Algebra II Learning Targets

Transcription

1 Chapter 0 Preparing for Advanced Algebra LT 0.1 Representing Functions Identify the domain and range of functions LT 0.2 FOIL Use the FOIL method to multiply binomials LT 0.3 Factoring Polynomials Use various techniques to factor polynomials LT 0.4 Counting Techniques Find the total number of outcomes using a variety of methods LT 0.5 Adding Probabilities Compute theoretical and experimental probabilities Compute probabilities of compound events LT 0.6 Multiplying Probabilities Find probabilities of independent and dependent events Use two-way frequency tables to find conditional probabilities LT 0.7 Congruent and Similar Figures Identify and use congruent and similar figures LT 0.8 The Pythagorean Theorem Use the Pythagorean Theorem and its converse LT 0.9 Measures of Center, Spread, and Position Find measures of center, spread, and position

2 Chapter 1 - Equations and Inequalities Simplify and evaluate algebraic expressions Solve linear and absolute value equations Solve and graph inequalities LT 1.1 Expressions and Formulas Use the order of operations to evaluate expressions Use formulas LT 1.2 Properties of Real Numbers Classify real numbers Use the properties of real numbers to evaluate expressions LT 1.3 Solving Equations Translate verbal expressions into algebraic expressions and equations, and vice versa Solve equations using the properties of equality LT 1.4 Solving Absolute Value Equations Evaluate expressions involving absolute values Solve absolute value equations LT 1.5 Solving Inequalities Solve one-step inequalities Solve multi-step inequalities LT 1.6 Solving Compound and Absolute Value Inequalities Solve compound inequalities Solve absolute value inequalities

3 Chapter 2 Linear Relations and Functions Use equations of relations and function Determine the slope of a line Use scatter plots and prediction equations Graph linear inequalities LT 2.1 Relations and Functions Analyze relations and functions Use equations of relations and functions LT 2.2 Linear Relations and Functions Identify linear relations and functions Write linear equations in standard form LT 2.3 Rate of Change and Slope Find rate of change Determine the slope of a line LT 2.4 Writing Linear Equations Write an equation of a line given the slope and a point on the line Write an equation of a line parallel or perpendicular to a given line LT 2.5 Scatter Plots and Lines of Regression Use scatter plots and prediction equations Model data using lines of regression LT 2.6 Special Functions Write and graph piecewise-defined functions Write and graph step and absolute value functions LT 2.7 Parent Functions and Transformations Identify and use parent functions Describe transformations of functions LT 2.8 Graphing Linear and Absolute Value Inequalities Graph linear inequalities Graph absolute value inequalities

4 Chapter 3 Systems of Equations and Inequalities Solve systems of linear equations and linear inequalities Solve problems by using linear programming Perform operations with matrices and determinants LT 3.1 Solving Systems of Equations Solve systems of linear equations graphically Solve systems of linear equations algebraically LT 3.2 Solving Systems of Inequalities by Graphing Solve systems of inequalities by graphing Determine the coordinates of the vertices of a region formed by the graph of a system of inequalities LT 3.3 Optimization with Linear Programming Find the maximum and minimum values of a function over a region Solve real-world optimization problems using linear programming LT 3.4 Systems of Equations in Three Variables Solve systems of linear equations in three variables Solve real-world problems using systems of linear equations in three variables LT 3.5 Operations with Matrices Analyze data in matrices Perform algebraic operations with matrices LT 3.6 Multiplying Matrices Multiply matrices Use the properties of matrix multiplication LT 3.7 Solving Systems of Equations Using Cramer s Rule Evaluate determinants Solve systems of linear equations by using Cramer s Rule LT 3.8 Solving Systems of Equations Using Inverse Matrices Find the inverse of a 2 X 2 matrix Write and solve matrix equations for a system of equations

5 Chapter 4 Quadratic Functions and Relations Graph quadratic functions Solve quadratic equations Perform operations with complex numbers Graph and solve quadratic inequalities LT 4.1 Graphing Quadratic Functions Graph quadratic function Find and interpret the maximum and minimum values of a quadratic function LT 4.2 Solving Quadratic Equations by Graphing Solve quadratic equations by graphing Estimate solutions of quadratic equations by graphing LT 4.3 Solving Quadratic Equations by Factoring Write quadratic equations in standard form Solve quadratic equations by factoring LT 4.4 Complex Numbers Perform operations with pure imaginary numbers Perform operations with complex numbers LT 4.5 Completing the Square Solve quadratic equations by using the Square Root Property Solve quadratic equations by completing the square LT 4.6 The Quadratic Formula and the Discriminant Solve quadratic equations by using the Quadratic Formula Use the discriminant to determine the number and type of roots of a quadratic equation LT 4.7 Transformations of Quadratic Graphs Write a quadratic function in the form y = a(x h) 2 + k Transform graphs of quadratic functions of the form y = a(x h) 2 + k LT 4.8 Quadratic Inequalities Graph quadratic inequalities in two variables Solve quadratic inequalities in one variable

6 Chapter 5 Polynomials and Polynomial Functions Add, subtract, multiply, divide, and factor polynomials Analyze and graph polynomial functions Evaluate polynomial functions and solve polynomial equations Find factors and zeros of polynomial functions LT 5.1 Operations with Polynomials Multiply, divide and simplify monomials and expressions involving powers Add subtract, and multiply polynomials LT 5.2 Dividing Polynomials Divide polynomials using long division Divide polynomials using synthetic division LT 5.3 Polynomial Functions Evaluate polynomial functions Identify general shapes of graphs of polynomial functions LT 5.4 Analyzing Graphs of Polynomial Functions Graph polynomial functions and locate their zeros Find the relative maxima and minima of polynomial functions LT 5.5 Solving Polynomial Equations Factor polynomials Solve polynomial equations by factoring LT 5.6 LT 5.7 The Remainder and Factor Theorems Evaluate functions by using synthetic substitution Determine whether a binomial is a factor of a polynomial by using synthetic substitution Roots and Zeros Determine the number and type of roots for a polynomial equation Find the zeros of a polynomial function LT 5.8 Rational Zero Theorem Identify possible rational zeros of a polynomial function Find all of the rational zeros of a polynomial function

7 Chapter 6 Inverses and Radical Functions and Relations Find compositions and inverses of functions Graph and analyze square root functions and inequalities Simplify and solve equations involving roots, radicals, and rational exponents LT 6.1 Operations on Functions Find the sum, difference, product, and quotient of functions Find the composition of functions LT 6.2 Inverse Functions and Relations Find the inverse of a function or relation Determine whether two functions or relations are inverses LT 6.3 Square Root Functions and Inequalities Graph and analyze square root functions Graph square root inequalities LT 6.4 nth Roots Simplify radicals Use a calculator to approximate radicals LT 6.5 Operations with Radical Expressions Simplify radical expressions Add, subtract, multiply, and divide radical expressions LT 6.6 Rational Exponents Write expressions with rational exponents in radical form and vice versa Simplify expressions in exponential or radical form LT 6.7 Solving Radical Equations and Inequalities Solve equations containing radicals Solve inequalities containing radicals

8 Chapter 7 Exponential and Logarithmic Functions and Relations Graph exponential and logarithmic functions Solve exponential and logarithmic equations and inequalities Solve problems involving exponential growth and decay LT 7.1 Graphing Exponential Functions Graph exponential growth functions Graph exponential decay functions LT 7.2 Solving Exponential Equations and Inequalities Solve exponential equations Solve exponential inequalities LT 7.3 Logarithms and Logarithmic Functions Evaluate logarithmic expressions Graph logarithmic functions LT 7.4 Solving Logarithmic Equations and Inequalities Solve logarithmic equations Solve logarithmic in equalities LT 7.5 Properties of Logarithms Simplify and evaluate expressions using the properties of logarithms Solve logarithmic equations using the properties of logarithms LT 7.6 Common Logarithms Solve exponential equations and inequalities using common logarithms Evaluate logarithmic expressions using the Change of Base Formula LT 7.7 Base e and Natural Logarithms Evaluate expressions involving the natural base and natural logarithm Solve exponential equations and inequalities using natural logarithms LT 7.8 Using Exponential and Logarithmic Functions Use logarithms to solve problems involving exponential growth and decay Use logarithms to solve problems involving logistic growth

9 Chapter 8 Rational Functions and Relations Simplify rational expressions Graph rational functions Solve direct, joint, and inverse variation problems Solve rational equations and inequalities LT 8.1 Multiplying and Dividing Rational Expressions Simplify rational expressions Simplify complex fractions LT 8.2 Adding and Subtracting Rational Expressions Determine the LCM of polynomials Add and subtract rational expressions LT 8.3 Graphing Reciprocal Functions Determine properties of reciprocal functions Graph transformations of reciprocal functions LT 8.4 Graphing Rational Functions Graph rational functions with vertical and horizontal asymptotes Graph rational functions with oblique asymptotes and point discontinuity LT 8.5 Variation Functions Recognize and solve direct and joint variation problems Recognize and solve inverse and combined variation problems

10 Chapter 9 Conic Sections Use the Midpoint and Distance Formulas Write and graph equations of parabolas, circles, ellipses, and hyperbolas Identify conic sections Solve systems of quadratic equations and inequalities LT 9.1 Midpoint and Distance Formulas Find the midpoint of a segment on the coordinate plane Find the distance between two points on the coordinate plane LT 9.2 Parabolas Write equations of parabolas in standard form Graph parabolas LT 9.3 Circles Write equations of circles Graph circles LT 9.4 Ellipses Write equations of ellipses Graph ellipses LT 9.5 Hyperbolas Write equations of hyperbolas Graph hyperbolas LT 9.6 Identifying Conic Sections Write equations of conic sections in standard form Identify conic sections from their equations LT 9.7 Solving Linear-Nonlinear Systems Solve systems of linear and nonlinear equations algebraically and graphically Solve systems of linear and nonlinear inequalities graphically

11 Chapter 10 Sequences and Series Use arithmetic and geometric sequences and series Use special sequences and iterate functions Expand powers by using the Binomial Theorem Prove statements by using mathematical induction LT 10.1 Sequences as Functions Relate arithmetic sequences to linear functions Relate geometric sequences to exponential functions LT 10.2 Arithmetic Sequences and Series Use arithmetic sequences Find sums of arithmetic series LT 10.3 Geometric Sequences and Series Use geometric sequences Find sums of geometric series LT 10.4 Infinite Geometric Series Find sums of infinite geometric series Write repeating decimals as fractions LT 10.5 Recursion and Iteration Recognize and use special sequences Iterate functions LT 10.6 The Binomial Theorem Use Pascal s triangle to expand powers of binomials Use the Binomial Theorem to expand powers of binomials LT 10.7 Proof by Mathematical Induction Prove statements by using mathematical induction Disprove statements by finding a counterexample

12 Chapter 11 Statistics and Probability Evaluate surveys, studies, and experiments Create and use graphs of probability distributions Use the Empirical Rule to find probabilities Compare sample statistics and population statistics LT 11.1 Designing a Study Classify study types Design statistical studies LT 11.2 Distributions of Data Use the shapes of distributions to select appropriate statistics Use the shapes of distributions to compare data LT 11.3 Probability Distributions Construct a probability distribution Analyze a probability distribution and its summary statistics LT 11.4 The Binomial Distribution Identify and conduct a binomial experiment Find probabilities using binomial distributions LT 11.5 The Normal Distribution Use the Empirical Rule to analyze normally distributed variables Apply the standard normal distribution and z-values LT 11.6 Confidence Intervals and Hypothesis Testing Find confidence intervals for normally distributed data Perform hypothesis tests on normally distributed data

13 Chapter 12 Trigonometric Functions Find values of trigonometric functions Solve problems by using right triangle trigonometry Solve triangles by using the Law of Sines and Law of Cosines Graph trigonometric functions LT 12.1 Trigonometric Functions in Right Triangles Find values of trigonometric functions for acute angles Use trigonometric functions to find side lengths and angle measures of right triangles LT 12.2 Angles and Angle Measure Draw and find angles in standard position Convert between degree measures and radian measures LT 12.3 Trigonometric Functions of General Angles Find values of trigonometric functions for general angles Find values of trigonometric functions by using reference angles LT 12.4 Law of Sines Find the area of a triangle using two sides and an included angle Use the Law of Sines to solve triangles LT 12.5 Law of Cosines Use the Law of Cosines to solve triangles Choose methods to solve triangles LT 12.6 Circular and Periodic Functions Find values of trigonometric functions based on the unit circle Use the properties of periodic functions to evaluate trigonometric functions LT 12.7 Graphing Trigonometric Functions Describe and graph the sine, cosine, and tangent functions Describe and graph other trigonometric functions LT 12.8 LT 12.9 Translations of Trigonometric Graphs Graph horizontal translations of trigonometric graphs and find phase shifts Graph vertical translations of trigonometric graphs Inverse Trigonometric Functions Find values of inverse trigonometric functions Solve equations by using inverse trigonometric functions

14 Chapter 13 Trigonometric Identities and Equations Use and verify trigonometric identities Use the sum and difference of angles identities Use the double-and half-angle identities Solve trigonometric equations LT 13.1 Trigonometric Identities Use trigonometric identities to find trigonometric values Use trigonometric identities to simplify expressions LT 13.2 Verifying Trigonometric Identities Verify trigonometric identities by transforming one side of an equation into the form of the other side Verify trigonometric identities by transforming each side of the equation into the same form LT 13.3 Sum and Difference of Angles Identities Find values of sine and cosine by using sum and difference identities Verify trigonometric identities by using sum and difference identities LT 13.4 Double-Angle and Half-Angle Identities Find values of sine and cosine by using double-angle identities Find values of sine and cosine by using half-angle identities LT 13.5 Solving Trigonometric Equations Solve trigonometric equations Find extraneous solutions from trigonometric equations