Algebra 2 Course Details

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Course Metrics

  • Common Core Algebra 2 SkillsSkills
    344
  • Video Lessons for Common Core Algebra iiTutorials
    339
  • Video LessonsVideo Lessons
    178
  • Free Response Question for Common Core Algebra iiExamples
    1205
  • Online practice assessment for Common Core Algebra 2Free Response Questions
    9758
  • Algebra 2 Off-line Practice SheetsMultiple Choice Questions
    3204
  • Math Activities for Common Core Algebra iiOnline Practice Assessments
    105
  • Graded Assessments for Online Algebra 2 CourseGraded Assessments
    107
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Overview

The Algebra II curriculum at Educo Learning Center (ELC) focuses on essential topics aligned with the Common Core standards. In Algebra 2, students build on foundational algebraic principles, focusing on complex topics like polynomial, rational, radical relationships, and trigonometric functions. They explore real and complex number systems, perform operations with vectors and matrices, and apply arithmetic to polynomials and rational expressions. Key areas include understanding and interpreting functions, constructing and comparing linear, quadratic, and exponential models, and extending the domain of trigonometric functions using the unit circle. Students also delve into statistical analysis, evaluating data, and understanding probability, aiming to develop advanced problem-solving skills and prepare for higher-level mathematics.

Educo Learning Center Algebra II Math curriculum offers a comprehensive learning experience with interactive tutorials, detailed lecture notes, lecture videos, unlimited online practice, printable practice sheets or e-workbooks, online assignments, and tests. Students benefit from instant feedback with solutions and detailed progress reports. The curriculum emphasizes real-world problem-solving and visual representations to achieve grade-level outcomes, ensuring students grasp essential topics aligned with Common Core standards.

"I Can" Statements For Math Algebra 2

Mathematics | High School—Number and Quantity

Domain: The Real Number System

HSN-RN

Cluster: Extend the properties of exponents to rational exponents.
Standard HSN-RN.A.1
Standard Description 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.
For example, we define 51/3 to be the cube root of 5 because we want (51/3) 3 = 5 (1/3)3 to hold, so (51/3) 3 must equal 5.
Online Corse Hierarchy 6.1, 7.4, 7.5
I Can Statements I can describe the relationship between rational exponents and radicals.
Standard HSN-RN.A.2
Standard Description 2. Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Online Corse Hierarchy 7.5
I Can Statements I can rewrite expressions that contain radicals and/or rational exponents using the properties of exponents.
Standard HSN-RN.B.3
Standard Description 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.
Online Corse Hierarchy 1.2
I Can Statements I can explain which operations are closed in the set of real numbers and its subsets of rational and irrational numbers.
Standard HSN-CN.A.1
Standard Description 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.
Online Corse Hierarchy 5.4
I Can Statements I can define complex numbers.
Standard HSN-CN.A.2
Standard Description 2. Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Online Corse Hierarchy 5.4
I Can Statements I can add, subtract, and multiply complex numbers.
Standard HSN-CN.A.3
Standard Description 3. (+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
Online Corse Hierarchy 5.4
I Can Statements I can find conjugates of complex numbers.
I can divide complex numbers.
Standard HSN-CN.C.7
Standard Description 7. Solve quadratic equations with real coefficients that have complex solutions.
Online Corse Hierarchy 5.5
I Can Statements I can solve quadratic equations with real coefficients that have complex solutions.
Standard HSN-CN.C.8
Standard Description 8. (+) Extend polynomial identities to the complex numbers.
For example, rewrite x2 + 4 as (x + 2i) (x – 2i)
Online Corse Hierarchy 5.5
I Can Statements I can extend polynomial identities to complex numbers.
Standard HSN-CN.C.9
Standard Description 9. (+) Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.
Online Corse Hierarchy 5.5
I Can Statements I can understand the Fundamental Theorem of Algebra.
Standard HSN-VM.A.1
Standard Description 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 (e.g., v, |v|, ||v||, v).
Online Corse Hierarchy 4.7
I Can Statements I can define vectors, their direction, and their magnitude.
Standard HSN-VM.A.2
Standard Description 2. (+) Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
Online Corse Hierarchy 4.7
I Can Statements I can find the components of a vector.
Standard HSN-VM.B.4
Standard Description 4. (+) Add and subtract vectors. a. Add vectors end-to-end, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
b. Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
c. Understand vector subtraction v – w as v + (–w), where –w is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and performing vector subtraction component-wise.
Online Corse Hierarchy 4.7
I Can Statements I can add and subtract vectors.
Standard HSN-VM.B.5
Standard Description 5. (+) Multiply a vector by a scalar
a. Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication component-wise, e.g., as c(vx, vy) = (cvx, cvy).
b. Compute the magnitude of a scalar multiple cv using ||cv|| = |c|v. Compute the direction of cv knowing that when |c|v ≠ 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Online Corse Hierarchy 4.7
I Can Statements I can multiply vectors by a scalar.
I can define dot product.
Standard HSN-VM.C.7
Standard Description 7. (+) Multiply matrices by scalars to produce new matrices, e.g., when all the payoffs in a game are doubled.
Online Corse Hierarchy 4.1
I Can Statements I can define a matrix.
I can multiply a matrix by a scalar.
Standard HSN-VM.C.8
Standard Description 8. (+) Add, subtract, and multiply matrices of appropriate dimensions.
Online Corse Hierarchy 4.1, 4.2
I Can Statements I can add and subtract matrices and multiply matrices.
Standard HSN-VM.C.9
Standard Description 9. (+) Understand that, unlike the multiplication of numbers, matrix multiplication for square matrices is not a commutative operation but still satisfies the associative and distributive properties.
Online Corse Hierarchy 4.2
I Can Statements I can multiply matrices and understand the properties of matrices.
Standard HSNVM.C.10
Standard Description 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.
Online Corse Hierarchy 4.4, 4.5, 4.6
I Can Statements I can find the determinant of matrices.
Standard HSNVM.C.12
Standard Description 12. (+) Work with 2 × 2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Online Corse Hierarchy 4.3, 4.4
I Can Statements I can define transformations with matrices.
I can find the area using determinants.

Mathematics | High School—Algebra

Standard HSA-SSE.A.1
Standard Description 1. Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
For example, interpret P(1+r)n as the product of P and a factor not depending on P
Online Corse Hierarchy 1.1, 1.4, 1.6, 6.3, 6.5, 11.1, 11.2
I Can Statements I can interpret algebraic expressions that describe realworld scenarios. This means:
I can interpret the parts of an expression including the factors, coefficients, and terms.
I can use grouping strategies to interpret expressions.
I can create and interpret quadratic and exponential algebraic expressions to describe real-world scenarios.
Standard HSA-SSE.A.2
Standard Description 2. Use the structure of an expression to identify ways to rewrite it.
For example, see x4 – y 4 as (x2 ) 2 – (y2 ) 2 , thus recognizing it as a difference of squares that can be factored as (x2 – y 2 )(x2 + y2 ).
Online Corse Hierarchy 6.5, 8.1, 8.2, 8.5
I Can Statements I can recognize the difference of squares.
I can recognize a quadratic perfect square trinomial.
Standard HSA-SSE.B.3
Standard Description 3. Choose and produce an equivalent form of an expression to reveal and explain the properties of the quantity represented by the expression.
a. Factor a quadratic expression to reveal the zeros of the function it defines.
Online Corse Hierarchy 6.3
I Can Statements I can determine if rewriting an expression will reveal important properties of the expression.
I can factor a quadratic expression to reveal its zeros.
Standard HSA-SSE.B.4
Standard Description 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.
For example, calculate mortgage payments
Online Corse Hierarchy 11.2
I Can Statements I can define geometric series.
I can 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.
Standard HSA-APR.A.1
Standard Description 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.
Online Corse Hierarchy 6.2, 6.3,
I Can Statements I can identify a polynomial expression.
I can add, subtract, multiply, and divide polynomials.
Standard HSA-APR.B.2
Standard Description 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).
Online Corse Hierarchy 6.7, 6.8
I Can Statements I can apply remainder and factor theorems.
I can define a relationship between roots and zeros.
Standard HSA-APR.B.3
Standard Description 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.
Online Corse Hierarchy 5.3, 6.4
I Can Statements I can identify zeros of polynomials by factorization.
Standard HSA-APR.C.5
Standard Description 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.
Online Corse Hierarchy 11.4
I Can Statements I can 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.
Standard HSA-APR.D. 6
Standard Description 6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Online Corse Hierarchy 8.1, 8.2, 8.3
I Can Statements I can simplify rational expressions.
Standard HSA-APR.D.7
Standard Description 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.
Online Corse Hierarchy 8.1, 8.2, 8.3
I Can Statements I can simplify rational expressions.
I can add, subtract, multiply, and divide rational expressions.
Standard HSA-CED.A.1
Standard Description 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.
Online Corse Hierarchy 1.3, 1.4, 1.5, 1.6, 5.3, 6.5
I Can Statements I can solve linear equations in one variable.
I can solve and graph inequalities.
I can solve absolute value equations and inequalities.
I can solve polynomial equations.
I can solve rational equations.
Standard HSA-CED.A.2
Standard Description 2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Online Corse Hierarchy 2.2, 2.4, 5.1, 8.3, 8.4
I Can Statements I can write and graph equations representing a relationship between two variables or quantities.
I can write and interpret quadratic equations and inequalities mathematically and in context, graphically and algebraically.
Standard HSA-CED.A.3
Standard Description 3. Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.
For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
Online Corse Hierarchy 6.6, 10.6
I Can Statements I can represent constraints with linear equations, inequalities, and systems of equations or inequalities.
I can determine whether solutions are viable or
non-viable options, given the constraints provided in a modeling context.
Standard HSA-CED.A.4
Standard Description 4. Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
For example, rearrange Ohm's law. V = IR to highlight resistance R.
Online Corse Hierarchy 1.3
I Can Statements I can solve formulas for a particular variable of interest.
Standard HSA-REI.A.1
Standard Description 1. Explain each step in solving a simple equation as following from the equality of numbers asserted in the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
Online Corse Hierarchy 1.3
I Can Statements I can explain and justify each step for solving multi-step linear equations.
Standard HSA-REI.A.2
Standard Description 2. Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Online Corse Hierarchy 7.4, 7.6, 8.5
I Can Statements I can solve radical equations.
I can solve rational equations.
Standard HSA-REI.B.3
Standard Description 3. Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Online Corse Hierarchy 1.3, 1.5, 1.6
I Can Statements I can solve multi-step linear equations in one variable, including equations with coefficients represented by letters.
I can solve multi-step linear inequalities in one variable.
Standard HSA-REI.B.4
Standard Description 4. Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula, and factoring as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.
Online Corse Hierarchy 5.3, 5.5
I Can Statements I can determine whether the solution of a quadratic equation will be real or complex.
I can find real solutions to quadratic equations in one variable using multiple methods and justify my solution method.
Standard HSA-REI.C.5
Standard Description 5. Prove that, given a system of two equations in two variables, replacing one equation with the sum of that equation and a multiple of the other produces a system with the same solutions.
Online Corse Hierarchy 3.1
I Can Statements I can write, solve, interpret, and justify my solution method for systems of linear equations using multiple methods (linear combination, substitution, and graphing).
Standard HSA-REI.C.6
Standard Description 6. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Online Corse Hierarchy 3.1
I Can Statements I can solve a system of linear equations using multiple methods (linear combination, substitution, and graphing).
Standard HSA-REI.C.7
Standard Description 7. Solve a simple system consisting of linear and quadratic equations in two variables algebraically and graphically.
For example, find the points of intersection between the line y = – 3x and the circle x 2 + y2 = 3.
Online Corse Hierarchy 10.6
I Can Statements I can solve a system of equations consisting of linear equations and quadratic equations algebraically and graphically.
Standard HSA-REI.C.9
Standard Description 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).
Online Corse Hierarchy 4.5, 4.6
I Can Statements I can find the inverse of a matrix.
I can use matrices to solve a system of equations.
Standard HSA-REI.D.10
Standard Description 10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
Online Corse Hierarchy 2.2
I Can Statements I can graphically describe and interpret the solution set of a system of equations and relate that to the algebraic solution.
Standard HSA-REI.D.11
Standard Description 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 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.
Online Corse Hierarchy 8.5, 10.6
I Can Statements I can solve a system of linear and quadratic equations.
I can solve rational equations.
Standard HSA-REI.D.12
Standard Description 12. Graph the solutions to a linear inequality in two variables as a halfplane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding halfplanes.
Online Corse Hierarchy 2.7, 3.3
I Can Statements I can describe and interpret the solutions to a system of linear inequalities graphically.

Mathematics | High School—Functions

Standard HSF-IF.A.1
Standard Description 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).
Online Corse Hierarchy 2.1
I Can Statements I can determine if a relation is a function.
I can represent a function using a graph, table, and equation and describe the relationship between each form using function notation.
Standard HSF-IF.A.2
Standard Description 2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of context.
Online Corse Hierarchy 2.1
I Can Statements I can evaluate a function using function notation and interpret the value in context.
I can determine the domain and range of a function.
Standard HSF-IF.A.3
Standard Description 3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
Online Corse Hierarchy 11.3
I Can Statements I can recognize that sequences are functions.
I can define arithmetic sequences.
Standard HSF-IF.B.4
Standard Description 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. Key features include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Online Corse Hierarchy 2.4, 5.1, 6.4, 7.2, 7.3, 8.3, 9.1, 9.2
I Can Statements I can interpret the graphical representation of linear and exponential functions. This means:
I can identify and interpret an appropriate domain and range.
I can interpret key elements of the graph, including the average rate of change,
y-intercept, x-intercepts.
I can sketch a graph showing key features given a particular scenario or context.
Standard HSF-IF.B.5
Standard Description 5. Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Online Corse Hierarchy 5.1, 6.4, 7.1, 7.2, 7.3, 8.4, 9.2
I Can Statements I can determine the appropriate domain of a function.
I can solve direct, joint, and inverse variation equations.
Standard HSF-IF.B.6
Standard Description 6. Calculate and interpret a function's average rate of change (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
Online Corse Hierarchy 2.3
I Can Statements I can calculate and interpret the rate of change of a function.
I can estimate the rate of change over a given interval from a graph.
Standard HSF-IF.C.7
Standard Description 7. Graph functions expressed symbolically and show key features of the graph by hand in simple cases and using technology for more complicated cases.
a. graph linear and quadratic functions and show intercepts, maxima, and minima.
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
c. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available and showing end behavior.
e. graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Online Corse Hierarchy 2.4, 5.1, 7.2, 7.3, 8.3, 9.1, 9.2, 14.1
I Can Statements I can graph linear, exponential, and quadratic functions that are expressed symbolically. This means:
I can show intercepts, maxima, and minima.
I can graph square root and cube root functions.
I can graph piecewisedefined functions, including step functions and absolute value functions.
I can graph polynomial functions.
I can graph a rational function.
I can graph exponential and logarithmic functions.
I can graph trigonometric functions.
Standard HSF-IF.C.8
Standard Description 8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of context.
b. Use the properties of exponents to interpret expressions for exponential functions.
For example, identify the percent rate of change in functions such as y = (1.02)t , y = (0.97)t , y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.
Online Corse Hierarchy 5.1, 5.3, 6.8, 8.3, 9.1, 9.5
I Can Statements I can factor to find the zeros of a quadratic function.
I can complete the square to show extreme values and symmetry.
I can interpret important points on a quadratic graph in terms of context.
I can model exponential growth and decay.
Standard HSF-IF.C.9
Standard Description 9. Compare properties of two functions, each represented differently (algebraically, graphically, numerically in tables, or by verbal descriptions).
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Online Corse Hierarchy 5.1, 7.2, 7.3
I Can Statements I can compare two functions, each represented differently (graphs, tables, equations, verbal descriptions), and draw conclusions based on those comparisons.
Standard HSF-BF.A.1
Standard Description 1. Write a function that describes a relationship between two quantities.
a. Determine an explicit expression, a recursive process, or steps for calculation from a context.
c. (+) Compose functions.
For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
Online Corse Hierarchy 7.1, 11.2
I Can Statements I can write and use recursive formulas for geometric sequences.
I can compose functions.
Standard HSF-BF.A.2
Standard Description 2. Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Online Corse Hierarchy 11.1, 11.2
I Can Statements I can explain that sequences are functions and are sometimes defined recursively.
Standard HSF-BF.B.3
Standard Description 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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
Online Corse Hierarchy 5.1, 8.3
I Can Statements I can determine the effect of a transformational constant on a linear function.
I can describe how a quadratic function can be transformed using a constant, k. This means:
I can experiment with different transformational constants and construct an argument about their effect on a quadratic function using technology.
I can determine the transformational constant from a graph of a quadratic (shifts and stretches, both vertical and horizontal).
Standard HSF-BF.B.4
Standard Description 4. Find inverse functions. a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse.
For example, f(x) =2x3 or f(x) = (x+1)/(x–1) for x ≠ 1.
b. (+) Verify by composition that one function is the inverse of another.
c. (+) Read values of an inverse function from a graph or a table, given that the function has an inverse. d. (+) Produce an invertible function from a non-invertible function by restricting the domain.
Online Corse Hierarchy 7.2
I Can Statements I can find and determine the inverse of relations and functions.
Standard HSF-BF.B.5
Standard Description 5. (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.
Online Corse Hierarchy 9.2, 9.3, 9.4, 9.5
I Can Statements I can understand the inverse relationship between exponents and logarithms.
I can use the properties of logarithms.
I can solve growth and decay problems.
Standard HSF-LE.A.1
Standard Description 1. Distinguish between situations that can be modeled with linear functions and with exponential functions.
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Online Corse Hierarchy 2.3
I Can Statements I can recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Standard HSF-LE.A.2
Standard Description 2. Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).
Online Corse Hierarchy 2.4
I Can Statements I can construct different forms of linear functions given a graph, a description of a relationship, or two input-output pairs (including reading these from a table).
Standard HSF-LE.A.4
Standard Description 4. For exponential models, express as a logarithm the solution to abct = d where a, c, and d are numbers, and the base b is 2, 10, or e; evaluate the logarithm using technology.
Online Corse Hierarchy 9.2, 9.4, 9.5
I Can Statements I can solve exponential and logarithmic equations and inequalities.
Standard HSF-LE.B.5
Standard Description 5. Interpret the parameters in a linear or exponential function in terms of a context.
Online Corse Hierarchy 2.4, 9.1
I Can Statements I can interpret the parameters in linear and exponential function models in terms of their contexts.
Standard HSF-TF.A.1
Standard Description 1. Understand the radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
Online Corse Hierarchy 13.1
I Can Statements I can define the radian measure of an angle.
Standard HSF-TF.A.2
Standard Description 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.
Online Corse Hierarchy 13.1
I Can Statements I can describe the importance of the unit circle for extending trigonometric functions to all real numbers.
Standard HSF-TF.A.3
Standard Description 3. (+) Use special triangles to determine geometrically the values of sine, cosine, and 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.
Online Corse Hierarchy 13.2, 13.3, 14.1
I Can Statements I can find circular functions of angles.
I can solve right triangle trigonometry.
Standard HSF-TF.B.5
Standard Description 5. Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
Online Corse Hierarchy 14.1
I Can Statements I can determine the trigonometric function that best models a situation based on period, amplitude, frequency, and midline.
I can graph trigonometric functions.
Standard HSF-TF.B.7
Standard Description 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.
Online Corse Hierarchy 13.5, 14.6
I Can Statements I can define inverse trigonometric functions.
I can solve trigonometric equations.
Standard HSF-TF.C.8
Standard Description 8. Prove the Pythagorean identity sin2 (θ) + cos2 (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.
Online Corse Hierarchy 14.2, 14.3, 14.5, 14.6
I Can Statements I can prove trigonometric identities.
Standard HSF-TF.C.9
Standard Description 9. (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
Online Corse Hierarchy 14.4
I Can Statements I can prove sum and difference trigonometric identities.

Mathematics | High School—Geometry

Standard HSG-SRT.C.6
Standard Description 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.
Online Corse Hierarchy 13.3
I Can Statements I can find and use trigonometric ratios.
Standard HSG-SRT.C.7
Standard Description 7. Explain and use the relationship between the sine and cosine of complementary angles.
Online Corse Hierarchy 13.3
I Can Statements I can explain and use the relationship between the sine and cosine of complementary angles.
Standard HSG-SRT.C.8
Standard Description 8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Online Corse Hierarchy 13.3
I Can Statements I can solve problems using the Pythagoras Theorem.
I can identify right triangles.
Standard HSG-SRT.D.9
Standard Description 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.
Online Corse Hierarchy 13.3
I Can Statements I can derive the formula
A = 1/2 ab sin(C) for the area of a triangle
Standard HSGSRT.D.10
Standard Description 10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
Online Corse Hierarchy 13.4
I Can Statements I can prove the Laws of Sines and Cosines and use them to solve problems
Standard HSGSRT.D.11
Standard Description 11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
Online Corse Hierarchy 13.4
I Can Statements I can apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles.
Standard HSG-GPE.A.1
Standard Description 1. Derive the equation of a circle of a given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Online Corse Hierarchy 10.3
I Can Statements I can derive the equation of a circle of a given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
Standard HSG-GPE.A.2
Standard Description 2. Derive the equation of a parabola given a focus and directrix.
Online Corse Hierarchy 10.2
I Can Statements I can derive the equation of a parabola given a focus and directrix.
Standard HSG-GPE.A.3
Standard Description 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.
Online Corse Hierarchy 10.4, 10.5
I Can Statements I can 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.
Standard HSG-GPE.B.5
Standard Description 5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Online Corse Hierarchy 2.4
I Can Statements I can find slopes of parallel and perpendicular lines.
I can find the equation of a line parallel or perpendicular to the given line.

Mathematics | High School—Statistics and Probability

Standard HSS-ID.A.2
Standard Description 2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Online Corse Hierarchy 12.4, 12.7
I Can Statements I can compare the center (mean and median) and spread (interquartile range and standard deviation) of two or more data sets based on the shape of the data distribution.
Standard HSS-ID.A.3
Standard Description 3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Online Corse Hierarchy 12.4
I Can Statements I can interpret differences in shape, center, and spread based on the context of the data set and determine possible effects of outliers on these measures.
Standard HSS-ID.A.4
Standard Description 4. Use a data set's mean and standard deviation to fit it to a normal distribution and estimate population percentages. Recognize that there are data sets for which such a procedure is inappropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.
Online Corse Hierarchy 12.7
I Can Statements I can define the normal distribution, z-scores.
I can estimate areas under the normal curve.
Standard HSS-ID.B.6
Standard Description 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems in the data context. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.
b. Informally assess the fit of a function by plotting and analyzing residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.
Online Corse Hierarchy 2.5
I Can Statements I can show two variable data on a scatter plot.
I can describe the relationship between the variables.
I can identify a function of best fit for the data set.
I can assess the fit of a function to a data set.
Standard HSS-IC.A.1
Standard Description 1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
Online Corse Hierarchy 12.8
I Can Statements I can define samples.
Standard HSS-IC.B.3
Standard Description 3. Recognize the purposes and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
Online Corse Hierarchy 12.8
I Can Statements I can classify data and analyze samples and surveys.
Standard HSS-IC.B.4
Standard Description 4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error using simulation models for random sampling.
Online Corse Hierarchy 12.8
I Can Statements I can find the margin of error.
Standard HSS-CP.A.1
Standard Description 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”).
Online Corse Hierarchy 12.2
I Can Statements I can find theoretical and experimental probabilities.
Standard HSS-CP.A.2
Standard Description 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.
Online Corse Hierarchy 12.2
I Can Statements I can understand independent events.
Standard HSS-CP.A.3
Standard Description 3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret the 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.
Online Corse Hierarchy 12.3
I Can Statements I can understand conditional probability.
Standard HSS-CP.B.6
Standard Description 6. Find the conditional probability of A given B as the fraction of B’s outcomes that also belong to A, and interpret the answer in terms of the model.
Online Corse Hierarchy 12.3
I Can Statements I can find conditional probability.
Standard HSS-CP.B.7
Standard Description 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.
Online Corse Hierarchy 12.3
I Can Statements I can find probabilities of mutually exclusive and overlapping events.
I can find probabilities of independent and dependent events using the addition rule.
Standard HSS-CP.B.8
Standard Description 8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
Online Corse Hierarchy 12.3
I Can Statements I can apply the multiplication rule of probability.
Standard HSS-CP.B.9
Standard Description 9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
Online Corse Hierarchy 12.1
I Can Statements I can use permutations and combinations to compute probabilities.
Standard HSS-MD.A.1
Standard Description 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.
Online Corse Hierarchy 12.5
I Can Statements I can define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space.
I can graph the corresponding probability distribution using the same graphical displays as for data distributions.
Standard HSS-MD.A.3
Standard Description 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.
For example, find the theoretical probability distribution for the number of correct answers obtained by guessing on all five questions of a multiple-choice test where each question has four choices, and find the expected grade under various grading schemes.
Online Corse Hierarchy 12.5
I Can Statements I can develop a probability distribution for a random variable defined for a sample space in which theoretical probabilities can be calculated.
Standard HSS-MD.A.4
Standard Description 4. (+) Develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically; find the expected value.
For example, find a current data distribution on the number of TV sets per household in the United States, and calculate the expected number of sets per household. How many TV sets would you expect to find in 100 randomly selected households?
Online Corse Hierarchy 12.5
I Can Statements I can develop a probability distribution for a random variable defined for a sample space in which probabilities are assigned empirically.
Standard HSS-MD.B.6
Standard Description 6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).
Online Corse Hierarchy 12.7
I Can Statements I can compute normal probabilities.
Standard HSS-MD.B.7
Standard Description 7. (+) Analyse decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
Online Corse Hierarchy 12.7
I Can Statements I can analyze decisions and strategies using probability concepts.
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E-Workbook

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Algebra 2

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Inside the e-Workbook

CHAPTER 1:
Equations and Inequalities
Expressions and Formulas
Properties of Real Numbers
Solving Equations and Literal Equations
Solving Absolute Value Equations
Solving Inequalities
Solving Absolute Value and Compound Inequalities
CHAPTER 2:
Linear Relations and Functions
Relations and Functions
Linear Equations in Two Variables
Slope
Writing Linear Equations
Statistics: Using Scatter Plots
Special Functions
Graphing Inequalities
CHAPTER 3:
Systems of Equations and Inequalities
Solving System of Linear Equations in Two Variables
Solve Linear Equations in Three Unknown
Solving a System of Linear Inequalities
Linear Programming
CHAPTER 4:
Matrices and Determinants
Determinants and Cramer's Rule
Inverse of a Matrix
Using Matrices to Solve System of Equations
Vectors
CHAPTER 5:
Quadratic Functions and Inequalities
Graphing Quadratic Functions
Solving Quadratic Equations Graphically
Solving Quadratic Equations by Factoring
Complex Numbers
Completing the Square and The Quadratic Formula
Graphing and Solving Quadratic Inequalities
CHAPTER 6:
Polynomial Functions
Properties of Exponents
Polynomial Functions and Operations with Polynomials
Dividing Polynomials
Graphs of Polynomial Functions
Factoring Trinomials
Solving Polynomial Equations
The Remainder and Factor Theorem
Roots and Zeros
CHAPTER 7:
Radical Equations and Inequalities
Operations on Functions
Inverse Functions and Relations
Square Root Functions and Inequalities and nth Roots
Operations with Radical Expressions
Rational Exponents
Solving Radical Equations and Inequalities
CHAPTER 8:
Rational Expressions and Equations
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Graphing Rational Functions
Direct, Joint and Inverse Variation
Solving Rational Equations and Inequalities
CHAPTER 9:
Exponential and Logarithmic Relations
The Exponential Function
Logarithmic Functions
Properties of Logarithms
Exponential and Logarithmic Equations and Inequalities
Growth and Decay Functions (Applications)
CHAPTER 10:
Conic Sections
Midpoint and Distance Formula
Parabolas
Circles
Ellipses
Hyperbolas
Solving Quadratic Systems
CHAPTER 11:
Sequences and Series
Arithmetic Sequences and Series
Geometric Sequences and Series
Recursion and Special Sequences
The Binomial Theorem
Mathematical Induction
CHAPTER 12:
Probability and Statistics
The Counting Principle, Permutations and Combinations
Introduction to Probability
Addition and Multiplication Rules of Probability
Measures of Dispersion Variance and SD
Discrete Probability Distributions
Binomial and Exponential Distribution
Normal Distribution
Sampling and Error
CHAPTER 13:
Trigonometric Functions
The Unit Circle and Measurement of Angles
Circular Functions of Angles
Right Triangle Trigonometry
The Law of Sines and Cosines
Inverse Trigonometric Functions
CHAPTER 14:
Trigonometric Graphs and Identities
Graphing Trigonometric Functions
Trigonometric Identities
Proving Identities in Trigonometric Function
Sum and Difference Identities
Double and Half Angle Identities
Solving Trigonometric Equations

Common Core Standards

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ELC courses cover 100% of skills defined in Common Core Math Standards for Algebra 2. In addition to CCSS skills, our Algebra 2 course covers essential pre-requisites skills from previous grades for review and more advanced skills for students who want to get ahead.

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How to read the grade level standards?

Algebra 2 Domains Summary:

Code Conceptual Category Domains Topics
HSN Number and Quantity The Real Number
System N-RN
  • Properties of Real Numbers
  • Properties of Exponents
  • Operations with Radical Expressions
  • Rational Exponents
The Complex Number System N-CN
  • Complex Numbers
Vector and Matrix
Quantities N-VM
  • Introduction to Matrices and
    Operations
  • Multiplying Matrices
  • Transformations with Matrices
  • Determinants and Cramer's Rule
  • Inverse of Matrix
  • Vectors
HSA Algebra Seeing Structure in
Expressions A-SSE
  • Expressions and Formulas
  • Factoring Trinomials
Arithmetic with
Polynomials and
Rational Expressions
A-APR
  • Polynomial Functions and Operations
    with Polynomials
  • Dividing Polynomials
  • Graphs of Polynomial Functions
  • The Remainder and Factor Theorem
  • The Binomial Theorem
  • Multiplying and Dividing Rational
    Expressions
  • Adding and Subtracting Rational
    Expressions
Creating Equations
A-CED
  • Solving Equations and Literal
    Equations
  • Solving Absolute Value Equations
  • Direct, Joint and Inverse Variation
  • Linear Equations in 2-Variables
  • Standard Form of Equation of a Line
  • Solving Polynomial Equations
Reasoning with
Equations and
Inequalities A-REI
  • Graphing Inequalities
  • Solving System of Linear Equations
    in Two Variables
  • Solving System of Linear Inequalities
  • Solving Quadratic Equations by
    Factoring
  • Completing the Square and The
    Quadratic Formula
  • Solving Radical Equations and
    Inequalities
  • Using Matrices to Solve System of
    Equations
  • Solving Rational Equations and
    Inequalities
  • Solving Inequalities
  • Solving Compound and Absolute
    Value Inequalities
HSF Functions Interpreting Functions
F-IF
  • Relations and Functions
  • Graphing Quadratic Functions
  • Operations on Functions
  • Inverse Functions and Relations
  • Square Root Functions and
    Inequalities and nth Roots
  • Graphing Rational Functions
  • Slope
  • Recursion and Special Sequences
  • Roots and Zeros
Building Functions F-BF
  • Logarithmic Functions
  • Properties of Logarithms
  • Arithmetic Sequences and Series
  • Geometric Sequences and Series
Linear and Exponential
Models F-LE
  • The Exponential Function
  • Exponential and Logarithmic
    Equations and Inequalities
  • Growth and Decay Functions
    (Applications)
  • Writing Linear Equations
Trigonometric
Functions F-TF
  • The Unit Circle and Measurement of
    Angles
  • Exponential and Logarithmic
    Equations and Inequalities
  • Circular Functions of Angles
  • Right Triangle Trigonometry
  • Inverse Trigonometric Functions
  • Graphing Trigonometric Functions
  • Trigonometric Identities
  • Proving Identities in Trigonometric
    Functions
  • Sum and Difference Identities
  • Double and Half Angle Identities
  • Solving Trigonometric Equations
HSG Geometry Similarity, Right
Triangles, and
Trigonometry G-SRT
  • The Law of Sines and Cosines
Expressing Geometric
Properties with
Equations G-GPE
  • Parabolas
  • Circles
  • Ellipses
  • Hyperbolas
HSS Statistics and Probability Interpreting
Categorical and
Quantitative Data S-ID
  • Statistics: Using Scatter Plots
  • Measures of Dispersion: Variance and
    SD
  • Normal Distribution
Making Inferences and
Justifying Conclusions
S-IC
  • Sampling and Error
Conditional Probability
and the Rules of
Probability S-CP
  • The Counting Principle, Permutations
    and Combinations
  • Introduction to Probability
  • Addition and Multiplication Rules of Probability
Using Probability to
Make Decisions S-MD
  • Discrete Probability Distribution

The following table summarizes what Math domains are covered in K-12 grades:

Domains Code Grades
Counting & Cardinality CC K
Operations & Algebraic Thinking OA K,1,2,3,4,5
Number & Operations in Base 10 NBT K,1,2,3,4,5
NUMBER & Operations - Fractions NF K,1,2,3,4,5
Measurement & Data MD K,1,2,3,4,5
Geometry G K,1,2,3,4,5,6,7,8
Ratio & Proportional Relationships RP 6,7
Number System NS 6,7,8
Expressions & Equations EE 6.7.8
Functions F 8
Statistics & Probability SP 6-7-8,
Number & Quantity HSN 9-12
Algebra HAS 9-12
Functions HSF 9-12
Modeling HSM 9-12
Geometry HSG 9-12
Statistics & Probability HSS 9-12

Click here to discover the comprehensive Common Core State Standards.

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