flagUtah
Secondary Mathematics III

Utah Secondary Mathematics III Curriculum

Video lessons and practice for every Secondary Mathematics III topic. Aligned to Utah Core Standards Math so Utah students can keep up, catch up, or get ahead.

Utah Secondary Mathematics III Curriculum | StudyPugHelp

Print

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.

Utah Secondary Mathematics III: Full Course Overview

Secondary Mathematics III is one of the most demanding courses in the Utah high school math sequence. It builds directly on Secondary Mathematics I and II, extending students' understanding into advanced algebra, trigonometry, statistics, and new number systems. StudyPug covers every standard in this course with video lessons and step-by-step practice problems aligned to Utah Core Standards Math.

Algebra and Functions

Students in Secondary Mathematics III work extensively with polynomial, rational, and radical expressions. Key skills include applying the Remainder Theorem, proving polynomial identities, using the Binomial Theorem, and rewriting rational expressions. The course also introduces logarithmic functions and their inverse relationship with exponential functions, allowing students to model real-world situations involving exponential growth and decay.

  • Interpret and rewrite algebraic expressions in equivalent forms
  • Add, subtract, multiply, and divide rational expressions
  • Solve rational and radical equations, including identifying extraneous solutions
  • Find inverse functions and understand logarithm-exponent relationships
  • Express exponential equations using logarithms and evaluate using technology

Trigonometric Functions

Trigonometry is a major focus of Secondary Mathematics III. Students move from right-triangle trigonometry into the full unit circle model, working with radian measure, special angles, and the graphs of sine, cosine, and tangent. They also explore inverse trigonometric functions and use them to solve modeling problems.

  • Understand radian measure and the unit circle
  • Evaluate sine, cosine, and tangent for special angles (π/3, π/4, π/6)
  • Model periodic phenomena using amplitude, frequency, and midline
  • Prove and apply the Pythagorean identity sin²(θ) + cos²(θ) = 1
  • Use addition and subtraction formulas for sine, cosine, and tangent
  • Apply the Law of Sines and Law of Cosines to solve triangles

Geometry and Modeling

Students derive equations for conic sections — parabolas, ellipses, and hyperbolas — using their geometric definitions. They also apply volume formulas for cylinders, cones, pyramids, and spheres, and use geometric methods to solve real-world design problems involving density and area.

  • Derive the equation of a parabola from its focus and directrix
  • Derive equations of ellipses and hyperbolas from their foci
  • Use volume formulas to solve problems with three-dimensional figures
  • Apply concepts of density and geometric modeling to real-world contexts

Statistics and Probability

The statistics strand in Secondary Mathematics III introduces normal distributions, two-way frequency tables, inference from samples, and probability distributions. Students learn to evaluate the results of surveys and randomized experiments, and to make decisions using expected value.

  • Fit data to a normal distribution and estimate population percentages
  • Interpret two-way frequency tables including joint and conditional relative frequencies
  • Distinguish between sample surveys, experiments, and observational studies
  • Use simulation to estimate margins of error and compare treatment effects
  • Define and graph probability distributions; calculate expected value
  • Use probability to analyze decisions and evaluate fairness

Complex Numbers and Advanced Algebra

Secondary Mathematics III formally introduces complex numbers. Students learn to represent, operate on, and graph complex numbers in both rectangular and polar form on the complex plane. The Fundamental Theorem of Algebra is introduced, confirming that every polynomial equation has a solution in the complex number system.

  • Define i and perform arithmetic with complex numbers
  • Find conjugates and compute moduli and quotients
  • Represent complex numbers on the complex plane in rectangular and polar form
  • Solve quadratic equations with complex solutions
  • Know and apply the Fundamental Theorem of Algebra

Vectors and Matrices

Students are introduced to vectors as quantities with both magnitude and direction, and to matrices as tools for representing and transforming data. Matrix operations, including multiplication and finding inverses, are used to solve systems of linear equations and to understand geometric transformations.

  • Represent vectors as directed line segments and find their components
  • Add, subtract, and scale vectors; solve problems involving velocity
  • Use matrices to represent data and perform operations
  • Understand matrix multiplication properties including non-commutativity
  • Use inverse matrices to solve systems of linear equations
  • Interpret 2×2 matrices as transformations of the plane

Sequences and Series

Students derive and apply the formula for the sum of a finite geometric series. This connects to exponential reasoning and lays groundwork for calculus-level thinking about infinite series.

  • Derive the formula for the sum of a finite geometric series
  • Apply the formula to solve real-world and mathematical problems