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Mathematics III

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Massachusetts Mathematics III Help: Master Concepts FastHelp

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ID

Standard

StudyPug Topic

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.REI.C.7

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

CC.HSA.APR.B.2

Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).

CC.HSA.APR.C.4

Prove polynomial identities and use them to describe numerical relationships.

CC.HSA.APR.C.5

Know and apply the Binomial Theorem for the expansion of (x + y)^n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.

CC.HSA.APR.D.6

Rewrite simple rational expressions in different forms.

CC.HSA.APR.D.7

Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

CC.HSA.REI.A.2

Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

CC.HSA.CED.A.4

Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

CC.HSA.REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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.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.B.6

Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.

CC.HSF.TF.B.7

Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.

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.HSF.TF.C.9

Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

CC.HSG.SRT.D.9

Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

CC.HSG.SRT.D.10

Prove the Laws of Sines and Cosines and use them to solve problems.

CC.HSG.SRT.D.11

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.

CC.HSG.GPE.A.2

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

CC.HSG.GPE.A.3

Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

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.2

Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

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.A.4

Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

CC.HSS.ID.B.5

Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

CC.HSS.IC.A.1

Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

CC.HSS.IC.A.2

Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

CC.HSS.IC.B.3

Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

CC.HSS.IC.B.4

Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

CC.HSS.IC.B.5

Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

CC.HSS.IC.B.6

Evaluate reports based on data.

CC.HSS.MD.A.1

Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions.

CC.HSS.MD.A.2

Calculate the expected value of a random variable; interpret it as the mean of the probability distribution.

CC.HSS.MD.A.3

Develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated; find the expected value.

CC.HSS.MD.B.7

Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

CC.HSN.CN.A.1

Know there is a complex number i such that i^2 = -1, and every complex number has the form a + bi with a and b real.

CC.HSN.CN.A.2

Use the relation i^2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

CC.HSN.CN.A.3

Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.

CC.HSN.CN.B.4

Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.

CC.HSN.CN.B.5

Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation.

CC.HSN.CN.B.6

Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.

CC.HSN.CN.C.9

Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

CC.HSN.VM.A.1

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes.

CC.HSN.VM.A.2

Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.

CC.HSN.VM.A.3

Solve problems involving velocity and other quantities that can be represented by vectors.

CC.HSN.VM.B.5

Multiply a vector by a scalar.

CC.HSN.VM.C.6

Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.

CC.HSN.VM.C.7

Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.

CC.HSN.VM.C.8

Add, subtract, and multiply matrices of appropriate dimensions.

CC.HSN.VM.C.9

Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.

CC.HSN.VM.C.10

Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.

CC.HSN.VM.C.11

Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.

CC.HSN.VM.C.12

Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.

CC.HSA.REI.C.5

Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

CC.HSA.REI.C.8

Represent a system of linear equations as a single matrix equation in a vector variable.

CC.HSA.REI.C.9

Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).

CC.HSA.SSE.B.4

Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.
Complete Massachusetts Mathematics III Coverage

Mathematics III Lessons

189

Video Explanations

1184

Practice Problems

1921

Massachusetts Standards

100% Aligned

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Complete Math III curriculum with video lessons on polynomials, trigonometry, statistics, complex numbers, and matrices. Includes practice problems, step-by-step solutions, and progress tracking for every topic.

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