2014 Algebra 2 Khan Academy Video Correlations By

2014 Algebra 2 Khan Academy Video Correlations By
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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