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Want additional help with Algebra 2?
Unit 1: Polynomial arithmetic
Unit 2: complex numbers, unit 3: polynomial factorization, unit 4: polynomial division, unit 5: polynomial graphs, unit 6: rational exponents and radicals, unit 7: exponential models, unit 8: logarithms, unit 9: transformations of functions, unit 10: equations, unit 11: trigonometry, unit 12: modeling.
Algebra 2 Worksheets with answer keys
Enjoy these free printable math worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.
- Absolute Value Equations
- Simplify Imaginary Numbers
- Adding and Subtracting Complex Numbers
- Multiplying Complex Numbers
- Dividing Complex Numbers
- Dividing Complex Number (advanced)
- End of Unit, Review Sheet
- Exponential Growth (no answer key on this one, sorry)
- Compound Interest Worksheet #1 (no logs)
- Compound Interest Worksheet (logarithms required)
- Simplify Rational Exponents
- Solve Equations with Rational Exponents
- Solve Equations with variables in Exponents
- Factor by Grouping
- 1 to 1 functions
- Evaluating Functions
- Composition of Functions
- Inverse Functions
- Operations with Functions
- Functions Review Worksheet
- Product Rule of Logarithms
- Power Rule of Logarithms
- Quotient Rule of Logarithms
- Logarithmic Equations Worksheet
- Dividing Polynomials Worksheet
- Solve Quadratic Equations by Factoring
- Solve Quadratic Equations by Completing the Square
- Quadratic formula Worksheet (real solutions)
- Quadratic Formula Worksheet (complex solutions)
- Quadratic Formula Worksheet (both real and complex solutions)
- Discriminant Worksheet
- Sum and Product of Roots
- Radical Equations
- Rationalizing the Denominator
- Simplify Rational Expressions Worksheet
- Dividing Rational Expressions
- Multiplying Rational Expressions
- Adding and Subtracting Rational Expressions (with like denominators)
- Adding and Subtracting Ratioal Expressions with Unlike Denominators
- Mixed Review on Rational Expressions
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About This Course
Welcome to the Math Medic Algebra 2 course! Here you will find a ready-to-be-taught lesson for every day of the school year, along with expert tips and questioning techniques to help the lesson be successful. Each lesson is designed to be taught in an Experience First, Formalize Later (EFFL) approach, in which students work in small groups on an engaging activity before the teacher formalizes the learning.
Our Algebra 2 course focuses on several function families and develops the graphical, analytical, verbal, and numerical analysis skills needed to flexibly work with these functions, with an emphasis on quadratics. The concept of function transformations is a big theme and woven throughout the course. This course was created using the Common Core State Standards as a guide. The standards taught in each Math Medic Algebra 2 lesson can be found here . The unit overviews and learning targets for the Math Medic Algebra 2 course can be found here .
Math Medic Help
Alg1.2 Linear Equations, Inequalities, and Systems
In this unit, students expand and deepen their prior understanding of expressions, equations, and inequalities. Students reason about equations, inequalities, and systems of equations and inequalities as ways to represent constraints, and they reason about the process of solving equations and inequalities in terms of finding values that satisfy those constraints. The process of finding solutions may involve rewriting and manipulating equations. Students learn to explain and validate the steps to do so. Throughout the unit, students practice reasoning about situations and mathematical representations, interpreting expressions and numbers in context, and using mathematical tools to model quantities and relationships.
Writing and Modeling with Equations
- 1 Planning a Pizza Party
- 2 Writing Equations to Model Relationships (Part 1)
- 3 Writing Equations to Model Relationships (Part 2)
- 4 Equations and Their Solutions
- 5 Equations and Their Graphs
Manipulating Equations and Understanding Their Structure
- 6 Equivalent Equations
- 7 Explaining Steps for Rewriting Equations
- 8 Which Variable to Solve for? (Part 1)
- 9 Which Variable to Solve for? (Part 2)
- 10 Connecting Equations to Graphs (Part 1)
- 11 Connecting Equations to Graphs (Part 2)
Systems of Linear Equations in Two Variables
- 12 Writing and Graphing Systems of Linear Equations
- 13 Solving Systems by Substitution
- 14 Solving Systems by Elimination (Part 1)
- 15 Solving Systems by Elimination (Part 2)
- 16 Solving Systems by Elimination (Part 3)
- 17 Systems of Linear Equations and Their Solutions
Linear Inequalities in One Variable
- 18 Representing Situations with Inequalities
- 19 Solutions to Inequalities in One Variable
- 20 Writing and Solving Inequalities in One Variable
Linear Inequalities in Two Variables
- 21 Graphing Linear Inequalities in Two Variables (Part 1)
- 22 Graphing Linear Inequalities in Two Variables (Part 2)
- 23 Solving Problems with Inequalities in Two Variables
Systems of Linear Inequalities in Two Variables
- 24 Solutions to Systems of Linear Inequalities in Two Variables
- 25 Solving Problems with Systems of Linear Inequalities in Two Variables
- 26 Modeling with Systems of Inequalities in Two Variables
Be Prepared
18 x + 30 18 x + 30
3 − 2 n 3 − 2 n
2 x − 6 2 x − 6
0.045 0.045
w − 3 w − 3
0.35 x + 0.4 0.35 x + 0.4
2 c + 3 2 c + 3
0.042 0.042
15 15 is greater than x x .
15 < x 15 < x
2 5 x + 4 2 5 x + 4
− x + 4 − x + 4
a. >; b. >; c. >; d. >
m = 2 m = 2
a = 0 a = 0
u = 2 u = 2
x = 4 x = 4
p = −2 p = −2
q = −8 q = −8
y = − 17 5 y = − 17 5
z = 0 z = 0
identity; all real numbers
conditional equation; q = − 9 11 q = − 9 11
conditional equation; k = 201 14 k = 201 14
contradiction; no solution
x = 1 2 x = 1 2
x = −2 x = −2
x = 12 x = 12
u = −12 u = −12
n = 2 n = 2
m = −1 m = −1
r = 1 r = 1
s = −8 s = −8
n = 9 n = 9
d = 16 d = 16
He bought two notebooks.
He did seven crosswords puzzles.
−15 , −8 −15 , −8
−29 , 11 −29 , 11
−33 , −32 , −31 −33 , −32 , −31
−13 , −12 , −11 −13 , −12 , −11
−10 , −8 , −6 −10 , −8 , −6
The average cost was $5,000.
The median price was $19,300.
ⓐ 36 ⓑ $26 ⓒ 125 % 125 %
ⓐ 33 ⓑ $36 ⓐ 175 % 175 %
8.8 % 8.8 %
ⓐ $600 ⓑ $1,800
ⓐ $2,975 ⓑ $11,475
He will earn $2,500.
She earned $7,020.
The rate of simple interest was 6%.
The rate of simple interest was 5.5%.
He paid $17,590.
She deposited $9,600.
b = 2 A h b = 2 A h
h = 2 A b h = 2 A b
C = 5 9 ( F − 32 ) C = 5 9 ( F − 32 )
b = 2 A − B h h b = 2 A − B h h
t = A − P P r t = A − P P r
r = A − P P t r = A − P P t
y = 9 − 4 x 7 y = 9 − 4 x 7
y = 1 − 5 x 8 y = 1 − 5 x 8
The window’s height is 12 meters.
The length of the base is 6 feet.
The measures of the angles are 20°, 70°, and 90°.
The measures of the angles are 30°, 60°, and 90°.
The length of the leg is 8.
The length of the leg is 12.
The length is 39 inches and the width is 16 inches.
The length is 17 yards and the width is 26 yards.
The lengths of the sides of the triangle are 5, 11 and 12 inches.
The lengths of the sides of the triangle are 4, 7 and 9 feet.
The length of the swimming pool is 70 feet and the width is 30 feet.
The length of the garden is 90 yards and the width is 60 yards.
The ladder reaches 12 feet.
He should attach the lights 8 feet from the base of the mast.
Jess has 41 nickels and 18 quarters.
Elane has 22 nickels and 59 dimes.
Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.
Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.
84 adult tickets, 31 student tickets
615 children’s tickets and 195 adult tickets
Orlando mixed five pounds of cereal squares and 25 pounds of nuts.
Becca mixed 21 gallons of fruit punch and seven gallons of soda.
The speed of the local train is 48 mph and the speed of the express train is 60 mph.
Jeromy drove at a speed of 80 mph and his mother drove 60 mph.
Christopher’s speed was 50 mph and his parents’ speed was 40 mph.
Ashley’s parents drove 55 mph and Ashley drove 62 mph.
Pierre and Monique will be 429 miles apart in 3 hours.
Thanh and Nhat will be 330 miles apart in 2.2 hours.
Suzy’s speed uphill is 1.8 1.8 mph and downhill is three mph.
The boat’s speed upstream is eight mph and downstream is12 mph.
Hamilton drove 40 mph in the city and 70 mph in the desert.
Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.
Angie can buy 7 packs of juice.
Daniel can have 11 people at the party.
Sergio and Lizeth can travel no more than 500 miles.
Rameen can use no more than 76 therms.
Caleb must work at least 96 hours.
Elliot must work at least 85 jobs.
Brenda must babysit at least 27 hours.
Josue must shovel at least 20 driveways.
The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.
The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.
ⓐ ± 2 ± 2 ⓑ no solution ⓒ 0
ⓐ ± 11 ± 11 ⓑ no solution ⓒ 0
x = 4 , x = − 2 3 x = 4 , x = − 2 3
x = −1 , x = 5 2 x = −1 , x = 5 2
x = 8 , x = 0 x = 8 , x = 0
x = 8 , x = 2 x = 8 , x = 2
No solution
x = − 2 5 , x = − 2 5 , x = 5 2 x = 5 2
x = 3 , x = 3 , x = 1 9 x = 1 9
The diameter of the rod can be between 79.991 and 80.009 mm.
The diameter of the rod can be between 74.95 and 75.05 mm.
Section 2.1 Exercises
y = 5 y = 5
w = −18 w = −18
q = 3 q = 3
x = 14 x = 14
c = 4 c = 4
c = 5 2 c = 5 2
y = −5 y = −5
s = 10 s = 10
p = −4 p = −4
c = −4 c = −4
h = 3 4 h = 3 4
m = 6 m = 6
conditional equation; j = 2 5 j = 2 5
conditional equation; m = 16 5 m = 16 5
x = −1 x = −1
y = −1 y = −1
a = 3 4 a = 3 4
w = 9 4 w = 9 4
b = 12 b = 12
p = −41 p = −41
x = − 5 2 x = − 5 2
n = −3 n = −3
u = 3 u = 3
x = 18 x = 18
x = 20 x = 20
d = 8 d = 8
L = 19.75 L = 19.75 feet
Answers will vary.
Section 2.2 Exercises
58 hardback books
−11 , −12 , −13 −11 , −12 , −13
−69 , −71 , −73 −69 , −71 , −73
ⓐ 54 ⓑ 108 ⓐ 30%
ⓐ 162.5 162.5 ⓑ $35 ⓐ 150%
$ 11.88 $ 11.88
−2.5 % −2.5 %
−11 % −11 %
ⓐ $ 26.97 $ 26.97 ⓑ $ 17.98 $ 17.98
ⓐ $576 ⓑ 30%
ⓐ $ 7.20 $ 7.20 ⓑ $ 23.20 $ 23.20
ⓐ $ 0.20 $ 0.20 ⓑ $ 0.80 $ 0.80
3.75 % 3.75 %
21.2 % 21.2 %
Section 2.3 Exercises
d = C π d = C π
L = V W H L = V W H
d 1 = 2 A d 2 d 1 = 2 A d 2
b 1 = 2 A h − b 2 b 1 = 2 A h − b 2
a = 2 h − 108 t t 2 a = 2 h − 108 t t 2
a = 180 − b − c a = 180 − b − c
p = 2 A − 2 B l p = 2 A − 2 B l
L = P − 2 W 2 L = P − 2 W 2
y = 15 − 8 x y = 15 − 8 x
y = −6 + 4 x y = −6 + 4 x
y = 4 + x y = 4 + x
y = 7 − 4 x 3 y = 7 − 4 x 3
y = 12 − 2 x 3 y = 12 − 2 x 3
y = 18 − 3 x −2 y = 18 − 3 x −2
45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °
30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °
18 meters, 11 meters
13.5 13.5 m, 12.8 12.8 m
25 ft, 50 ft
12 ft, 13 ft, 14 ft
3 ft, 6 ft, 8 ft
120 yd, 160 yd
40 ft, 85 ft
104 ° F 104 ° F
ⓐ Answers will vary. ⓑ The areas are the same. The 2 × 8 2 × 8 rectangle has a larger perimeter than the 4 × 4 4 × 4 square. ⓒ Answers will vary.
Section 2.4 Exercises
nine nickels, 16 dimes
ten $10 bills, five $5 bills
63 dimes, 20 quarters
16 nickels, 12 dimes, seven quarters
330 day passes, 367 tournament passes
40 postcards, 100 stamps
15 $10 shares, five $12 shares
34 general, 61 youth
114 general, 246 student
Four pounds of macadamia nuts, eight pounds almonds
3.6 3.6 lbs Bermuda seed, 5.4 5.4 lbs Fescue seed
$33,000 in Fund A, $22,000 in Fund B
5.9 % 5.9 %
Kathy 5 mph, Cheryl 3 mph
commercial 550 mph, private plane 340 mph
Violet 65 mph, Charlie 55 mph
Ethan 22 mph, Leo 16 mph
DaMarcus 16 mph, Fabian 22 mph
uphill 1.6 1.6 mph, downhill 4.8 4.8 mph
light traffic 54 mph, heavy traffic 30 mph
freeway 67 mph, mountain road 22.3 mph
running eight mph, walking three mph
ⓐ 15 minutes ⓑ 20 minutes ⓒ one hour (d) 1:25
Section 2.5 Exercises
A maximum of 14 people can safely ride in the elevator.
five drinks
260 messages
62 necklaces
seven lawns
Section 2.6 Exercises
5 ≤ n ≤ 24 5 ≤ n ≤ 24
6 ≤ w ≤ 12 6 ≤ w ≤ 12
ⓐ answers vary ⓑ answers vary
Section 2.7 Exercises
ⓐ x = 4 , x = −4 x = 4 , x = −4 ⓑ no solution ⓒ z = 0 z = 0
ⓐ x = 3 , x = −3 x = 3 , x = −3 ⓑ no solution ⓒ z = 0 z = 0
x = 1 , x = − 1 2 x = 1 , x = − 1 2
x = −1 , x = − 5 2 x = −1 , x = − 5 2
x = 7 , x = 1 x = 7 , x = 1
x = 1 , x = −5 x = 1 , x = −5
no solution
x = −1 , x = − 2 3 x = −1 , x = − 2 3
x = −3 , x = 3 x = −3 , x = 3
x = 2 , x = 1 4 x = 2 , x = 1 4
x = 3 , x = 2 x = 3 , x = 2
x = 3 , x = − 11 3 x = 3 , x = − 11 3
x = 3 2 , x = − 1 2 x = 3 2 , x = − 1 2
The minimum to maximum expected production is 207,500 to 2,225,000 bottles
The acceptable weight is 22.5 to 25.5 ounces.
Review Exercises
s = −22 s = −22
m = −14 m = −14
q = 18 q = 18
k = 3 4 k = 3 4
k = 23 k = 23
x = 5 x = 5
There are 116 people.
−3 , −10 −3 , −10
$ 3.89 $ 3.89
ⓐ $105 ⓑ 52.5 % 52.5 %
d 2 = 2 A d 1 d 2 = 2 A d 1
y = 4 x 3 − 4 y = 4 x 3 − 4
22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °
24.5 24.5 cm, 12.5 12.5 cm
9 ft, 14 ft, 12 ft
nine pennies, six dimes, 12 quarters
57 students, 68 general admission
2.2 2.2 lbs of raisins, 7.8 7.8 lbs of nuts
9.7 % 9.7 %
Louellen 65 mph, Tracy 66 mph
upstream 3 mph, downstream 5 mph
heavy traffic 32 mph, light traffic 68 mph
$33 per day
at least $300,000
at least 112 jobs
x = 2 , x = 2 3 x = 2 , x = 2 3
x = 9 , x = −3 x = 9 , x = −3
The minimum to maximum expected usage is 210,000 to 220,000 bottles
Practice Test
x = −5 x = −5
a = 41 a = 41
x = 6 x = 6
x = −2 , x = − 1 3 x = −2 , x = − 1 3
−57 , −55 −57 , −55
12 dimes, seven quarters
2.5 2.5 hours
At most $55.56 per costume.
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Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
- Authors: Lynn Marecek, Andrea Honeycutt Mathis
- Publisher/website: OpenStax
- Book title: Intermediate Algebra 2e
- Publication date: May 6, 2020
- Location: Houston, Texas
- Book URL: https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
- Section URL: https://openstax.org/books/intermediate-algebra-2e/pages/chapter-2
© Jan 23, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.
IMAGES
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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. ... Section 1-2: Properties of Real Numbers. Section 1-3: Algebraic Expressions. Page 25: Mid-Chapter Quiz. Section 1-4: Solving Equations. Section 1-5: Solving Inequalities. Section 1-6 ...
Standards Alignment - Powered by EdGate. Table of Contents and Standards Alignment for Common Core Algebra II. Unit 1 - Algebraic Essentials Review. Unit 2 - Functions as the Cornerstones of Algebra II. Unit 3 - Linear Functions, Equations, and Their Algebra. Unit 4 - Exponential and Logarithmic Functions. Unit 5 - Sequences and Series.
Now, with expert-verified solutions from Algebra 2, Volume 1 1st Edition, you'll learn how to solve your toughest homework problems. Our resource for Algebra 2, Volume 1 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems ...
Alg2.1 Sequences and Functions. This unit provides an opportunity to revisit representations of functions (including graphs, tables, and expressions) at the beginning of the Algebra 2 course, and also introduces the concept of sequences. Through many concrete examples, students learn to identify geometric and arithmetic sequences.
A1 SpringBoard Algebra 2, Unit 1 Practice LeSSon 1-1 1. 65 5 15h 1 3 2.4 hours; the cost of renting a bike for 4 hours is $63. 3.$13; it costs $78 to rent the bike for 5 hours since 15(5) 1 3 5 78. This is $13 more than Aaron has, 78 2 65 5 13. 4. B 5. a.No; there are 5 quarter-hour segments from 7:00 p.m. to 8:15 p.m. Using the equation
Find step-by-step solutions and answers to Algebra 2, Volume 2 - 9780544385900, as well as thousands of textbooks so you can move forward with confidence. ... Now, with expert-verified solutions from Algebra 2, Volume 2 1st Edition, you'll learn how to solve your toughest homework problems. Our resource for Algebra 2, Volume 2 includes ...
The Algebra 2 course, often taught in the 11th grade, covers Polynomials; Complex Numbers; Rational Exponents; Exponential and Logarithmic Functions; Trigonometric Functions; Transformations of Functions; Rational Functions; and continuing the work with Equations and Modeling from previous grades. Khan Academy's Algebra 2 course is built to deliver a comprehensive, illuminating, engaging, and ...
Multiplying Complex Numbers. Dividing Complex Numbers. Dividing Complex Number (advanced) End of Unit, Review Sheet. Exponential Growth (no answer key on this one, sorry) Compound Interest Worksheet #1 (no logs) Compound Interest Worksheet (logarithms required) Exponent Worksheets. Simplify Rational Exponents.
Increased , -bqet-her MULTIPLICATION , Date: Class: SUBTRACTION Itss -Hun S(.Lbfrac+tÅ. decreased b9 DIVISON divided sc and Watch out for subtraction! Phrases like indicate that you need to reverse the order! Directions: Translate each expression. Words "five more than a numbed' "the quotient of a number and -2" "twice a number" "a number ...
7.4 Day 1 Homework: Worksheet Answer Key. 7.1 Homework: "Write the following expressions using rational exponents and then evaluate using a calculator." Pg 433 Problem Set 1-9. (On 4-6 you do Not have to evaluate, just convert.) 7.2 Homework: "Graph the following square root functions. Use your calculator to check your answers."
The standards taught in each Math Medic Algebra 2 lesson can be found here. The unit overviews and learning targets for the Math Medic Algebra 2 course can be found here. Units. Unit 1: Sequences and Linear Functions. Unit 2: Linear Systems. Unit 3: Function Families and Transformations. Unit 4: Working with Functions.
Algebra 2 -25 - Functions, Equations, and Graphs WARM UP Solve each equation for y. 1) 12y=3x 2) −10y=5x 3) 3 4 y=15x y= 1 4 x y=− 1 2 x y=20x KEY CONCEPTS AND VOCABULARY Direct Variation- a linear function defined by an equation of the form y=kx, where k ≠ 0. Constant of Variation - k, where k = y/x GRAPHS OF DIRECT VARIATIONS
Home / For Teachers / Common Core Algebra II / Unit 2 - Functions as the Cornerstones of Algebra II. ... LESSON/HOMEWORK. LESSON VIDEO. ANSWER KEY. EDITABLE LESSON. EDITABLE KEY. Lesson 7 Key Features of Functions. ... Unit 2 Mid-Unit Quiz (Through Lesson 3).Form A ASSESSMENT. ANSWER KEY. EDITABLE ASSESSMENT.
Step 1 Step 2 Step 3. 9. Draw Step 4 and Step 5. 10. Dan explained that the middle tower is always the same number as the step number. He also pointed out that the two arms on each side of the tower contain one less block than the step number. Create an equation that fits Dan's way of seeing the relationship. 11.
View ALGEBRA 2 UNIT 1 LESSON 2 - REAL NUMBER PROPERTIES .pdf from ALGEBRA 2 at Marcus H S. Alg2 Metting U1L2 ALGEBRA 2 UNIT 1 LESSON 2 Relations and Properties COMMUTATIVE Property (a, b and c ... homework. quadratic-factoring-algebra-2-worksheet.pdf. Dawson High School. AP CALCULUS AB 100. ... Answer Choice A Note Re inspection and retest as ...
Alg1.2 Linear Equations, Inequalities, and Systems. In this unit, students expand and deepen their prior understanding of expressions, equations, and inequalities. Students reason about equations, inequalities, and systems of equations and inequalities as ways to represent constraints, and they reason about the process of solving equations and ...
Answer Key Chapter 2 - Intermediate Algebra 2e | OpenStax. Our mission is to improve educational access and learning for everyone. OpenStax is part of Rice University, which is a 501 (c) (3) nonprofit. Give today and help us reach more students.
Our resource for Algebra 1: Homework Practice Workbook includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers ...
Standards Alignment - Powered by EdGate. Table of Contents for Algebra 2 with Trigonometry. Unit 1 - Introduction to Functions. Unit 2 - Linear Relations and Functions. Unit 3 - Quadratic Functions and Their Algebra. Unit 4 - Radicals and the Quadratic Formula. Unit 5 - Complex Numbers. Unit 6 - Polynomials and Rational Functions.
This unit reviews and reinforces students previous knowledge of linear relationships. Students explore the meaning of slope as rate of change. They develop equations for representing linear functions. Using these equations, students model linear phenomena, both with physics based and regression based equations.