OregonOregon Algebra 2 Curriculum
Video lessons and practice for every Algebra 2 topic. Aligned to Oregon Mathematics Standards so Oregon high school students can keep up or get ahead.
Oregon Algebra 2 Curriculum | StudyPugHelp
ID | Standard | StudyPug Topic |
|---|---|---|
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.A.2 | Rewrite expressions involving radicals and rational exponents using the properties of exponents. |
CC.HSF.IF.A.1 | Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). |
CC.HSF.IF.A.2 | Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. |
CC.HSF.IF.A.3 | Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. |
CC.HSF.IF.B.4 | For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. |
CC.HSF.IF.B.5 | Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. |
CC.HSF.IF.B.6 | Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. |
CC.HSF.IF.C.7 | Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. |
CC.HSF.IF.C.8 | Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. |
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.A.1 | Write a function that describes a relationship between two quantities. |
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.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.1 | Distinguish between situations that can be modeled with linear functions and with exponential functions. |
CC.HSF.LE.A.2 | Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). |
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.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.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.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.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.BF.B.4 | Find inverse functions. |
CC.HSF.BF.B.5 | Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents. |
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.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. |
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.7 | Solve quadratic equations with real coefficients that have complex solutions. |
CC.HSN.CN.C.8 | Extend polynomial identities to the complex numbers. |
CC.HSN.CN.C.9 | Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. |
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.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.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.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.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.B.9 | Use permutations and combinations to compute probabilities of compound events and solve problems. |
Oregon Algebra 2: What Students Learn
Oregon Algebra 2 is a rigorous high school math course that extends skills from Algebra 1 and Geometry. Students working through this course encounter a wide range of topics that build the mathematical foundation needed for pre-calculus, calculus, and college-level math. Every topic below aligns to the Oregon Mathematics Standards.
Rational Exponents and Radicals
Students begin by extending the properties of integer exponents to rational exponents. This unit connects radical notation with exponential notation, allowing students to rewrite expressions in equivalent forms and apply exponent rules fluently.
Functions and Their Properties
A major focus of Algebra 2 is the formal study of functions. Students learn function notation, evaluate functions for given inputs, interpret key features of graphs and tables, and calculate average rates of change. They also explore how transformations such as f(x) + k and f(kx) affect graphs, and compare functions represented algebraically, graphically, and numerically.
Polynomial and Rational Expressions
Students add, subtract, multiply, and factor polynomials, applying the Remainder Theorem to identify zeros and sketch graphs. The unit extends to rational expressions, where students rewrite, add, subtract, multiply, and divide them, and solve rational and radical equations while identifying extraneous solutions.
- Polynomial identities and numerical relationships
- Binomial Theorem and Pascal's Triangle
- Rational expression operations and simplification
Exponential and Logarithmic Functions
Students explore the inverse relationship between exponents and logarithms, solve exponential equations by expressing solutions as logarithms, and use technology to evaluate them. They also distinguish between linear and exponential growth models and construct functions from graphs, tables, and verbal descriptions.
Trigonometric Functions
Oregon Algebra 2 includes a full trigonometry unit. Students study radian measure, the unit circle, special triangle values, and the graphs of sine, cosine, and tangent. They prove the Pythagorean identity, apply addition and subtraction formulas, model periodic phenomena, and use inverse trigonometric functions to solve real-world problems. The Laws of Sines and Cosines are also introduced for solving non-right triangles.
Complex Numbers
Students learn that complex numbers have the form a + bi where i² = -1. They add, subtract, multiply, and divide complex numbers, represent them on the complex plane in rectangular and polar form, and solve quadratic equations with complex solutions. The Fundamental Theorem of Algebra is introduced in this context.
Matrices
Students represent systems of linear equations as matrix equations, perform matrix operations including addition, subtraction, scalar multiplication, and matrix multiplication, and find inverse matrices to solve systems. Key properties such as non-commutativity of matrix multiplication and the roles of zero and identity matrices are explored.
Conic Sections
Students derive equations for parabolas using focus and directrix, and derive equations for ellipses and hyperbolas using the definition based on distances from foci. These geometric connections reinforce algebraic reasoning.
Statistics and Probability
The course concludes with data analysis and probability. Students fit data to normal distributions, interpret two-way frequency tables, apply conditional probability, use permutations and combinations, and determine whether two events are independent.
How StudyPug Supports Oregon Algebra 2 Students
StudyPug offers Algebra 2 video lessons for every topic listed above. Each lesson is 5-15 minutes and can be paused, rewound, and replayed. After each lesson, students can work through practice problems to check their understanding. Whether your student is preparing for a test, catching up after a missed class, or working ahead, StudyPug provides on-demand support aligned to Oregon Mathematics Standards.