Download Pearson - Swampscott High School

Swampscott High School
Math Department
Algebra II Curriculum
Algebra 2 331:
Book: Algebra 2 Common Core - Pearson
Chapter 1: Expressions, Equations, and Inequalities (Review of Algebra 1)
Essential Question(s)
•
How do variables help you model real world situations? (You can use variables to represent variable quantities in real-world
situations and patterns)
•
How can you use the properties of real numbers to simplify algebraic expressions? (The properties that apply to real numbers
also apply to variables that represent them)
•
How do you solve an equation or inequality? (You can use properties of numbers and equality (or inequality) to solve an
equation (or inequality) by finding increasingly simpler equations (or inequalities) which have the same solution as the original
equation or inequality)
CC
Standard
A.SSE.3
Lesson:
Objective
1.1 Patterns and Expressions
(This is review of Algebra 1)
To Identify and Describe patterns
N.RN.3
1.2 Properties of Real Numbers
(This is review of Algebra 1)
1.3 Algebraic Expressions
(This is review of Algebra 1)
To graph and order real numbers
To identify properties of real numbers
To model words with an algebraic equation
To evaluate algebraic expressions
To simplify algebraic expressions
To solve equations: one step, multi-step, equations with no solutions and
identities
To solve literal equations
To solve problems by writing equations
To solve and graph inequalities
To write and solve compound inequalities
A.SSE.1a
A.SSE.1a
A.CED.4
1.4 Solving Equations
A.CED.1
1.5 Solving Inequalities
A.SSE.1b
A.CED.1
1.6 Absolute Value Equation and
Inequalities
To write and solve equations and inequalities involving absolute value
Chapter 2: Functions, Equations, and Graphs (Review of Algebra 1)
Essential Question(s)
•
Does it matter which form of a linear equation you use? You can use either slope-intercept, point-slope, or standard form to
represent linear functions. You can transform one version to another as needed)
•
How do you use transformations to help graph absolute value functions? (You can use the values of a, h, and k in the form 𝑦 =
𝑎|𝑥 − ℎ| + 𝑘 to determine how the parent function 𝑦 = |𝑥| has been transformed
•
How can you model data with a linear function? (You can use the equation of a trend line or line of best fit to model data that
cluster in a linear pattern.)
CC
Standard
Lesson
Objective
F.1F.1
F.1F.2
2.1 Relations and Functions
(Algebra 1 - F.1F.2)
A.CED.2
2.2 Direct Variation
A.CED.2
F.1F.4
2.3 Linear Functions and Slope
Intercept Form
F.1F.8
F.1F.9
F.1F.2
2.4 More about Linear Equations
To graph relations,
To find the domain and range of a function,
To identify functions
To write and evaluate a function
To identify direct variation from tables
To identify direct variation from equations
To solve direct variation equations using proportions
To use direct variation equations to solve a problem
To find the slope of a line
To write equations of lines in slope-intercept form
To graph a linear equation
To write an equation of a line given its slope and a point on the line
To write an equation of a line given two points
To write an equation of a line in standard form
A.CED.2
Graph an equation of a line using intercepts
To write equations of parallel and perpendicular lines
To graph piecewise-defined functions, including step functions and absolute
value functions
F.1F.7.b
Piecewise Functions
F.1F.4
A.CED.2
F.1F.6
2.5 Using Linear Models
To write linear equations that model real-world data
To make predictions from linear models
To describe the correlation of a scatter plot
To write an equation of a trend line
To find the line of best fit using a calculator
F.BF.3
F.BF.3
F.1F.7.b
2.6 Families of Functions
2.7 Absolute Value Functions and
Graphs
A.CED.2
F.1F.7b
2.8 Two-Variable Inequalities
To analyze transformations of functions: vertical, horizontal, reflections
To graph absolute value functions
To identify transformations of an absolute value function from a graph
To write an absolute value function given the graph
To graph two variable inequalities
To Graph an absolute value inequality
To write an absolute value inequality based on a graph
Chapter 3 : Linear Systems (Review of Algebra 1 except 3.4 and 3.5)
Essential Question(s)
•
How does representing functions graphically help you solve a system of equations? (Find a point of intersection (x,y) of the
graphs of functions f and g and you have found a solution to the system y = f(x), y = g(x)
•
How does writing equivalent equations help you solve a system of equations? (If the equations of two systems are equivalent,
then a solution of the system that is easier to solve is also a solution of the more difficult system)
CC Standard Lesson
A.CED.2
3.1 Solving Systems Using tables and Graphs
A.REI.6
A.REI.11
Objectives
To solve a linear system using a graph or table
To solve a system using linear regression on the calculator
To classify a system as independent, dependent, or inconsistent
A.CED.3
A.REI.6
A.REI.5
A.CED.2
A.REI12
A.REI.6
A.CED.3
3.2 Solving Systems algebraically
To solve linear systems algebraically using substitution and elimination
3.3 Systems of Inequalities
To solve systems of linear inequalities
To solve a linear/absolute value system
A.CED.3
3.4 Linear Programming
To solve problems using linear programming
To solve linear programming using the graphing calculator
A.REI.6
3.5 Systems with three variables
To solve systems in three variables using elimination
To solve systems in three variables using substitution
Chapter 4: Quadratic Functions and Equations
Essential Question(s)
•
What are the advantages of a quadratic function in vertex form? (Vertex form of a quadratic function shows the vertex of the
parabola. Standard form is “calculator ready.” Both forms give additional information.)
•
How is any quadratic function related to the parent quadratic function? (Any quadratic function is possibly a stretch or
compression, a reflection, and a translation of y = x2)
•
How are the real solutions of a quadratic equation related to the graph of the related quadratic function? ( The real solutions of
a quadratic equation show the zeros of the related quadratic function and the x-intercepts of its graph)
CC
Standard
F.BF.3
A.CED.1
F.1F.4
F.1F.6
Lesson
Objective
4.1 Quadratic Functions and
Transformations
To identify and graph quadratic functions
To identify vertex form
To use vertex form to identify transformations of a quadratic function
To write a quadratic function in vertex form given the vertex and a point
A.CED.2
F.1F.4
4.2 Standard Form of a
Quadratic Function
To graph quadratic functions in standard form
F.1F.6
F.1F.8
F.1f.9
F.1F.5
F.1F.4
4.3 Modeling with Quadratic
Functions
F.1F.6
Concept Byte: Identifying
Quadratic Data
4.4 Factoring Quadratic
Expressions
Square Roots and Radicals
A.SSE.2
Reviews
N.RN.2
A.CED.1
A.APR.3
A.SSE.1.a
A.REI.4.b
To identify the features of a quadratic function including the axis of symmetry, the minimum
or maximum value, the domain and range, and the y-intercept
To convert standard form to vertex form
To interpret a quadratic graph
To model data with quadratic functions
To write an equation of a parabola given three points
To use quadratic regression to find a quadratic model
To determine if data represents perfect quadratic data
To find common and binomial factors of quadratic expression
To factor special quadratic expressions: perfect square trinomials, difference of two squares
To simplify radical expressions
4.5 Quadratic Equations
To solve quadratic equations by factoring
To solve quadratic equations by graphing
4.6 Completing the Square
To solve by finding the square roots
To solve equations by completing the square
To re-write a quadratic function in standard form to vertex form by completing the square
To solve quadratic equations using the Quadratic formula
To determine the number of solutions by using the discriminant
To identify, graph, and perform operations with complex numbers
To find complex number solutions of quadratic equations
A.REI.4.b
4.7 The Quadratic Formula
N.CN.1
N.CN.2
N.CN.7
N.CN.8(+)
A.CED.3
A.REI.7
A.REI.11
4.8 Complex Numbers
4.9 Quadratic Systems
To solve and graph systems of linear and quadratic equations
To solve and graph systems of quadratic inequalities
Chapter 5: Polynomials and Polynomial Functions
Essential Question(s)
•
What does the degree of a polynomial tell you about its related polynomial function? (A polynomial of degree n has n linear
factors. The graph of the related function crosses the x-axis an even or odd number of times depending on whether n is even or odd.)
•
For a polynomial function, how are the factors, zeros, and x-intercepts related? ( (x - a) is a linear factor if and only if a is a
zero, and if and on if (a , 0) is an x-intercept when a is a real number.)
•
For a polynomial equation, how area the factors and roots related? ((x - a) is a linear factor if and only if a is a root of the
related polynomial equation.
CC
Standard
F.1F.7.c
A.SSE.1.a
Lesson
Objective
5.1 Polynomial Functions
F.1F.7.c
A.APR.3
5.2 Polynomials, Linear Factors,
and Zeros
A.REI.11
A.SSE.2
A.APR.2
A.APR.1
A.APR.6
N.CN.7
N.CN.8(+)
N.CN.8 (+)
N.CN.9 (+)
5.3 Solving Polynomial Equations
To classify polynomials by degree and number of terms
To describe the end behavior of polynomial functions
To graph polynomial functions
To look at a table of values and using differences to determine the degree of the
polynomial
To write a polynomial in factored form
To find the zeros of a polynomial function in factored form
To write a polynomial function from its zeros
To find the multiplicity of a zero
To identify a relative maximum and minimum
To solve polynomial equations by factoring
To solve polynomial equations by graphing
To divide polynomials using long division
To divide polynomials using synthetic division
5.4 Dividing Polynomials
5.5 Theorems About Roots of
Polynomial Equations
5.6 The Fundamental Theorem of
Algebra
To solve equations using the Rational Root Theorem
To use the conjugate root theorem (+)
To use the Fundamental Theorem of Algebra to solve polynomial equations with complex
solutions
A.APR.3
A.APR.5
(+)
F.1F.5
F.1F.4
F.1F.6
F.BF.3
F.1F.7.c
F.1F.8
F.1F.9
Concept Byte: Graphing
Polynomials Using Zeros
5.7 The Binomial Theorem (+)
5.8 Polynomial Models in the Real
World
5.9 Transforming Polynomial
Functions
To identify zeros when suitable factorizations are available and use the zeros to construct a
rough graph of the function defined by the polynomial
To expand a binomial using Pascal’s Triangle
To use the binomial theorem
To fit data to linear, quadratic, cubic or quartic models
To use interpolation and Extrapolation
To apply transformations to graphs of polynomials
Chapter 6: Radical Functions and Rational Exponents
Essential Questions
 To simplify the nth root of an expression, what must be true about the expression? (You can simplify the nth root of an
𝑛


𝑛
expression that contains an nth power as a factor √𝑥n = 𝑥 𝑛 = x if n is odd or |𝑥| if n is even. )
When you square each side of an equation, is the resulting equation equivalent to the original? ( When you square each side of
an equation, the resulting equation may have more solutions than the original equaltion.)
How are a function and its inverse function related? ( If f and f—1 are inverse functions and if one maps a to b, then the other
maps b to a, i.e., (𝑓°𝑓 −1 )(𝑎) = (𝑓 −1 °𝑓)(𝑎) = 𝑎 . )
CC Standard Lesson
Objective
Prepares for
N.RN.1
A.SSE.2
Concept Byte: Properties of Exponents
Simplify expressions using the properties of exponents
6.1 Roots and Radical Expressions
A.SSE.2
6.2 Multiplying and Dividing Radical Expressions
A.SSE.2
6.3 Binomial Radical Expressions
To find nth roots
To simplify radical expressions
To multiply and divide radical expressions
To rationalize the denominator when simplifying a radical expression
To add and subtract radical expressions
To multiply binomial radical expressions
To multiply conjugates
Reviews
N.RN.2
N.RN.1
A.REI.2
A.CED.4
F.BF.1.b
F.BF.1.c
F.BF.4.a
F.BF.4.c
F.1F.7.b
F.1F.8
6.4 Rational Exponents
To simplify expressions with rational exponents
To convert between exponential and radical forms
To combine radical expressions
To simplify numbers with rational exponents
6.5 Solving Square Root and Other Radical Equations To solve square root and other radical equations
To check for extraneous solutions
6.6 Function Operations
To add, subtract, multiply and divide functions
To find the composite of two functions
6.7 Inverse Relations and Functions
To find the inverse of a relation or function
To graph a function and its inverse
To identify the domain and range of a function and its inverse
To find the composition of inverse functions
6.8 Graphing Radical Functions
To graph square root and other radical functions
To solve a radical equation by graphing
To re-write a radical function so you can graph it using transformations
Chapter 7: Exponential and Logarithmic Functions
Essential Questions:
• How do you model a quantity that changes regularly over time by the same percentage? (The function y=𝑎𝑏 𝑥 , 𝑎 > 0, 𝑏 > 1,
represents exponential growth. 𝑦 = 𝑎𝑏 𝑥 models exponential decay if 0 < b < 1. )
 How are exponents and logarithms related? (Logarithms are exponents. In fact, 𝑙𝑜𝑔𝑏 𝑎 = 𝑐 if and only if 𝑏 𝑐 = 𝑎)
 How are exponential and logarithmic functions related? (The exponential function y = bx and the
Logarithmic function y = logbx are inverse functions
CC Standard Lesson
F.1F.7.e
7.1 Exploring Exponential Models
A.CED.2
F.1F.8
Objective
To graph an exponential function
To identify exponential growth and decay
To model exponential growth and decay
A.SSE.1.b
F.1F.8
F.1F.7.e
F.BF.1.b
A.CED.2
A.SSE.1.b
7.2 Properties of Exponential Functions
To write an exponential function
To explore the properties of the form y = abx
To graph translations of the parent function
To graph exponential functions with base e
To calculate continuously compounded interest problems
F.BF.4.a
F.1F.7.e
ASSE.1.b
F.1F.8
F.1F.9
7.3 Logarithmic Functions as Inverses
To write exponential equations in logarithmic form
To evaluate a logarithmic expression
To graph a logarithmic function
To graph translations of logarithmic functions
Prepares for
F.LE.4
7.4 Properties of Logarithms
To use the properties of logarithms to simplify and expand logarithmic expressions
To use the change of base formula
F.LE.4
A.REI.11
7.5 Exponential and Logarithmic Equations To solve an exponential equation with a common base
To solve an exponential equation with different bases
To solve an exponential equation with a graph or table
To solve a logarithmic equation using exponents, graph or table
7.6 Natural Logarithms
To evaluate and simplify natural logarithmic expressions
To solve equations using natural logarithms
F.LE.4
Chapter 8 Rational Functions
Essential Questions:
 Are two quantities inversely proportional if an increase in one corresponds to a decrease in the other? Quantities x and y are inversely
1
proportional only if growing x by the factor k (k > 1) means shrinking y by the factor 𝑘.
 What kinds of asymptotes are possible for a rational function? A rational function may have no asymptote, one horizontal or oblique
asymptote, and any number of vertical asymptotes
𝑥+𝑎
1
 Are a rational expression and its simplified form equivalent? 𝑓(𝑥) = 𝑥 2 −𝑎2 , 𝑥 ≠ ±𝑎 and 𝑔(𝑥) = 𝑥−𝑎 , 𝑥 ≠ ±𝑎 , are equivalent
CC
Standard
A.CED.2
Lesson
Objective
8.1 Inverse Variation
F.BF.3
A.CED.2
A.APR.1
A.APR.3
F.BF.1.b
8.2 The Reciprocal Function Family
To identify direct and inverse variations
To recognize and use inverse variation
To use joint and other variations
To graph an inverse variation function
To identify Reciprocal function transformations
To graph translations of reciprocal functions
To identify properties of rational functions – to find points of discontinuity, to identify
vertical and horizontal asymptotes
To graph rational functions
A.SSE.2
A.SSE.1.b
A.SSE.1.a
A.APR.7
8.4 Rational Expressions
A.SSE.1a
8.8 Factoring by Grouping
8.3 Rational Functions and Their
Graphs
8.5 Adding and Subtracting Rational
Expressions
To simplify rational expressions
To multiply and divide rational expressions
To use rational expressions to solve a problem
To find the least common multiple
To add and subtract rational expressions
To simplify a complex fraction
To use rational expressions to solve problems
Factor higher degree polynomials by grouping
Chapter 9: Sequences and Series
Essential Question(s)
 How can you model a geometric sequence? How can you model its sum?
CC Standards
Lesson
Objective
Prepares for ASSE.4 9.1Mathematical Patterns To identify mathematical patterns found in a sequence
A.SSE.4
A.SSE.4
9.3 Geometric Series
9.5 Geometric Series
To use a formula to find the nth term of a sequence
To define, identify, and apply geometric series
To define geometric series and find their sums
Chapter 11: Probability and Statistics
Essential Question(s)
 What is the difference between experimental and theoretical probability? (You base experimental probability on past – and theoretical
probability on possible occurrences.)
 How are measures of central tendency different from standard deviation? (Probability concepts can be used to analyze data and make
decisions. Standard deviation describes how data spread out from a particular middle, central tendency, value.)
Prepares
for
S.IC.2
S.MD.6
S.MD.7
S.MD.6
S.MD.7
S.ID.4
S.IC.6
S.IC.1
S.IC.3
S.IC.4
S.IC.6
S.ID.4
S.IC.4
S.IC.5
11.2 Probability
To find the probability of an event using theoretical , experimental, and simulation models
11.5 Probability Models
To use probabilities to make fair decisions and analyze decisions
11.6 Analyzing Data
To calculate measures of central tendency
To draw and interpret box and whisker plots
To find the standard deviation and variance of a set of values
To apply standard deviation and variance
To identify sampling methods
To recognize bias in samples and surveys
11.7 Standard Deviation
11.8 Samples and Surveys
11.10 Normal Distributions
Concept Byte: Margin of Error
Concept Byte: Drawing
Conclusions from Samples
To use a normal distribution
Activities
Compare samples to determine if the difference in mean or proportion for a large
population, based on a given confidence level, is significant
Chapter 13: Periodic Functions and Trigonometry
Essential Questions:



F.IF.4
How can you model periodic behavior? ( You can use combinations of circular functions (sine and cosine) to model natural periodic
behavior).
What function has as its graph a sine curve with amplitude 4, period π, and a minimum at the origin? (The graph of
𝜋
𝑦 = 4𝑠𝑖𝑛2 (𝑥 − 4 ) + 4 has amplitude 4, period π, midline 𝑦 = 4, and a minimum at the origin)
If you know the value of sin 𝜃, how can you find cos𝜃, 𝑡𝑎𝑛𝜃, 𝑐𝑠𝑐𝜃, 𝑠𝑒𝑐𝜃, and 𝑐𝑜𝑡𝜃? (If you know the value of 𝑠𝑖𝑛𝜃, find an angle with
measure 𝜃 in standard position on the unit circle to find values of the other trigonometric functions)
13.1 Exploring Periodic Data
To identify cycles and periods and periodic functions
To find the amplitude of periodic functions
Prepares for 13.2 Angles and The Unit Circle To work with angles in standard position
F.TF.2
To find coordinates of points on the unit circle
Identify Coterminal Angles
Find cosines and sines of angles
Determine exact values of cosine and sine
F.TF.1
13.3 Radian Measure
To use radian measure for angles
To find the length of an arc of a circle
F.TF.2
13.4 The Sine Function
To identify properties of the sine function
F.TF.5
To graph sine curves
F.TF.5
13.5 The Cosine Functions
To graph and write cosine functions
F.TF.4
To solve trigonometric equations