Chapter 1 – Equations and Inequalities
Main Outcome:
To use properties to evaluate and simplify expressions, solve linear and absolute value equations and inequalities, and use problem solving strategies and models to translate verbal phrases into expressions, equations, and inequalities.
Detailed Outcomes:
To understand, interpret, and apply the vocabulary associated with equations and inequalities.
To identify number sets (real, natural, whole, integers, rational, irrational numbers), give examples of numbers in each set, and understand the relationship between the sets.
To graph any real number on a number line.
To simplify and evaluate expressions using order of operations and properties of real numbers by hand and using a graphing calculator.
To identify and apply algebraic properties given an equation.
To determine if a given number is a solution to an equation or inequality and explain what a solution means.
To solve linear equations and rewrite formulas and equations for a given variable.
To determine an equation from a word problem by using a formula, creating a table, looking for a pattern, or drawing a diagram.
To solve linear inequalities, including conjunction and disjunction inequalities, and graph the solution set on a number line or give an inequality when given the graph.
To solve and graph absolute value equations and inequalities as they relate to number lines and algebraically.
To use problem solving strategies and models to translate verbal phrases and sentences into expressions, equations, and inequalities.
Chapter 2 – Linear Equations and Functions
Main Outcome:
To determine and represent relations and functions, graph linear equations and inequalities in two variables and write linear equations and inequalities in two variables.
Detailed Outcomes:
To understand what a linear equation and function is and understand, interpret, and apply the vocabulary associated with linear equations and functions.
To identify if a set of ordered pairs, table, graph, or mapping diagram represents a relation or function and to find the domain and range of the relation or function given a set of ordered pairs, table, or graph.
To create a table, graph, or mapping diagram for a function given an equation by hand and on the graphing calculator.
To determine if a function is linear and evaluate functions.
To identify discrete and continuous functions from graphs or word problems.
To find the slope and rate of change given two points, a table, graph, or word problem and understand the relationship of slope and rate of change in a word problem.
To find slopes of parallel and perpendicular lines and determine if two given lines are parallel, perpendicular or neither.
To find x and y intercepts given an equation or graph, by hand and on the graphing calculator, and to create a graph using the x and y intercepts.
To graph linear equations by hand using a table of points and on the graphing calculator.
To graph linear equations and functions written in various forms including slope-intercept form and standard form by hand and on the graphing calculator.
To determine the equation of a line in standard form and slope-intercept form given points, a graph of a line, or a word problem.
To model direct variation with an equation or graph and apply direct variations to solve problems.
To draw scatter plots describe type of correlation and estimate the correlation coefficient.
To find the equation of a line of best fit by hand or use linear regression on the graphing calculator to find an equation and to use the equation to make predictions.
To recognize and compare the graphs of absolute value functions, and determine equations and graphs given a transformation on the absolute value function.
To recognize and graph piecewise functions.
To graph linear inequalities in two variables and absolute value inequalities.
Chapter 3 – Linear Systems and Matrices
Main Outcome:
To solve systems of linear equations using a variety of methods, graph systems of equations and inequalities, and apply the vocabulary associated with matrices to add, subtract, and multiply matrices and to find determinants and inverse matrices.
Detailed Outcomes:
To understand what linear systems and matrices are and understand, interpret, and apply the vocabulary associated with linear systems and matrices.
To solve linear systems in two variables by graphing by hand and on the graphing calculator, substitution, or elimination (linear combination) method.
To graph systems of linear inequalities.
To determine if systems are independent or dependent and consistent or inconsistent.
To solve linear programming problems.
To solve systems of linear equations in three variables.
To add, subtract, and multiply matrices.
To find determinants of 2 x 2 and 3 x 3 matrices.
To find inverses of 2 x 2 matrices and use them to solve linear systems of equations by hand and using the graphing calculator.
Chapter 4 – Quadratic Functions and Factoring
Main Outcome:
To graph and write quadratic functions in several forms, solve quadratic equations using a variety of methods, and perform operations with square roots and complex numbers.
Detailed Outcomes:
To understand what a quadratic function is and understand, interpret, and apply the vocabulary associated with quadratic functions.
To graph and compare quadratic functions by hand and using the graphing calculator.
To know the relationships and properties of quadratic functions and their graphs.
To find the vertex, axis of symmetry, maximum or minimum point, and x and y-intercepts of a quadratic function given an equation or graph by hand and using the graphing calculator.
To convert between standard form and vertex form for a quadratic function.
To factor quadratic functions using the greatest common factor, recognizing factoring rules, grouping, and the guess and check method.
To use the factors of quadratic functions to determine zeros by hand and using the graphing calculator.
To perform operations with complex numbers and plot complex numbers.
To solve quadratic functions with real and complex solutions by using square roots, factoring, completing the square and quadratic formula.
To find the value of the discriminant and use it to determine the nature of the roots of a quadratic function.
To solve and graph quadratic inequalities.
To create a quadratic function to model a situation from a word problem, graph, table, or set of points and explain what the variable in the function mean.
To use quadratic regression on the graphing calculator to find an equation and to use the equation to make predictions.
Chapter 5 – Polynomials and Polynomial Functions
Main Outcome:
To graph polynomial functions, perform operations with polynomials, and solve polynomial equations and find zeros.
Detailed Outcomes:
To understand what a polynomial is and understand, interpret, and apply the vocabulary associated with polynomials.
To simplify numerical and variable expressions using properties of exponents, including scientific notation.
To evaluate by substitution and synthetic division, graph polynomial functions, and describe the end behavior of the graph given an equation.
To add, subtract, and multiply polynomials.
To factor polynomial equations using greatest common factor, recognizing factoring patterns including the sum and differences of two cubes, grouping, and the guess and check method..
To solve polynomial equations and inequalities and those determined from word problems.
To divide polynomials using long division and synthetic division.
To apply the Remainder and Factor Theorems to determine factors and zeros by hand.
To use a graphing calculator to graph polynomials and determine zeros and factors.
To apply the Fundamental Theorem of Algebra to find the number of zeros, zeros of a polynomial function and use the zeros to write a polynomial function.
To analyze and compare graphs of polynomial functions and estimate x-intercepts, zeros, and local maximums and minimums.
To evaluate and write polynomial functions and models given a graph or table.
Chapter 6 – Rational Exponents and Radical Functions
Main Outcome:
To simplify expressions and solve equations with rational exponents, perform function operations and find inverse functions, and graph radical functions and solve radical equations.
Detailed Outcomes:
To understand what rational exponents and radical functions are and understand, interpret, and apply the vocabulary associated with rational exponents and radical functions.
To evaluate nth roots.
To simplify expressions and solve equations with rational exponents using properties of rational exponents.
To perform function operations and function composition.
To recognize whether a function has an inverse and find the inverse, and verify that functions are inverses.
To recognize a square root or cube root function by its graph.
To graph and compare square root and cube root functions including translations.
To solve radical equations and determine when solutions are extraneous.
Chapter 7 – Exponential and Logarithmic Functions
Main Outcome:
To graph exponential and logarithmic functions, evaluate and simplify logarithmic expressions, solve exponential and logarithmic equations, and write exponential functions.
Detailed Outcomes:
To understand what exponential and logarithmic functions are and understand, interpret, and apply the vocabulary associated with exponential and logarithmic functions.
To recognize and graph exponential growth and decay functions and determine domain, range, and asymptotes.
To recognize e as a constant, simplify expressions and graph functions involving e.
To evaluate and simplify logarithmic expressions using properties of logarithms and the relationship between exponential and logarithmic functions including common logarithms and natural logarithms.
To convert between logarithmic and exponential equations.
To evaluate logarithms using the change of base formula and inverse properties.
To recognize and graph logarithmic functions and determine the domain and range.
To find the inverse equation of a given function.
To solve exponential and logarithmic equations and determine when solutions are extraneous.
To determine if a given table, graph, equation, or worded problem represents an exponential function and write and apply the exponential function represented.
Chapter 8 – Rational Functions
Main Outcome:
To graph rational functions, perform operations with rational expressions, and solve rational equations.
Detailed Outcomes:
To understand what rational functions are and understand, interpret, and apply the vocabulary associated with rational functions.
To determine if an equation, table or verbal model represents a direct or inverse variation.
To model inverse and joint variation with an equation.
To graph rational functions and determine domain, range, and the equations of the asymptotes by hand and using the graphing calculator.
To add, subtract, multiply, and divide rational expressions.
To solve rational equations and determine when solutions are extraneous.
To solve rational inequalities algebraically and using the graphing calculator.
Chapter 9 – Quadratic Relations and Conic Sections
Main Outcome:
To write equations of conic sections, graph conic sections, and solve quadratic systems.
Detailed Outcomes:
To understand what quadratic relations and conic sections are and understand, interpret, and apply the vocabulary associated with quadratic relations and conic sections.
To apply the distance and midpoint formulas.
To recognize equations and graphs of circles, ellipses, parabolas, and hyperbolas.
To write equations to represent circles, ellipses, parabolas, and hyperbolas.
To draw the graphs of circles, ellipses, parabolas, and hyperbolas.
To translate and classify conic sections.
To solve quadratic systems of equations with two variables using graphs and algebraic methods.
Chapter 10 – Counting Methods and Probability
Main Outcome:
To apply counting principles, permutations, and combinations, find probabilities and odds, and interpret binomial distributions.
Detailed Outcomes:
To understand, interpret, and apply the vocabulary associated with counting methods and probability.
To apply the counting principles, permutations, and combinations.
To use Pascal’s Triangle and the Binomial Theorem.
To calculate the probability and odds of an event occurring, including probabilities of disjoint and overlapping events and independent and dependent events.
To understand and apply the vocabulary and notation of set theory and their associated Venn diagrams.
To construct and interpret binomial distributions.
Chapter 11 – Data Analysis
Main Outcome:
To find measures of central tendency and dispersion, apply normal distributions, and analyze samples.
Detailed Outcomes:
To understand, interpret, and apply the vocabulary associated with data analysis.
To find and analyze the measures of central tendency (mean, median, and mode).
To find and analyze the measures of dispersion (range, quartile values, variance and standard deviation).
To apply transformations to data.
To recognize, analyze, and apply normal distributions using a statistical table.
To draw conclusions from samples and determine biased samples and margins of error.
To choose the best model for two-variable data (linear, quadratic, cubic, exponential, and power functions).
Chapter 12 – Sequences and Series
Main Outcome:
To determine the type of sequence, find missing terms, write formulas to represent a sequence or series, find sums of series, and use recursive rules.
Detailed Outcomes:
To understand what sequences and series are and understand, interpret, and apply the vocabulary associated with sequences and series.
To determine if a sequence is arithmetic, geometric or neither.
To analyze arithmetic and geometric sequences and series by finding missing values of a sequence, and determine a formula to represent a sequence or series.
To use sigma notation to represent a series.
To find the sums of finite arithmetic and geometric series and determine if there is a sum and if possible find the sum for an infinite geometric series.
To use and determine recursive rules with sequences and functions.
Chapter 13 – Trigonometric Ratios and Functions
Main Outcome:
To apply the six trigonometric functions, the Law of Sines, and the Law of Cosines.
Detailed Outcomes:
To understand, interpret, and apply the vocabulary associated with trigonometric ratios and functions.
To evaluate and find ratios of the six trigonometric functions in right triangles.
To know and apply the 30-60-90 and 45-45-90 triangle relationships.
To use a calculator to find values of trigonometric functions.
To apply the sine, cosine, and tangent ratios to solve right triangle problems.
To draw angles in standard position and find coterminal angles.
To convert between degrees and radians.
To determine arc length and sector area using radians.
To evaluate trigonometric functions of any angle by using the unit circle and reference angles when necessary.
To evaluate inverse trigonometric functions in radians and degrees.
To apply the Law of Sines and the Law of Cosines to find sides and angles of any triangle.
To find the area of triangles using trigonometric formulas.
Chapter 14 – Trigonometric Graphs, Identities, and Equations
Main Outcome:
To recognize and graph the six trigonometric functions, solve trigonometric equations, and apply trigonometric formulas.
Detailed Outcomes:
To understand, interpret, and apply the vocabulary associated with trigonometric graphs, identities and equations.
To recognize and graph the six trigonometric functions.
To translate and reflect the six trigonometric graphs.
To determine the amplitude, period, x-intercepts, and maximum and minimum values of a trigonometric function given an equation or graph.
To simplify trigonometric expressions and prove trigonometric identities.
To solve trigonometric equations.
To write trigonometric functions and models.
To apply sum and difference formulas for angles, and double and half angles formulas for sine, cosine, and tangent.
Overall Outcomes for Algebra 2:
Recognize and apply the unique vocabulary, properties, and symbolism of algebra.
Apply problem solving strategies and models to translate verbal problems into expressions, equations, and inequalities.
Simplify, perform operations, and evaluate numerical, linear, quadratic, polynomial, exponential, logarithmic, rational, radical, and trigonometric expressions.
Solve linear, quadratic, polynomial, exponential, logarithmic, rational, radical, and trigonometric equations with real and complex solutions.
Solve systems of linear and quadratic equations and inequalities graphically and algebraically including the use of matrices with linear systems.
Determine when a problem is complete and the reasonableness of solutions, including sign, size, relative accuracy, units of measurement, and extraneous solutions.
Recognize linear, quadratic, exponential, logarithmic, rational, radical, and trigonometric functions and conic sections by equations and graphs.
Draw the graphs and write equations, and analyze characteristics of absolute value, linear, quadratic, discrete, piecewise, exponential, logarithmic, rational, radical, and trigonometric functions and conic sections.
Apply concepts of counting principles, permutations, combinations, probabilities, odds, binomial and normal distributions, measures of central tendency and dispersion, and samples.
Determine types of sequences, find missing terms, write formulas to represent a sequence or series, find sums of series, and use recursive rules.
Apply the six trigonometric functions, the Law of Sines, the Law of Cosines, and trigonometric formulas.
Apply algebraic concepts to geometric problems and make further connections between algebraic and geometric concepts.
Use the graphing calculator to solve problems and analyze functions graphically, by using the table, and by using other operations and functions of the graphing calculator.
Communicate mathematics and explain solutions to problems both orally and in well written sentences.
Review Sheets for each unit can be found on the files to download page.