2014 Algebra 2 Khan Academy Video Correlations By SpringBoard Activity SB Activity Unit 1: Equations, Inequalities, Functions Activity 1 Creating Equations 1-1 Learning Targets: • Create an equation in one variable from a real-world context. • Solve an equation in one variable. 1-2 Learning Targets: • Create equations in two variables to represent relationships between quantities. • Graph two-variable equations 1-3 Learning Targets: • Write, solve, and graph absolute value equations. • Solve and graph absolute value inequalities. Video(s) One-Variable Equations Representing a relationship with a simple equation Linear equation word problem Word problem: solving equations Solving equations with the distributive property Ex 2: Multi-step equation Variables on both sides Two-Variable Equations Constructing linear equations to solve word problems Exploring linear relationships Graphs of linear equations Application problem with graph Absolute Value Equations and Inequalities Absolute value equations Absolute value equations Absolute value equations 1 Absolute value equation example Absolute value equations example 1 Absolute value equation example 2 Absolute value equation with no solution Absolute Value Inequalities Absolute value inequalities Absolute value inequalities example 1 Absolute inequalities 2 Absolute value inequalities example 3 Activity 2 Graphing to Find Solutions 2-1 Learning Targets: • Write equations in two variables to represent relationships between quantities. Writing Linear Equations Constructing linear equations to solve word problems Graphing and Interpreting Two-Variable Equations Graphing a line in slope intercept form Graph equations on coordinate axes with labels and scales. 2-2 Learning Targets: • Represent constraints by equations or inequalities. • Use a graph to determine solutions of a system of inequalities. Activity 3 Systems of Linear Equations 3-1 Learning Targets: • Use graphing, substitution, and elimination to solve systems of linear equations in two variables. • Formulate systems of linear equations in two variables to model real-world situations. 3-2 Learning Targets: • Solve systems of three linear equations in three variables using substitution and Gaussian elimination. • Formulate systems of three linear equations in three variables to model a real-world situation. 3-3 Learning Targets: • Add, subtract, and multiply matrices. • Use a graphing calculator to perform operations on matrices. 3-4 Learning Targets: • Solve systems of two linear equations in two variables by using graphing calculators with matrices. • Solve systems of three linear equations in three variables by using graphing calculators with matrices. • Interpreting intercepts of linear functions Graphing Systems of Inequalities Graphing systems of inequalities Graphing systems of inequalities 2 Visualizing the solution set for a system of inequalities Solving Systems of Two Equations in Two Variables: Graphing Solving linear systems by graphing Solving systems graphically Graphing systems of equations Graphical systems application problem Example 2: Graphically solving systems Example 3: Graphically solving systems Solving Systems of Two Equations in Two Variables: Substitution Example 1: Solving systems by substitution Example 2: Solving systems by substitution Example 3: Solving systems by substitution The substitution method Substitution method 2 Substitution method 3 Practice using substitution for systems Solving Systems of Two Equations in Two Variables: Elimination Example 1: Solving systems by elimination Example 2: Solving systems by elimination Example 3: Solving systems by elimination Addition elimination method 1 Addition elimination method 2 Addition elimination method 3 Addition elimination method 4 Simple elimination practice Systems with elimination practice Consistent, Inconsistent, Dependent, and Independent Systems Consistent and inconsistent systems Independent and dependent systems Solving Systems of Three Equations in Three Variables Systems of three variables Systems of three variables 2 Solutions to three variable system Solutions to three variable system 2 Three equation application problem Matrix Operations Introduction to the matrix Representing data with matrices Matrix addition and subtraction Matrix multiplication introduction Multiplying a matrix by a matrix Defined and undefined matrix operations Solving Matrix Equations Matrix equations and systems Activity 4 Piecewise-Defined Functions 4-1 Learning Targets: • Graph piecewise-defined functions. • Write the domain and range of functions using interval notation, inequalities, and set notation. 4-2 Learning Targets: • Graph step functions and absolute value functions. • Describe the attributes of these functions. 4-3 Learning Targets: • Identify the effect on the graph of replacing f(x) by f(x) + k, k · f(x), f(kx), and f(x + k). • Find the value of k, given these graphs. Activity 5 Function Composition and Operations 5-1 Learning Targets: • Combine functions using arithmetic operations. • Build functions that model real-world scenarios. Piecewise Defined Functions What is a function? Finding a piecewise function definition from graph Absolute Value Functions Graphs of absolute value functions Absolute value graphing exercise example Operations with Functions Sum of functions Difference of functions Product of functions Quotient of functions Composition of Functions Introduction to function composition 5-2 Learning Targets: • Write functions that describe the Creating new function from composition relationship between two quantities. Evaluating composite functions example • Explore the composition of two functions Modeling with function composition through a real-world scenario. 5-3 Learning Targets: • Write the composition of two functions. • Evaluate the composition of two functions. Inverse Functions Activity 6 Introduction to function inverses Inverse Functions 6-1 Learning Targets: Introduction to the inverse of a function • Find the inverse of a function. Function inverse example 1 • Write the inverse using the proper Function inverses example 2 notation. 6-2 Learning Targets: Function inverses example 3 • Use composition of functions to determine if functions are inverses of each other. • Graph inverse functions and identify the symmetry. Unit 2: Quadratic Functions Analyzing a Quadratic Function Activity 7 Graphing a parabola with a table of values Applications of Quadratic Functions 7-1 Learning Targets: Parabola vertex and axis of symmetry • Formulate quadratic functions in a Finding the vertex of a parabola example problem-solving situation. Graphing a parabola by finding the roots and vertex • Graph and interpret quadratic functions. 7-2 Learning Targets: Graphing a parabola using roots and vertex • Factor quadratic expressions of the form x2 Multiple examples graphing parabolas using roots and + bx + c. vertices • Factor quadratic expressions of the form Factoring Quadratic Expressions ax2 + bx + c. Factoring quadratic expressions 7-3 Learning Targets: • Solve quadratic equations by factoring. Examples: Factoring simple quadratics • Interpret solutions of a quadratic Example 1: Factoring quadratic expressions equation. • Create quadratic equations from solutions. Example 1: Factoring trinomials with a common factor Solving Quadratic Equations by Factoring 7-4 Learning Targets: Solving a quadratic equation by factoring • Solve quadratic inequalities. Dimensions from volume of box • Graph the solutions to quadratic inequalities. More Uses for Factors Quadratic inequalities Quadratic inequalities (visual explanation) Activity 8 Introduction to Complex Numbers The Imaginary Unit , i Introduction to i and imaginary numbers 8-1 Learning Targets: • Know the definition of the complex number i. • Know that complex numbers can be written as a + bi, where a and b are real numbers. • Graph complex numbers on the complex plane. 8-2 Learning Targets: • Add and subtract complex numbers. • Multiply and divide complex numbers. 8-3 Learning Targets: • Factor quadratic expressions using complex conjugates. • Solve quadratic equations with complex roots by factoring. Activity 9 Solving ax2 + bx + c = 0 9-1 Learning Targets: • Solve quadratic equations by taking square roots. • Solve quadratic equations ax2 + bx + c = 0 by completing the square. 9-2 Learning Targets: • Derive the Quadratic Formula. • Solve quadratic equations using the Quadratic Formula. 9-3 Learning Targets: • Solve quadratic equations using the Quadratic Formula. • Use the discriminant to determine the nature of the solutions of a quadratic equation. Activity 10 Writing Quadratic Equations 10-1 Learning Targets: • Derive a general equation for a parabola based on the definition of a parabola. • Write the equation of a parabola given a graph and key features. 10-2 Learning Targets: • Explain why three points are needed to determine a parabola. • Determine the quadratic function that passes through three given points on a plane. Imaginary roots of negative numbers i as the principal root of -1 (a little technical) Plotting complex numbers on the complex plane Operations with Complex Numbers Calculating i raised to arbitrary exponents Adding complex numbers Subtracting complex numbers Multiplying complex numbers Complex conjugates example Dividing complex numbers Completing the Square and Taking Square Roots Solve quadratic equations by square roots Solving quadratic equations by completing the square Example 1: Completing the square Example 2: Completing the square Example 3: Completing the square The Quadratic Formula Proof of quadratic formula How to use the quadratic formula Solutions of Quadratic Equations Example: Complex roots for a quadratic Discriminant of quadratic equations Discriminant for types of solutions for a quadratic Parabolas and Quadratic Equations Parabola intuition example 1 Focus and directrix introduction Writing the Equation of a Parabola Using the focus and directrix to find the equation of a parabola Equation for parabola from focus and directrix Finding focus and directrix from vertex 10-3 Learning Targets: • Find a quadratic model for a given table of data. • Use a quadratic model to make predictions. Activity 11 Transformations of y = x2 11-1 Learning Targets: • Describe translations of the parent function f(x) = x2. • Given a translation of the function f(x) = x2, write the equation of the function. 11-2 Learning Targets: • Describe transformations of the parent function f(x) = x2. • Given a transformation of the function f(x) = x2, write the equation of the function. 11-3 Learning Targets: • Write a quadratic function in vertex form. • Use transformations to graph a quadratic function in vertex form. Activity 12 Graphing Quadratics and Quadratic Inequalities 12-1 Learning Targets: • Write a quadratic function from a verbal description. • Identify and interpret key features of the graph of a quadratic function. 12-2 Learning Targets: • Write a quadratic function from a verbal description. • Identify and interpret key features of the graph of a quadratic function. 12-3 Learning Targets: • Identify key features of a quadratic function from an equation written in standard form. • Use key features to graph a quadratic function. 12-4 Learning Targets: • Use the discriminant to determine the nature of the solutions of a quadratic equation. Transformations of y = x2 Shifting and scaling parabolas Graphing a parabola in vertex form Key Features of Quadratic Functions Parabola vertex and axis of symmetry Graphing Quadratic Functions Examples: Graphing and interpreting quadratics Graphing a parabola with a table of values Finding the vertex of a parabola example Graphing a parabola by finding the roots and vertex Graphing a parabola using roots and vertex Multiple examples graphing parabolas using roots and vertices The Discriminant Discriminant of quadratic equations Discriminant for types of solutions for a quadratic Use the discriminant to help graph a quadratic function. 12-5 Learning Targets: • Graph a quadratic inequality in two variables. • Determine the solutions to a quadratic inequality by graphing. • Activity 13 Systems of Linear and Nonlinear Equations 13-1 Learning Targets: • Use graphing to solve a system consisting of a linear and a nonlinear equation. • Interpret the solutions of a system of equations. 13-2 Learning Targets: • Use substitution to solve a system consisting of a linear and nonlinear equation. • Determine when a system consisting of a linear and nonlinear equation has no solution. Systems of Nonlinear Equations Non-linear systems of equations 1 Non-linear systems of equations 2 Non-linear systems of equations 3 Systems of nonlinear equations 1 Systems of nonlinear equations 2 Systems of nonlinear equations 3 Unit 3: Polynomials Activity 14 Introduction to Polynomials 14-1 Learning Targets: • Write a third-degree equation that represents a real-world situation. • Graph a portion of this equation and evaluate the meaning of a relative maximum. 14-2 Learning Targets: • Sketch the graphs of cubic functions. • Identify the end behavior of polynomial functions. 14-3 Learning Targets: • Recognize even and odd functions given an equation or graph. • Distinguish between even and odd functions and even-degree and odddegree functions. Polynomial Basics Terms coefficients and exponents in a polynomial Activity 15 Polynomial Operations Adding and Subtraction Polynomials Addition and subtraction of polynomials End Behavior Of Polynomial Functions Polynomial end behavior Polynomial end behavior example Another polynomial end behavior example Polynomial end behavior exercise example Even and Odd Functions Recognizing odd and even functions Connection between even and odd numbers and functions 15-1 Learning Targets: • Use a real-world scenario to introduce polynomial addition and subtraction. • Add and subtract polynomials. 15-2 Learning Targets: • Add, subtract, and multiply polynomials. • Understand that polynomials are closed under the operations of addition, subtraction, and multiplication. 15-3 Learning Targets: • Determine the quotient of two polynomials. • Prove a polynomial identity and use it to describe numerical relationships. Multiplying Polynomials Multiplying polynomials example Activity 16 Binomial Theorem 16-1 Learning Targets: • Find the number of combinations of an event. • Create Pascal’s triangle. 16-2 Learning Targets: • Know the Binomial Theorem. • Apply the Binomial Theorem to identify the coefficients or terms of any binomial expansion. Pascal’s Triangle Pascal’s triangle for binomial expansion Activity 17 Factors of Polynomials 17-1 Learning Targets: • Determine the linear factors of polynomial functions using algebraic methods. • Determine the linear or quadratic factors of polynomials by factoring the sum or difference of two cubes and factoring by grouping. 17-2 Learning Targets: • Know and apply the Fundamental Theorem of Algebra. • Write polynomial functions, given their degree and roots. Factoring Polynomials: Algebraic Methods Factor by grouping and factoring completely Multiplying polynomials example 2 Dividing Polynomials Polynomial division Polynomial divided by monomial Dividing polynomials 1 Dividing polynomials with remainders Dividing polynomials with remainders example Binomial theorem Binomial Theorem Determining coefficient in binomial expansion Connecting Pascal’s triangle to binomial combinatorics Algorithm for mentally computing binomial expansion coefficients Binomial theorem combinatorics connection Example: basic grouping Example 1: Factoring by grouping Example 2: Factoring by grouping Example 3: Factoring by grouping Example 4: Factoring by grouping Example 5: Factoring by grouping Example 6: Factoring by grouping Difference of cubes factoring Factoring sum of cubes The Fundamental Theorem of Algebra Fundamental theorem of algebra Fundamental theorem of algebra for quadratic Possible number of real roots Activity 18 Graphs of Polynomials 18-1 Learning Targets: • Graph polynomial functions by hand or using technology, identifying zeros when suitable factorizations are available, and showing end behavior. • Recognize even and odd functions from their algebraic expressions. 18-2 Learning Targets: • Know and apply the Rational Root Theorem and Descartes’ Rule of Signs. • Know and apply the Remainder Theorem and the Factor Theorem. 18-3 Learning Targets: • Compare properties of two functions each represented in a different way. • Solve polynomial inequalities by graphing. Graphing Polynomial Functions Polynomial end behavior Polynomial end behavior example Another polynomial end behavior example Polynomial end behavior exercise example Recognizing odd and even functions Connection between even and odd numbers and functions Finding the Roots of a Polynomial Function Synthetic division Synthetic division example 2 Why synthetic division works Polynomial remainder theorem Polynomial remainder theorem example Polynomial remainder theorem to test factor Polynomial remainder theorem proof Comparing Polynomial Functions Recognizing features of functions (example 1) Recognizing features of functions (example 2) Recognizing features of functions (example 3) Unit 4: Series, Exponential and Logarithmic Functions Arithmetic Sequences Activity 19 Explicit and recursive definitions of sequences Arithmetic Sequences and Series 19-1 Learning Targets: Arithmetic sequences • Determine whether a given sequence is Finding the 100th term in a sequence arithmetic. Equations of sequence patterns • Find the common difference of an arithmetic sequence. Arithmetic Series • Write an expression for an arithmetic Explicitly defining a series sequence, and calculate the nth term. Sigma Notation 19-2 Learning Targets: Sigma notation for sums • Write a formula for the nth partial sum of Writing a series in sigma notation an arithmetic series. • Calculate partial sums of an arithmetic series. 19-3 Learning Targets: • Identify the index, lower and upper limits, and general term in sigma notation. • Express the sum of a series using sigma notation. • Find the sum of a series written in sigma notation. Activity 20 Geometric Sequences and Series 20-1 Learning Targets: • Identify the index, lower and upper limits, and general term in sigma notation. • Express the sum of a series using sigma notation. • Find the sum of a series written in sigma notation. 20-2 Learning Targets: • Derive the formula for the sum of a finite geometric series. • Calculate the partial sums of a geometric series. 20-3 Learning Targets: • Determine if an infinite geometric sum converges. • Find the sum of a convergent geometric series. Geometric Sequences Geometric sequences introduction Activity 21 Exponential Functions and Graphs 21-1 Learning Targets: • Identify data that grow exponentially. • Compare the rates of change of linear and exponential data. 21-2 Learning Targets: • Identify and write exponential functions. • Determine the decay factor or growth factor of an exponential function. 21-3 Learning Targets: • Determine when an exponential function is increasing or decreasing. • Describe the end behavior of exponential functions. • Identify asymptotes of exponential Exponential Functions Understanding linear and exponential models Geometric sequences Geometric Series Series as sum of sequence Geometric series Formula for a finite geometric series Sum of an infinite geometric series Another derivation of the sum of an infinite geometric series Convergence and Divergence Geometric series convergence and divergence examples Exponential growth and decay word problems Decay of cesium 137 example Modeling ticket fines with exponential function Graphs of Exponential Functions Graphing exponential functions Constructing linear and exponential functions from graphs functions. 21-4 Learning Targets: • Explore how changing parameters affects the graph of an exponential function. • Graph transformations of exponential functions. 21-5 Learning Targets: • Graph the function f(x) = ex. • Graph transformations of f(x) = ex. Activity 22 Logarithms and Their Properties 22-1 Learning Targets: • Complete tables and plot points for exponential data. • Write and graph an exponential function for a given context. • Find the domain and range of an exponential function. 22-2 Learning Targets: • Use technology to graph y = log x. • Evaluate a logarithm using technology. • Rewrite exponential equations as their corresponding logarithmic equations. • Rewrite logarithmic equations as their corresponding exponential equations. 22-3 Learning Targets: • Make conjectures about properties of logarithms. • Write and apply the Product Property and Quotient Property of Logarithms. • Rewrite logarithmic expressions by using properties. 22-4 Learning Targets: • Make conjectures about properties of logarithms. • Write and apply the Power Property of Logarithms. • Rewrite logarithmic expressions by using their properties. Exponential Functions Graphing exponential functions Activity 23 Inverse Functions: Exponential and Logarithmic Functions 23-1 Learning Targets: Logarithms in Other Bases Change of base formula Constructing linear and exponential functions from data Matching functions to their graphs Logarithms Logarithms Writing in logarithmic and exponential form Introduction to logarithm properties Introduction to logarithm properties (part 2) Change of base formula proof Graphing Logarithmic Functions Use composition to verify two functions as inverse. • Define the logarithm of y with base b. • Write the Inverse Properties for logarithms. 23-2 Learning Targets: • Apply the properties of logarithms in any base. • Compare and expand logarithmic expressions. • Use the Change of Base Formula. 23-3 Learning Targets: • Find intercepts and asymptotes of logarithmic functions. • Determine the domain and range of a logarithmic function. • Write and graph transformations of logarithmic functions. Graphing logarithmic functions Activity 24 Logarithmic and Exponential Equations and Inequalities 24-1 Learning Targets: • Write exponential equations to represent situations. • Solve exponential equations. 24-2 Learning Targets: • Solve exponential equations using logarithms. • Estimate the solution to an exponential equation. • Apply the compounded interest formula. 24-3 Learning Targets: • Solve logarithmic equations. • Identify extraneous solutions to logarithmic equations. • Use properties of logarithms to rewrite logarithmic expressions. 24-4 Learning Targets: • Solve exponential inequalities. • Solve logarithmic inequalities. Exponential Equations Solving exponential equation • Graphs of logarithmic functions Solving exponential equation with logarithm Logarithmic Equations Solving logarithmic equations Solving logarithmic equations Application: Compound Interest Introduction to compound interest and e Compound interest and e (part 2) Compound interest and e (part 3) Compound interest and e (part 4) Unit 5: Radical and Rational Functions Activity 25 Square Root and Cube Root Functions Graphing Radical Functions Flipping and shifting radical functions 25-1 • Learning Targets: Graph and describe transformations of the square root function y=√x. • Interpret key features of a graph that models a relationship between two quantities. 25-2 Learning Targets: • Solve square root equations. • Identify extraneous solutions. 25-3 Learning Targets: • Graph transformations of the cube root function y=3√x. . • Identify key features of a graph that models a relationship between two quantities. 25-4 Learning Targets: • Solve cube root equations. • Check the reasonableness of solutions. Activity 26 Inverses: Roots, Squares, and Cubes 26-1 Learning Targets: • Graph and write the inverse of square root functions. • Find a square root model for a given table of data. 26-2 Learning Targets: • Graph and write the inverse of square root functions. • Find the inverse relations of quadratic functions. 26-3 Learning Targets: • Graph and write the inverse of cube root functions. • Find the inverse relations of cubic functions. Activity 27 Introduction to Rational Functions 27-1 Learning Targets: • Formulate rational equations that model real-world situations. • Graph equations on coordinate axes. 27-2 Learning Targets: • Formulate rational equations that model Matching radical functions with graphs exercise example Solving Radical Equations Equations for radical functions example Solving radical equations Solving radical equations 1 Solving radical equations 2 Solving radical equations 3 Extraneous solutions to radical equations Applying Radical Equations Applying radical equations 1 Applying radical equations 2 Applying radical equations 3 Inverse Functions Introduction to function inverses Function inverses example 2 Function inverses example 3 Graphs of Rational Functions Matching rational functions to their graphs Another rational function graph example real-world situations. • Graph equations on coordinate axes. 27-3 Learning Targets: • Determine the horizontal and vertical asymptotes of a rational function. • Graph a rational function on the coordinate plane. A third example of graphing a rational function Activity 28 Inverse Variation and Rational Functions 28-1 Learning Targets: • Create, solve, and graph an equation involving inverse variation. • Solve an equation involving combined variation. 28-2 Learning Targets: • Describe transformations of the parent function f(x)=1/x and sketch the graphs. • Identify the x-intercepts, y-intercepts, and asymptotes of transformations of the parent function f(x)=1/x. Activity 29 Simplifying Rational Expressions 29-1 Learning Targets: • Simplify rational expressions. • Multiply and divide rational expressions. 29-2 Learning Targets: • Add and subtract rational expressions. • Simplify complex fractions. 29-3 Learning Targets: • Identify the vertical asymptotes of rational functions by finding the domain values that make the functions undefined. • Use the degrees of the numerator and denominator of rational functions to identify the horizontal asymptotes. 29-4 Learning Targets: • Analyze and graph rational functions, identifying any asymptotes, intercepts, and holes. • Analyze and graph rational functions representing real-world scenarios. Direct and Inverse Variation Direct and inverse variation Asymptotes of Rational Functions Asymptotes of rational functions Horizontal and vertical asymptotes of function Recognizing direct and inverse variation Multiplying and Dividing Rational Expressions Simplifying rational expressions introduction Simplifying rational expressions 1 Simplifying rational expressions 2 Simplifying rational expressions 2 Simplifying rational expressions 3 Multiplying and simplifying rational expressions Multiplying and dividing rational expressions 1 Multiplying and dividing rational expressions 2 Multiplying and dividing rational expressions 3 Adding and Subtracting Rational Expressions Adding and subtracting rational expressions Adding and subtracting rational expressions 2 Subtracting rational expressions Simplifying first for subtracting rational expressions Rationalizing denominators of expressions Finding Horizontal and Vertical Asymptotes Asymptotes of rational functions Horizontal and vertical asymptotes of function Graphing Rational Functions Matching rational functions to their graphs Another rational function graph example A third example of graphing a rational function Activity 30 Rational Equations and Inequalities 30-1 Learning Targets: • Solve rational equations, identifying any extraneous solutions. • Create and solve rational equations that represent work problems. 30-2 Learning Targets: • Solve rational inequalities by graphing. • Solve rational inequalities by finding the sign of the inequality on either side of the numerator and denominator zeros. Solving Rational Equations Ex 1: Multi step equation Rational equations Solving rational equations 1 Solving rational equations 2 Solving rational equations 3 Applying rational equations 1 Applying rational equations 2 Applying rational equations 3 Extraneous solutions to rational equations Solving Rational Inequalities Rational inequalities Rational inequalities 2 Unit 6: Trigonometry Radian Measure Activity 31 Introduction to radians Understanding Radian Measure 31-1 Learning Targets: Introduction to the unit circle • Develop formulas for the length of an arc. Rotation by radians and quadrants • Describe radian measure. Arc Length 31-2 Learning Targets: Arc length as a fraction of circumference • Develop and apply formulas for the length of an arc. Finding arc length from radian angle measure • Apply radian measure. Radian and Degree Measure Example: Radian measure and arc length Radians and degrees Example: Converting degrees to radians Example: Converting radians to degrees Radian and degree conversion practice Activity 32 Trigonometric Functions 32-1 Learning Targets: • Explore angles drawn in standard position on the coordinate plane. • Find the sine of θ and the cosine of θ. 32-2 Learning Targets: The Unit Circle Introduction to the unit circle Solving triangle in unit circle Trigonometric Ratios Matching ratios to trig functions Find the sine of θ and the cosine of θ using special right triangles. • Find the tan of θ. Activity 33 Trigonometric Identities: Pythagorean Connection 33-1 Learning Targets: • Prove the Pythagorean identity. • Use the Pythagorean identity to find sin θ, cos θ, or tan θ, given the value of one of these functions and the quadrant of θ. 33-2 Learning Targets: • Define the three reciprocal trigonometric functions. • Use the Pythagorean identity and the reciprocal trigonometric functions to prove other trigonometric identities. Activity 34 Graphs of Trigonometric Functions 34-1 Learning Targets: • Identify periodic functions. • Find the period, midline, and amplitude of periodic functions. 34-2 Learning Targets: • Graph the sine function, y = a sin b x. • Find the period, midline, and amplitude of sine functions. 34-3 Learning Targets: • Graph the cosine function, y = a cos bx. • Find the period, midline, and amplitude of cosine functions. 34-4 Learning Targets: • Graph the tangent function, y = a tan b x. • Find the period, and midline of tangent functions. 34-5 Learning Targets: • Describe and graph functions of the form y = a sin b(x − h) + k, y = a cos b(x − h) + k, and y = a tan b(x − h) + k. • Find the period, amplitude, and midline of these trigonometric functions. Activity 35 Choosing Functions to Model Periodic Phenomena 35-1 Learning Targets: • Use trigonometric functions to model realworld periodic phenomena. • Pythagorean Identities Pythagorean trig identity from soh cah toa Pythagorean trig identity from unit circle Using the Pythagorean trig identity Examples using pythagorean identities to simplify trigonometric expressions Reciprocal Functions Secant (sec), cosecant (csc) and cotangent (cot) example Example: Using trig to solve for missing information Periodic Functions Midline, amplitude and period of a function Example: Amplitude and period Plotting maxima, minima and midline intersections of trig function Sine Function Example: Graph, domain, and range of sine function Cosine Function Example: Graph of cosine Example: Intersection of sine and cosine Transformations Example: Amplitude and period transformations Example: Amplitude and period cosine transformations Tangent graph Tangent Function Modeling Periodic Phenomena Modeling annual temperature variation with trigonometry Applying inverse trig function with model Modeling temperature through the day • Identify key features of these functions. Day length in Alaska Example: Figure out the trig function Determining the equation of a trig function Unit 7: Probability and Statistics Distribution Activity 36 Comparing means of distributions Normal Distribution 36-1 Learning Targets: Means and medians of different distributions • Represent distribution with appropriate Normal Distribution data plots. • Interpret shape of a distribution and relate Introduction to the normal distribution shape to measures of center and spread. 36-2 Learning Targets: normal distribution problems: Qualitative sense of • Recognize characteristics of a normal normal distributions distribution. • Use mean and standard deviation to completely describe a normal distribution. 36-3 Learning Targets: • Estimate probabilities associated with zscores using normal curve sketches. • Determine probabilities for z-scores using a standard normal table. 36-4 Learning Targets: • Determine probabilities for z-scores using technology. • Use a normal distribution, when appropriate, as a model for a population from which a sample of numeric data has been drawn. Activity 37 Random Sampling 37-1 Learning Targets: • Explain why random sampling is advantageous when conducting a survey 37-2 Learning Targets: • Explain why random allocation of treatments is critical to a good experiment. 37-3 Learning Targets: • .Identify a confounding variable in an observational study. Activity 38 Simulations Activity 39 Sampling Introduction to random sampling Random sampling intuition Reasonable samples Inferring population mean from sample mean N/A Error Margin of Error 39-1 Learning Targets: • Use margin of error in an estimate of a population proportion. • Use simulation models for random samples. 39-2 Learning Targets: • Use margin of error in an estimate of a population proportion. • Relate margin of error to the population proportion and to the sample size. Activity 40 Designing and Conducting Simulations Standard error of the mean Population standard deviation Sample standard deviation and bias Sampling distribution of the sample mean Sampling distribution of the sample mean 2 Sampling distribution example problem N/A

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