Common Core Algebra 2 Math (Worksheets, Homework, Lesson Plans)
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Looking for video lessons that will help you in your Common Core Algebra 2 math classwork or homework? Looking for Common Core Math Worksheets and Lesson Plans that will help you prepare lessons for Algebra 2 students?
The following lesson plans and worksheets are from the New York State Education Department Common Core-aligned educational resources. Eureka/EngageNY Math Algebra 2 Worksheets.
These Lesson Plans and Worksheets are divided into five modules.
Algebra 2 Homework, Lesson Plans and Worksheets
| Topics and Objectives (Module 1) |
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| Polynomial, Rational, and Radical Relationships : Successive Differences in Polynomials ( ) : The Multiplication of Polynomials ( ) : The Division of Polynomials ( ) : Comparing Methods—Long Division, Again? ( ) : Putting It All Together ( ) : Dividing by 𝒙 − 𝒂 and by 𝒙 + 𝒂 ( ) : Mental Math ( ) : The Power of Algebra—Finding Primes ( ) : Radicals and Conjugates ( ) : The Power of Algebra—Finding Pythagorean Triples ( ) : The Special Role of Zero in Factoring ( ) |
| Factoring—Its Use and Its Obstacles : Overcoming Obstacles in Factoring ( ) : Mastering Factoring ( ) : Graphing Factored Polynomials ( ) : Structure in Graphs of Polynomial Functions ( ) : Modeling with Polynomials—An Introduction ( ) : Modeling with Polynomials—An Introduction ( ) : Overcoming a Second Obstacle in Factoring—What If There Is a Remainder? ( ) : The Remainder Theorem ( ) : Modeling Riverbeds with Polynomials ( ) : Modeling Riverbeds with Polynomials ( ) |
| Solving and Applying Equations—Polynomial, Rational, and Radical : Equivalent Rational Expressions ( ) : Comparing Rational Expressions ( ) : Multiplying and Dividing Rational Expressions ( ) : Adding and Subtracting Rational Expression ( ) : Solving Rational Equations: Solving Rational Equations ( ) : Word Problems Leading to Rational Equations ( ) : A Focus on Square Roots ( ) : Solving Radical Equations ( ) : Linear Systems in Three Variables ( ) : Systems of Equations ( ) : Graphing Systems of Equations ( ) : The Definition of a Parabola ( ) : Are All Parabolas Congruent? ( ) : Are All Parabolas Similar? ( ) |
| A Surprise from Geometry—Complex Numbers Overcome All Obstacles : Overcoming a Third Obstacle to Factoring—What If There Are No Real Number Solutions? ( ) : A Surprising Boost from Geometry ( ) : Complex Numbers as Solutions to Equations ( ) : Factoring Extended to the Complex Realm ( ) : Obstacles Resolved—A Surprising Result ( ) |
| Topics and Objectives (Module 2) |
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| The Story of Trigonometry and Its Contexts : Ferris Wheels—Tracking the Height of a Passenger Car ( ) : The Height and Co-Height Functions of a Ferris Wheel ( ) : The Motion of the Moon, Sun, and Stars—Motivating Mathematics ( ) : From Circle-ometry to Trigonometry ( ) : Extending the Domain of Sine and Cosine to All Real Numbers : Why Call It Tangent? : Secant and the Co-Functions : Graphing the Sine and Cosine Functions : Awkward! Who Chose the Number 360, Anyway? : Basic Trigonometric Identities from Graphs |
| Understanding Trigonometric Functions and Putting Them to Use : Transforming the Graph of the Sine Function : Ferris Wheels—Using Trigonometric Functions to Model Cyclical Behavior : Tides, Sound Waves, and Stock Markets : Graphing the Tangent Function : What Is a Trigonometric Identity? : Proving Trigonometric Identities : Trigonometric Identity Proofs |
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| Module 4 |
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Free Printable Math Worksheets for Algebra 2
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- Order of operations
- Evaluating expressions
- Simplifying algebraic expressions
- Multi-step equations
- Work word problems
- Distance-rate-time word problems
- Mixture word problems
- Absolute value equations
- Multi-step inequalities
- Compound inequalities
- Absolute value inequalities
- Discrete relations
- Continuous relations
- Evaluating and graphing functions
- Review of linear equations
- Graphing absolute value functions
- Graphing linear inequalities
- Direct and inverse variation
- Systems of two linear inequalities
- Systems of two equations
- Systems of two equations, word problems
- Points in three dimensions
- Systems of three equations, elimination
- Systems of three equations, substitution
- Basic matrix operations
- Matrix multiplication
- All matrix operations combined
- Matrix inverses
- Geometric transformations with matrices
- Operations with complex numbers
- Properties of complex numbers
- Rationalizing imaginary denominators
- Properties of parabolas
- Vertex form
- Graphing quadratic inequalities
- Factoring quadratic expressions
- Solving quadratic equations w/ square roots
- Solving quadratic equations by factoring
- Completing the square
- Solving equations by completing the square
- Solving equations with the quadratic formula
- The discriminant
- Naming and simple operations
- Factoring a sum/difference of cubes
- Factoring by grouping
- Factoring quadratic form
- Factoring using all techniques
- Factors and Zeros
- The Remainder Theorem
- Irrational and Imaginary Root Theorems
- Descartes' Rule of Signs
- More on factors, zeros, and dividing
- The Rational Root Theorem
- Polynomial equations
- Basic shape of graphs of polynomials
- Graphing polynomial functions
- The Binomial Theorem
- Evaluating functions
- Function operations
- Inverse functions
- Simplifying radicals
- Operations with radical expressions
- Dividing radical expressions
- Radicals and rational exponents
- Simplifying rational exponents
- Square root equations
- Rational exponent equations
- Graphing radicals
- Graphing & properties of parabolas
- Equations of parabolas
- Graphing & properties of circles
- Equations of circles
- Graphing & properties of ellipses
- Equations of ellipses
- Graphing & properties of hyperbolas
- Equations of hyperbolas
- Classifying conic sections
- Eccentricity
- Systems of quadratic equations
- Graphing simple rational functions
- Graphing general rational functions
- Simplifying rational expressions
- Multiplying / dividing rational expressions
- Adding / subtracting rational expressions
- Complex fractions
- Solving rational equations
- The meaning of logarithms
- Properties of logarithms
- The change of base formula
- Writing logs in terms of others
- Logarithmic equations
- Inverse functions and logarithms
- Exponential equations not requiring logarithms
- Exponential equations requiring logarithms
- Graphing logarithms
- Graphing exponential functions
- Discrete exponential growth and decay word problems
- Continuous exponential growth and decay word problems
- General sequences
- Arithmetic sequences
- Geometric sequences
- Comparing Arithmetic/Geometric Sequences
- General series
- Arithmetic series
- Arithmetic/Geometric Means w/ Sequences
- Finite geometric series
- Infinite geometric series
- Right triangle trig: Evaluating ratios
- Right triangle trig: Missing sides/angles
- Angles and angle measure
- Co-terminal angles and reference angles
- Arc length and sector area
- Trig ratios of general angles
- Exact trig ratios of important angles
- The Law of Sines
- The Law of Cosines
- Graphing trig functions
- Translating trig functions
- Angle Sum/Difference Identities
- Double-/Half-Angle Identities
- Sample spaces and The Counting Principle
- Independent and dependent events
- Mutualy exclusive events
- Permutations
- Combinations
- Permutations vs combinations
- Probability using permutations and combinations
- Math Lessons
- Math Formulas
- Calculators
Math Calculators, Lessons and Formulas
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- Rational Expressions
Multiplying and Dividing Rational Expressions
| Simplifying Rational Expressions |
Multiplication
To Multiply a rational expression:
1. Factor all numerators and denominators.
2. Cancel all common factors.
3. Either multiply the denominators and numerators together or leave the solution in factored form.
Multiply and then simplify the product
$\frac{{2x + 4}}{x} \cdot \frac{3}{{6x + 12}}$
Multiply the following rational expressions:
$\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}} \cdot \frac{{3x - 9}}{{{x^2} + 2x - 3}}$
1 : Factor all numerators and denominators:
$\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}} \cdot \frac{{3x - 9}}{{{x^2} + 2x - 3}} = \frac{{(x + 3)(x + 3)}}{{(x - 3)(x + 3)}} \cdot \frac{{3(x - 3)}}{{(x + 3)(x - 1)}}$
2 : Cancel all common factors:
$\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}} \cdot \frac{{3x - 9}}{{{x^2} + 2x - 3}} = \frac{{\cancel{{(x + 3)}}\cancel{{(x + 3)}}}}{{\cancel{{(x - 3)}}\cancel{{(x + 3)}}}} \cdot \frac{{3\cancel{{(x - 3)}}}}{{\cancel{{(x + 3)}}(x - 1)}}$
3 : Multiply the denominators and numerators:
$\frac{{{x^2} + 6x + 9}}{{{x^2} - 9}} \cdot \frac{{3x - 9}}{{{x^2} + 2x - 3}} = \frac{{\cancel{{(x + 3)}}\cancel{{(x + 3)}}}}{{\cancel{{(x - 3)}}\cancel{{(x + 3)}}}} \cdot \frac{{3\cancel{{(x - 3)}}}}{{\cancel{{(x + 3)}}(x - 1)}} = \frac{1}{1} \cdot \frac{3}{{x - 1}} = \frac{3}{{x - 1}}$
| Try yourself | |||||||
| $$ \color{blue}{\frac{{4 + 2x}}{{{x^2} - 4}} \cdot \frac{{{x^2} - 4x + 4}}{{x - 2}}} $$ | |||||||
| $ \frac{2}{{x - 2}} $ | $ \frac{{x - 2}}{2} $ | $ 2 $ | $ $ | ||||
Division of rational expressions
When we divide rational functions we multiply by the reciprocal.
Perform the indicated operations:
$\frac{{2{x^2} + x - 6}}{{{x^2} - 2x - 8}}:\frac{{2{x^2} - x - 3}}{{{x^2} - 3x - 4}}$
Solution 3:
$$\frac{{2{x^2} + x - 6}}{{{x^2} - 2x - 8}}:\frac{{2{x^2} - x - 3}}{{{x^2} + 3x - 4}} = $$ $$ = \frac{{2{x^2} + x - 6}}{{{x^2} - 2x - 8}} \cdot \frac{{{x^2} - 3x - 4}}{{2{x^2} - x - 3}} = $$ $$ = \frac{{2\left( {x - \frac{3}{2}} \right)(x + 2)}}{{(x + 2)(x - 4)}} \cdot \frac{{(x - 4)(x + 1)}}{{2\left( {x - \frac{3}{2}} \right)(x + 1)}} = $$ $$ = \frac{{\bcancel{{(2x - 3)}}\cancel{{(x + 2)}}}}{{\cancel{{(x + 2)}}\bcancel{{(x - 4)}}}} \cdot \frac{{\bcancel{{(x - 4)}}\cancel{{(x + 1)}}}}{{\bcancel{{(2x - 3)}}\cancel{{(x + 1)}}}} = 1$$
$\frac{{\frac{{x + 4}}{{2x - 6}}}}{{\frac{{3x + 12}}{{4x - 12}}}}$
Solution 4:
$$\frac{{\frac{{x + 4}}{{2x - 6}}}}{{\frac{{3x + 12}}{{4x - 12}}}} = \frac{{x + 4}}{{2x - 6}} \cdot \frac{{4x - 12}}{{3x + 12}} = $$ $$ = \frac{{\cancel{{x + 4}}}}{{2\cancel{{(x - 3)}}}} \cdot \frac{{4\cancel{{(x - 3)}}}}{{3\cancel{{(x + 4)}}}} = \frac{1}{2} \cdot \frac{4}{3} = \frac{2}{3}$$
| Try yourself | |||||||
| $$ \frac{{x - 2}}{{x + 2}} $$ | |||||||
| $ \color{blue}{\frac{{{x^2} - 3x + 2}}{{2x - 4}} \cdot \frac{{x - 1}}{{{x^2} - 2x + 1}}} $ | $ \frac{2}{{x - 1}} $ | $ \frac{1}{2} $ | $ \frac{{x - 1}}{2} $ | ||||
- Roots and Radicals Simplify Expression Adding and Subtracting Multiplying and Dividing
- Complex Numbers Arithmetic Polar representation
- Polynomials Multiplying Polynomials Division of Polynomials Zeros of Polynomials
- Rational Expressions Simplifying Multiplying and Dividing Adding and Subtracting
- Solving Equations Linear Equations Absolute Value Equations Quadratic Equation Equations with Radicals
- Systems of Equations Substitution Method Elimination Method Row Reduction Cramers Rule Inverse Matrix Method
- Exponential Functions Introduction Exponential Equations Logarithmic Functions
- Trigonometry Trigonometric Formulas Trigonometric Equations Law of Cosines
- Progressions Arithmetic Progressions Geometric Progressions
- Differentiation Common formulas Product and Quotient Rule Chain Rule
- Limits Properties of Limits Rational Function Irrational Functions Trigonometric Functions L'Hospital's Rule
- Integrals Integration Formulas Exercises
- Integral techniques Substitution Integration by Parts Integrals with Trig. Functions Trigonometric Substitutions
- Integral Applications Area Volume Arc Length
Analytic geometry
- Analytic Geometry 2D Basic Concepts Lines Parallel and Perpendicular Lines Polar Coordinates
- Conic Sections Circle Ellipse Hyperbola
- Analytic Geometry 3D Line in 3D Planes
Linear Algebra
- Matrices Definitions Addition and Multiplication Gauss-Jordan elimination
- Determinants Introduction to Determinants Applications of Determinants
- Vectors Basic Operations Dot Product Cross Product
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Algebra 2 Common Core: Home List of Lessons Semester 1 > > > > > > Semester 2 > > > > > > ... 3.2 Multiply and Divide Rational Expressions. Common Core Standard: A-APR.D.6. Packet. To purchase this lesson packet, or lessons for the entire course, please click here. Practice Solutions. alg2_3.2_practice_solutions.pdf: File Size: 454 kb: File ...
e is also valid for real numbers.Discussion (2 minutes) To multiply rational expressions, we follow the same procedure we use when multiplying rational numbers: we multiply togeth. the numerators and multiply together the denomina. If , , , and are rational expressions with , , thenLead students throug.
LESSON 3 MULTIPLYING AND DIVIDING RATIONAL EXPRESSIONS COMMON CORE ALGEBRA II Multiplication of rational expressions follows the same principles as those involved in simplifying them. Exercise #1: Simplify each of the following rational expressions. (a) (b) The ability to cross-cancel with fractions is a result of the two facts: ( í) to multiply fractions
Find video lessons, worksheets, and homework for Common Core Algebra 2 topics such as polynomials, rational expressions, trigonometry, and more. Browse the modules and topics from the New York State Education Department resources.
Learn how to multiply and divide rational expressions and functions using factoring, distributive property, and reciprocal rules. See examples, exercises, and tips for factoring and canceling common factors.
Yay Math In Studio is back with a short and sweet foray into multiplying and dividing rational expressions. Do we need a common denominator here? Nope! That'...
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Learn how to simplify, multiply and divide rational expressions with examples and exercises. Find the excluded values, common factors and simplified forms of rational expressions.
"Correction:" 16:00 On Exercise #3(a), Kirk mistakenly forgets to rewrite the 6 in the denominator of the first fraction. The final correct answer should be ...
Free Printable Math Worksheets for Algebra 2
Learn how to multiply and divide rational expressions by factoring, canceling and multiplying numerators and denominators. See examples, solutions and exercises with online calculator.
est form.MULTIPLYING RATIONAL EXPRESSIONSExample 1. Multiply, 15 14. 49 45. First, reduce by dividing out the common factors from numerator and denominator (15 and 7 ) 2 . 7 3. her and the denominators together2 21Our AnswerWhen multiplying rational expressions, we first divide. e numerators and denominators by any common factors. T.
Find step-by-step solutions and answers to Algebra 2 Common Core - 9780133186024, as well as thousands of textbooks so you can move forward with confidence. ... Multiplying and Dividing Radical Expressions. Section 6-3: ... Rational Expressions. Page 389: Mid-Chapter Quiz. Section 6-5: Solving Square Root and Other Radical Equations. Section 6 ...
Divide out common factors. Multiplying Rational Expressions The rule for multiplying rational expressions is the same as the rule for multiplying numerical fractions: multiply numerators, multiply denominators, and write the new fraction in simplifi ed form. Similar to rational numbers, rational expressions are closed under multiplication. KEY IDEA
Click here 👆 to get an answer to your question ️ Multiplying and Dividing Rational Expressions Common Core Algebra II Homework
This is a lesson based on a Common Core Algebra 2 curriculum. This lesson explores multiplying and dividing rational expressions.
Learn how to multiply and divide rational expressions, which are fractions with polynomial numerators and denominators. Find the values for which a rational expression is undefined, simplify rational expressions, and multiply and divide rational functions.
Rational expressions are multiplied together using exactly the same three steps. Since rational expressions tend to be longer than arithmetic fractions, we can simplify the multiplication process by adding one more step. Method for Multiplying Rational Expressions. Factor all numerators and denominators. Reduce to lowest terms first by dividing ...
Section 10.2 Multiply and Divide Rational Expressions. A2.5.9 Use function notation to indicate operations on functions and use properties from number systems to justify steps in combining and simplifying functions; Traditional Algebra 2 - 10.2 Multiply & Divide Rational Expressions - YouTube.
Semester 1. Semester 2. Teacher Resources. UNIT 3. Rational Expressions. 3.1 Simplify Rational Expressions. 3.2 Multiply and Divide Rational Expressions. 3.3 Add and Subtract Rational Expressions. 3.4 Solve Rational Equations.
Definition 5.1.1. A rational expression is an expression of the form p q, where p and q are polynomials and q ≠ 0. Here are some examples of rational expressions: − 24 56 5x 12y 4x + 1 x2 − 9 4x2 + 3x − 1 2x − 8. Notice that the first rational expression listed above, − 24 56, is just a fraction. Since a constant is a polynomial ...
Find the video lessons, worksheets and quizzes for each unit of Algebra 2 Common Core course. Learn polynomials, rational expressions, radicals, exponential and logarithmic functions, trigonometry, sequences and series, probability and more.
When adding or subtracting rational expressions with a common denominator, add or subtract the expressions in the numerator and write the result over the common denominator. To find equivalent rational expressions with a common denominator, first factor all denominators and determine the least common multiple.
Algebra 2 Common Core: Home List of Lessons Semester 1 > > > > > > Semester 2 > > > > > > > Teacher Resources 3.1 Simplify Rational Expressions. Common ... 3.1 Simplify Rational Expressions. Common Core Standard: A-APR.D.6. Packet. To purchase this lesson packet, or lessons for the entire course, please click here.