Algebra 2 Syllabus

TOPIC

Skills, Strategies & Concept

Linked Common Core Standards

Students will be able to:

Unit 1

Review Lessons- 

Equations and Inequalities

(5 Days)

-Variables, Like Terms, and Expressions

- Solving Linear Equations

-Common Algebraic Expressions

-Basic Exponent Manipulation

- Multiplying Polynomials

- Exponents

A-CED.1

N-RN.2

A-SSE.2

• Reason quantitatively and use units to solve problems
• Represent and solve equations and inequalities graphically.

Unit 2

Intro to Functions 

(10 Days)

- Intro to functions

• Key pieces to functions
• Vertical Line Test

-Function Notation

-Function Composition

-Domain and Range

-One to One Functions

• Horizontal Line Test

-Inverse Functions

-Key Features of Functions

• Graphs
• Increasing/Decreasing Intervals
• Zeroes, max, min, etc

F-IF.7c               

F-IF.3

F-BF.1b      - Embedded in

N-Q.2             everything

F-BF.4a

F-IF.9 F-IF.4

F-BF.3

• Build a function that models a relationship between two quantities.
• Build new functions from existing functions.
• Analyze functions using different representations.
• Use interval notation to find the domain and range of a function graphically and algebraically
• Perform transformations on functions
• Perform operations with functions
• Find the inverse of a function algebraically and graphically

Linear Functions, Equations, and their Algebra 

(7 Days)

- Direct Variation

-Average Rate of Change

-Forms of a line

• Slope intercept
• Point-Slope

-Linear Modeling

-Inverses of Linear Functions

F-IF.6

F-LE.2

F-LE.5

F-BF.4

A-REI.11

A-REI.6

• Identify features of linear functions from equations, verbal descriptions, tables and graphs
• Write linear functions that represent contextual situations
• Solve for desired quantity in a linear function
• find the inverse of a contextual situation graphically and describe the meaning of the function and its inverse
• Find the inverse algebraically

Unit 3

Quadratic Functions 

(16 Days)

- Features of Quadratic Functions

-Factoring

• GCF
• Difference of Perfect Squares

-Factoring Trinomials ( a=1, a>1)

-Complete factoring

• Mix of all factoring covered so far

-Factoring by Grouping

-The Zero Product Law

-Quadratic Inequalities in One Variable

• Set and Interval Notation
• Graph solutions

-Completing the Square and Shifting Parabolas

- Modeling with Quadratic Functions

-Equations of Circles

• Distance formula
• Center/Radius Form

-The Locus definition of a Parabola

• Focus and Directrix

F-IF.4

A.SSE.2

A.SSE.2

A.SSE.2

A.SSE.2

A.APR.3     A-REI.4b

A-CED.1

F-BF.3

A-CED.1

A-REI.7

G-GPE.2

• Identify features of quadratic functions from equations and use these features to graph quadratic functions
• Identify the y-intercept and vertex of a quadratic function written in standard form through inspection and finding the axis of symmetry.
• Graph quadratic equations on the graphing calculator.
• describe the domain, range, and intervals where the function is decreasing and increasing.
• Write the quadratic equation in intercept form by factoring
• Factor polynomials using various methods of factoring such as GCF, Trinomial, sum/difference of 2 cubes, and grouping (AC).
• Solve polynomial equations using various methods such as completing the square and quadratic formula.
• Determine the multiplicity of a polynomial
• Find and use x-intercepts to graph a function
• Analyze polynomial functions
• Determine the end behavior of polynomial graphs
• Graph a polynomial without using a calculator
• Find the relative maximum and minimum of a polynomial function
• Write the equation of a cubic function given a graph
• Find average rate of change algebraically and graphically

Unit 4

Complex Numbers 

(10 Days)

***Potential to be shorter***

Define and use the imaginary unit i. Add, subtract, and multiply complex numbers. Find complex solutions and zeros.

-Imaginary Numbers

-Complex Numbers

-Solving Quadratic Equations with Complex Solutions

-The Discriminant of a Quadratic

SPED Strategies:

Relate the idea of adding, subtracting and multiplying complex numbers to whole numbers. 

Explain the background of complex numbers and connect to real life by explaining how they are used in electrical circuits.

Use the example of the cyclical nature of the ones digit in the powers of 3 and connect it to the cyclical nature of the powers of i. 

Develop a reference document with students with verbal and pictorial descriptions.

ELL Strategies:

Discuss how to determine whether two complex numbers are equal. 

Explain that you want to add two complex numbers. “What would make sense for (6 + 3i) + (2 − 5i)?

Describe and explain orally and in writing how to use properties of operations to add, subtract, and multiply complex numbers in the student’s native language and/or use selected technical vocabulary in phrases and short sentences with equations to explain the solution.

Encourage students to highlight like terms - use one color for the real parts and another color for the imaginary parts. Make a table with the words: Imaginary Unit, Complex Number and Imaginary Number, then write an example for each word in the column.

N-CN.1

N-CN.1,2

A-REI.4   N-CN.7

A-REI.2

A-REI.4

• Define imaginary and complex numbers
• Add, subtract, multiply and divide complex numbers
• Determine the nature of the roots of a quadratic function using the discriminant
• Identify solutions that are non-real from graphs and an equation using the discriminant.
• Find the sum and product of roots of a quadratic equation.
• Leave answers in a + bi form
• Identify the powers of i
• Find the multiplicative inverse

What are the subsets of the set of complex numbers? 

What are the subsets of the set of complex numbers? Give an example of a number in each subset.

Is it possible for a number to be both whole and natural? natural and rational? rational and irrational? real and imaginary? Explain your reasoning. 

What does the graph of f(x) = 4x2 + 20 look like?”

Unit 5

Radicals and the Quadratic Formula

 (13 Days)

- Square Root Functions

-Solving Square Root Equations

-The Basic Exponent Properties

-Fractional Exponents Revisited

-More Exponent Practice

-The Quadratic Formula

-More work with the Quadratic Formula

F-IF.4

A-REI.2

N-RN.2

N-RN.1,2

N-RN.2

A-REI.4b

A-REI.4b

• Simplify Radicals
• Perform addition, subtraction, and multiplication on radicals
• Divide radicals and rationalize the denominator of a fraction
• Solve radical equations
• Identify solutions that are non-real from graphs and an equation using the discriminant.

Unit 6

Exponential Functions 

(10 days)

• How do we find the domain and range of a function graphically and algebraically?
• How do we perform transformations on functions?
• How do we perform operations with functions?
• How do we find the inverse of a function algebraically and graphically?
• How do we perform a composition of functions?
• How do we determine whether a function is odd, even, or neither?
• How do we evaluate expressions with negative and fractional exponents?
• How do we solve equations with fractional exponents?
• How do we solve exponential equations with common bases?
• How do we model exponential growth and decay using functions?
• How do we model exponential growth and decay based on time?
• Shifting Functions
• Reflecting Parabolas
• Vertically Stretching of Functions
• Horizontal Stretching of Functions

IF.B.5, 

LE.A.1, 

A.1.C, 

LE.A.3, 

LE.B.5

• Use interval notation to find the domain and range of a function graphically and algebraically
• Perform transformations on functions
• Perform operations with functions
• Find the inverse of a function algebraically and graphically
• Determine whether a function is odd, even, or neither
• Evaluate expressions with negative and fractional exponents
• Solve equations with fractional exponents
• Solve exponential equations with common bases
• Model exponential growth and decay using functions
• Model exponential growth and decay based on time

Unit 7

Polynomials 

(14 Days)

- Power Functions

-Graphs and Zeroes of a Polynomial

-Creating Polynomial Equations

-Polynomial Identities

-Intro to Rational Functions

-Simplifying Rational Expressions

-Mult./Div. Rational Expressions

-Add./Sub. Rational Expressions

-Complex Fractions

F-IF.4   F-BF.3

A-APR.3   F-IF.4   F-IF.7

F-IF.7

A-APR.4

F-IF.4   

A-APR.6

A-APR.6

A-APR.6

A-APR.6

• Classify polynomials through identification of degree and leading coefficient.
• identify features of polynomial functions including end behavior where the function is positive or negative, and domain and range of a function
• Match and compare equations and graphs of polynomials and identify transformations
• Multiply polynomials, identify factors, degrees,  and number of real roots.
• Identify features of a polynomial in standard form
• Factor polynomials using various methods of factoring and simplify rational expressions.
• Add and subtract rational expressions by finding a common denominator.
• Multiply rational expressions
• Divide rational expressions by changing the division symbol to a multiplication symbol and following rules for multiplication
• Find what values would make the expression undefined
• Simplify complex fractions by using rules for adding, subtracting, multiplying and dividing rational expressions
• Model rate, work, and mixture “real world problems” using rational equations, which then can be solved and answered in context to the problem

Unit 8

Rational Functions

 (9 Days)

-Polynomial Long Division

-The Remainder Theorem

- Synthetic Division  *** ADDITIONAL

-Solving Rational (Fractional) Equations

-Solving Rational Inequalities

-Reasoning about Radical and Rational Equations

A-APR.6

A-APR.2    A-APR.6

A-REI.2

A-CED.1

A-REI.1

• Perform addition, subtraction, and multiplication on polynomial expressions and prove polynomial identities.
• Apply long division in a variety of situations.
• Find remainders using long division and the Remainder Theorem.
• Analyze the Factor Theorem.
• Examine the relationship between polynomial graphs and the Remainder Theorem.
• Use polynomial expressions to solve word problems.

Unit 9

Logarithmic Functions
(11 Days)

-Intro to logarithms

-Graphs of logarithms

- Logarithm Laws

• Product, quotient, power rules

-Solving Exponential Equations with Logarithms

-The number e and natural logarithms

-Compound Interest

- Real-world Applications

F-IF.4   F-IF.7e

F-LE.4

F-LE.4

F-IF.8   F-BF.1a   A-SSE.3

F-BF.1b

• Analyze and construct exponential functions that model contexts
• Write and change the form of exponential functions that model compounding interest
• Define and use e in continuous and compounding situations
• Describe and evaluate simple numeric logarithms
• Describe logarithms as the inverse of exponential functions and graph logarithmic functions
• Evaluate common and natural logs using tables, graphs, and calculators.
• Develop and use the product and quotient properties of logarithms to write equivalent expressions.
• Develop and use the power property of logarithms to write equivalent expressions.
• Solve equations with logarithms
• Use logarithms to solve exponential modeling problems

Unit 10

Trigonometry

(15 Days)

-Rotations and Angle Terminology

-Radian Angle Measurement

• Conversion both ways 
• S=θr
• Use of Calculator for DegMinSec

-Unit Circle

• Pythagorean Theorem
• 30,45,60 - coordinates of unit circle

-Def. of Sine and Cosine Functions

• Pythagorean Identity (Algebraically)

-More Sine and Cosine Functions

-Basic Graphs of Sine and Cosine 

-Vertical Shifting of Sine Graphs

• Identify starting value and shift

-Frequency and Period of Sine Graphs

• Identifying parts

-Sine Modeling

• Word Problems
• Writing functions from word problems

-Tangent Function

• Basic idea of tangent

-Reciprocal Functions

• Reciprocals of SOH CAH TOA
• Finding any of the 6 trig functions from a single one
• Negative/positive quadrant locations

F-TF.1

F-TF.2

F-TF.2   F-TF.8

F-TF.2   F-TF.8

F-TF.5   F-IF.7e

F-TF.5   F-IF.7e

F-TF.5   F-IF.7e

F-TF.5   F-IF.7e

F-TF.8

F-TF.8

• Extend the domain of trigonometric functions using the unit circle.
• Prove and apply trigonometric identities.
• Derive and verify trigonometric identities using transformations and equivalent of functions
• Derive and use the Pythagorean identity to write equivalent expressions
• Verify trigonometric identities using Pythagorean and reciprocal identities
• Solve Trigonometric Equations
• Find the angle measures using inverse trig functions in right triangles
• Analyze inverse trigonometric functions graphically
• Solve linear trigonometric equations
• Solve quadratic trigonometric equations
• Solve trigonometric equations using identities
• Advance Identities and Solving Trigonometric Equations
• Evaluate expressions using sum and difference formulas
• Solve equations and prove identities using sum and difference formulas
• Derive double angle formulas and use them to solve equations and prove identities
• Use trigonometric identities to analyze graphs of functions
• Applications and Extensions of Trigonometric Function
• Use the Law of Sines to find the missing side lengths and angle measures in acute triangles
• Find the missing side lengths and angle measures using the Law of Cosines in acute triangles

Unit 11

Sequence and Series 

(7 Days)

- Sequences

-Arithmetic and Geometric Sequences

-Summation Notation

-Arithmetic Series

-Geometric Series

- Real-World Applications

F-IF.3   F-BF.2

F-BF.2   F-LE.2

A-SSE.4

A-SSE.4

A-SSE.4

• Identify, model and analyze geometric sequences
• Describe the derivation of the formula for the sum of finite geometric series and use it to solve problems
• find the sum of an infinite geometric series

Unit 11

Probability 

(8 Days)

- Intro to Probability

-Sets and Probability

• Set theory notation
• Helpful uses of diagrams

-Adding Probabilities

-Conditional Probabilities

-Independent and dependent probabilities

• Formula to identify independence

-Multiplying Probabilities

S-CP.1

S-CP.7

S-CP.3, S-CP.4, S-CP.5, 

S-CP.6

S-CP.2, S-CP.4, S-CP.5, 

S-CP.2, S-CP.4

• Understand independence and conditional probability and use them to interpret data
• Determine probabilities of mutually exclusive events
• Determine probabilities of events that are not mutually exclusive 
• Calculate conditional probabilities
• Use the rules of probability to compute probabilities of compound events in a uniform probability model.
• Calculate relative frequencies in two-way tables to analyze data and determine independence
• Use conditional probability to make decisions about medical testing

Statistics

(10 Days)

- Variability and Sampling

• Real world scenarios

-Population parameters

-The Normal Distributions (Calculator)

-The Normal Distribution and Z-Scores

-Sample Means

-Sample Proportions

-The Difference in Sample Means

• Simulation Comparisons
• Normal Curve

-Linear Regression and Lines of Best Fit

• Calculator work
• Comparisons

- Other Types of Regression

• Quadratic, Exponential, logarithm, etc.
• Calculator work

-Margin of Error

S-IC.3

S-ID.4                    

S-ID.4                    

S-IC.1, S-IC.2 S-IC.5

S-IC.1 S-IC.4

S-IC.5

S-ID.6a

S-ID.6a

• The Normal Distribution
• Describe the center, shape, and spread of distributions by reasoning visually about the mean, standard deviation and shape of a histogram
• Derive and Calculate population percentages based on normal distribution of data
• Use z-scores to identify population percentiles

• Describe and compare statistical study methods
• Use multiple random samples to estimate a population mean or proportion and verify the validity of the sampling method by analyzing the means and standard errors of sample
• Calculate and describe the margin of error in context and use larger sample sizes to minimize the margin of error
• Compare two treatments in experimental data and determine the difference between the two treatments is significant.