent
  • Use special triangles to find exact trigonometric values for key angles
  • Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1
  • Model periodic phenomena using trigonometric functions with specified amplitude, frequency, and midline

Probability and Statistics

The probability strand builds students' ability to reason about uncertainty and data. Topics include:

  • Describing events using set notation — unions, intersections, and complements
  • Understanding and applying conditional probability and independence
  • Constructing and interpreting two-way frequency tables
  • Applying the Addition Rule and Multiplication Rule for probability
  • Using permutations and combinations to compute probabilities of compound events

How StudyPug Supports Massachusetts Mathematics II Students

StudyPug offers video lessons and practice problems for every topic listed above, fully aligned to the Massachusetts Mathematics Curriculum Framework. Whether a student is preparing for an upcoming test, catching up after a tough week, or getting ahead before the next unit, StudyPug is available on any device — anytime. Students can watch short 5–15 minute lessons, replay any section, and build confidence through guided practice problems with worked solutions.