Algebra II

Completion: 0%

Quadratic Functions

HSA-SSE.3HSA-REI.4HSF-IF.8
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Complete the Square (a = 1)--
Complete the Square (a ≠ 1)--
Find the Vertex--
Quadratic Formula (Integer Roots)--
Quadratic Formula (Irrational/Complex)--
Discriminant & Nature of Roots--

Polynomial Functions

HSA-APR.2HSA-APR.3HSA-APR.6
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Evaluate Polynomials--
End Behavior--
Polynomial Long Division--
Synthetic Division--
Remainder Theorem--
Find Rational Zeros--

Rational Expressions

HSA-APR.6HSA-APR.7HSA-REI.2
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Simplify Rational Expressions--
Multiply/Divide Rational Expressions--
Add/Subtract (Same Denominator)--
Add/Subtract (Different Denominators)--
Solve Rational Equations--

Radical Expressions & Equations

HSN-RN.1HSN-RN.2HSA-REI.2
0%
Simplify Square Roots--
Add/Subtract Radicals--
Multiply Radicals--
Rationalize Denominators--
Solve Radical Equations--

Exponential & Logarithmic Functions

HSF-BF.5HSF-LE.4HSF-IF.7e
0%
Evaluate Exponential Expressions--
Evaluate Logarithms--
Logarithm Properties (Expand)--
Logarithm Properties (Condense)--
Solve Exponential Equations--
Solve Logarithmic Equations--

Systems of Equations

HSA-REI.5HSA-REI.6HSA-REI.7
0%
Substitution Method--
Elimination Method--
Three-Variable Systems--
Nonlinear Systems--

Sequences & Series

HSF-BF.2HSF-LE.2HSA-SSE.4
0%
Arithmetic Sequence (nth term)--
Arithmetic Series (sum)--
Geometric Sequence (nth term)--
Geometric Series (finite sum)--
Infinite Geometric Series--

Common Core Standards

N-RN — The Real Number System

Extend the properties of exponents to rational exponents.
  • HSN-RN.1Explain 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.
  • HSN-RN.2Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Use properties of rational and irrational numbers.
  • HSN-RN.3Explain 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.

N-Q — Quantities

Reason quantitatively and use units to solve problems.
  • HSN-Q.1Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
  • HSN-Q.2Define appropriate quantities for the purpose of descriptive modeling.
  • HSN-Q.3Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.

A-SSE — Seeing Structure in Expressions

Interpret the structure of expressions.
  • HSA-SSE.1Interpret expressions that represent a quantity in terms of its context.
  • HSA-SSE.2Use the structure of an expression to identify ways to rewrite it.
Write expressions in equivalent forms to solve problems.
  • HSA-SSE.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • HSA-SSE.4Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems.

A-APR — Arithmetic with Polynomials & Rational Expressions

Perform arithmetic operations on polynomials.
  • HSA-APR.1Understand 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.
Understand the relationship between zeros and factors of polynomials.
  • HSA-APR.2Know and apply the Remainder Theorem.
  • HSA-APR.3Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

A-CED — Creating Equations

Create equations that describe numbers or relationships.
  • HSA-CED.1Create equations and inequalities in one variable and use them to solve problems.
  • HSA-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • HSA-CED.3Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
  • HSA-CED.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI — Reasoning with Equations & Inequalities

Understand solving equations as a process of reasoning and explain the reasoning.
  • HSA-REI.1Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution.
  • HSA-REI.2Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Solve equations and inequalities in one variable.
  • HSA-REI.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • HSA-REI.4Solve quadratic equations in one variable.
Solve systems of equations.
  • HSA-REI.5Prove 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.
  • HSA-REI.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • HSA-REI.7Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
Represent and solve equations and inequalities graphically.
  • HSA-REI.10Understand 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).
  • HSA-REI.11Explain 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).
  • HSA-REI.12Graph the solutions to a linear inequality in two variables as a half-plane (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 half-planes.

F-IF — Interpreting Functions

Understand the concept of a function and use function notation.
  • HSF-IF.1Understand 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.
  • HSF-IF.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • HSF-IF.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Interpret functions that arise in applications in terms of the context.
  • HSF-IF.4For 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.
  • HSF-IF.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • HSF-IF.6Calculate 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.
Analyze functions using different representations.
  • HSF-IF.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • HSF-IF.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • HSF-IF.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

F-BF — Building Functions

Build a function that models a relationship between two quantities.
  • HSF-BF.1Write a function that describes a relationship between two quantities.
  • HSF-BF.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
Build new functions from existing functions.
  • HSF-BF.3Identify 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.
  • HSF-BF.4Find inverse functions.

F-LE — Linear, Quadratic, & Exponential Models

Construct and compare linear, quadratic, and exponential models and solve problems.
  • HSF-LE.1Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • HSF-LE.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs.
  • HSF-LE.3Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Interpret expressions for functions in terms of the situation they model.
  • HSF-LE.5Interpret the parameters in a linear or exponential function in terms of a context.

G-CO — Congruence

Experiment with transformations in the plane.
  • HSG-CO.1Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
  • HSG-CO.2Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs.
  • HSG-CO.3Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
  • HSG-CO.4Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  • HSG-CO.5Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software.
Understand congruence in terms of rigid motions.
  • HSG-CO.6Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure.
  • HSG-CO.7Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
  • HSG-CO.8Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

G-SRT — Similarity, Right Triangles, & Trigonometry

Understand similarity in terms of similarity transformations.
  • HSG-SRT.1Verify experimentally the properties of dilations given by a center and a scale factor.
  • HSG-SRT.2Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles.
  • HSG-SRT.3Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarity.
  • HSG-SRT.4Prove theorems about triangles.
  • HSG-SRT.5Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Define trigonometric ratios and solve problems involving right triangles.
  • HSG-SRT.6Understand 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.
  • HSG-SRT.7Explain and use the relationship between the sine and cosine of complementary angles.
  • HSG-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

S-ID — Interpreting Categorical & Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable.
  • HSS-ID.1Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • HSS-ID.2Use 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.
  • HSS-ID.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
Summarize, represent, and interpret data on two categorical and quantitative variables.
  • HSS-ID.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data.
  • HSS-ID.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
Interpret linear models.
  • HSS-ID.7Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
  • HSS-ID.8Compute (using technology) and interpret the correlation coefficient of a linear fit.
  • HSS-ID.9Distinguish between correlation and causation.