Mrs. Samuel's Algebra Extra Resources

Welcome!! Use this resource as needed to help you study and be successful in Algebra 1

Remember this is just a resource!! Don't be overwhelmed! Look for the topic you need more help on.

Delta Math - Teacher Code 435293

Remind -

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PARCC Review

https://parcctrng.testnav.com/client/index.html#login?username=17MTA1PTOE01010100&password=PCPRACTICE - PARCC Unit 1 Online Practice Test - 2 sections (calculator and non -calculator sections) 14 questions. Self grading on multiple choice. Very useful to practice using the testing tools including graphing calculator

https://parcctrng.testnav.com/client/index.html#login?username=17MTA1PTOE01010200&password=PCPRACTICE - PARCC Unit 2 Online Practice Test - 15 questions

https://parcctrng.testnav.com/client/index.html#login?username=17MTA1PTOE01010300&password=PCPRACTICE PARCC Unit 3 Online Practice Test - 12 questions

https://parcc.pearson.com/resources/Practice-Tests/AKD/AlgI/PARCC_Math_-_Alg1_Spring_2016_Online_Practice_Test_Answer_Doc.pdf Answer key to all of the above units including BCRs

https://www.youtube.com/watch?v=-Z8rEiUyjjQ - video working through 3 practice PARCC Algebra Practice problems

https://www.youtube.com/watch?v=duQrtJV282E - additional video on working through practice PARCC problems

http://www.lumoslearning.com/llwp/resources/common-core-practice-tests-and-sample-questions/practice-test.html?type=Teacher&state=MD&cur=1448&btn=start - 8th Grade Math Practice (might be useful since you guys didn't take the 8th Grade PARCC test but will have to know the material on it) It is broken up to many different sections

Unit 1

Square Root

https://www.mathsisfun.com/square-root.html Notes, what is a square and square root with 10 practice problems

https://www.youtube.com/watch?v=nUyLnjgGumg - Have to solve a perfect square in seconds video - great time saver!

http://www.math.com/school/subject1/lessons/S1U1L9DP.html - solving non perfect squares (in most cases, estimating it it between two numbers closer to the one number is close enough. For example: Square Root of 23. I know that 4*4= 16 and 5*5=25. So I know that my answer is between 4 and 5. Since 23 is closer to 25, it is going to be closer to 5. I can plug it into a calc and see that it is 4.79


Writing Expressions

Equivalent Expressions

Equations

Adding and Subtracting - Basic

http://www.math-play.com/math-basketball-one-step-equations/math-basketball-one-step-equations.html - basketball game with addition and subtraction (only positive solutions that are either whole numbers or decimals)

http://www.math-play.com/soccer-math-one-step-equations-game/one-step-equations-game.html soccer game with addition and subtraction (only positive solutions that are either whole numbers or decimals)

http://www.aplusmath.com/Flashcards/algebra.html - adding and subtracting "flash cards"

http://www.math-play.com/One-Step-Equation-Game.html - top game, adding and subtracting basketball (negative numbers)

Multiplying and Dividing - Basic

http://www.math-play.com/One-Step-Equation-Game.html - bottom game, multiplying and dividing basketball (negative numbers)

http://www.xpmath.com/forums/arcade.php?do=play&gameid=105 - Pong Game, all four operations (negative numbers, 5 levels)

http://www.softschools.com/quizzes/algebra/solving_linear_equations_by_multiplication_or_division/quiz4940.html - quiz

Mixed Review - IXL J3

2 Step Equations - Basic

https://braingenie.ck12.org/subjects/81 - pick from

  1. Solving Two-Step Equations by Dividing and Adding/Subtracting

    1. Solving Two-Step Equations by Dividing and Adding/Subtracting Given Integers

    2. Solving Two-Step Equations by Dividing and Adding/Subtracting Given Decimals

    3. Solving Two-Step Equations by Dividing and Adding/Subtracting Given Fractions

  2. Solving Two-Step Equations by Multiplying and Adding/Subtracting

    1. Solving Two-Step Equations by Multiplying and Adding/Subtracting Given Integers

    2. Solving Two-Step Equations by Multiplying and Adding/Subtracting Given Decimals

    3. Solving Two-Step Equations by Multiplying and Adding/Subtracting Given Fractions

http://www.quia.com/ba/143047.html - battleship game with 2 step equations (negative numbers)

http://www.softschools.com/quizzes/math/solving_linear_equations_using_the_distributive_property/quiz2014.html - test with distributive property

http://www.aplusmath.com/Flashcards/algebra.html - create your own "flash cards" all operations

http://www.mathplayground.com/AlgebraEquations.html - use tiles to model

http://pbskids.org/cyberchase/math-games/poddle-weigh-in/ - using algebraic logic

http://www.quia.com/cb/77775.html - jeopardy. Solve basic equations, two-step equations, equations with variables on both sides, pot-luck mixture equations and literal equations.

IXL - J3

Writing 2 Step Equations from Word Problems - Basic

https://braingenie.ck12.org/skills/105348

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-linear-eq-word-probs/e/linear-equation-world-problems-2

Multi-Step Equations

IXL - J5 Solve advanced linear equations

IXL - J7 Solve equations: complete the solution (using properties to justify each step)

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-equations-with-parentheses/a/multi-step-equations-review - notes review and practice problems

https://www.quia.com/rr/168572.html - Who wants to be a millionaire?

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-equations-with-parentheses/e/multistep_equations_with_distribution - Equations with Parentheses Practice

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-equations-with-parentheses/e/multi-step-equations-rational - Equations with Decimals and Fractions Practice

https://www.mathgames.com/skill/8.40-solve-multi-step-equations - multi-step practice

http://www.softschools.com/quizzes/algebra/solving_equations_with_multiple_steps/quiz5075.html - Solving Equations with Multiple Steps Quiz

https://jeopardylabs.com/play/solving-multi-step-equations1 - Jeopardy - Solving by Combining Like Terms, Solving by Using Distributive Property, Expressions, Equation Grab Bag, and Word Problems

https://www.mangahigh.com/en-us/games/algebrameltdown - Algebra Meltdown Game - 4 levels of play

Variables on Both Sides

IXL - J6 Solve equations with variables on both sides

IXL - J8 Find the number of solutions

IXL - J9 Create equations with no solution or infinitely many solutions

IXL - J10 Solve linear equations: word problems

IXL - J11 Solve linear equations: mixed review

https://www.proprofs.com/quiz-school/story.php?title=NjQyNjA5M5XK - 5 question mixed practice quiz

https://www.quia.com/rr/380806.html- Who Wants to be a Millionaire?

https://jeopardylabs.com/play/solving-equations-with-variables-on-both-sides3 - Jeopardy

http://www.shodor.org/interactivate/activities/AlgebraFour/ - multiple ways to play, 4 levels of difficulty; variable on both sides, distributive property, two-step problems

https://www.mangahigh.com/en-us/math_games/algebra/solving_linear_equations/solve_linear_equations_with_an_unknown_on_both_sides - game

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-variables-on-both-sides/e/linear_equations_3 - practice problems

Solving Equations and Justifying

http://blog.wsd.net/lrwright/files/2014/06/1-5.pdf - worksheet with answer key included

https://mathbitsnotebook.com/Algebra1/LinearEquations/LEJustifyPractice.html - 2 practice problems

Solving Literal Equations

https://za.ixl.com/math/grade-10/solve-literal-equations - This is IXL of other counties, USA doesn't have the skill on IXL. I believe if you sign in, it will automatically take you to the US site. So, don't sign in.

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/linear-equations-with-unknown-coefficients/e/solving_for_a_variable - practice problems with link to video for help

https://www.proprofs.com/quiz-school/story.php?title=final-review-quiz-1-literal-equations - 5 multiple choice questions

http://www.algebralab.org/practice/practice.aspx?file=Algebra1_3-6.xml - 10 practice problems

https://www.quia.com/rr/518684.html - Who wants to be a millionaire?

IXL: https://www.ixl.com/math/algebra-1/rearrange-multi-variable-equations I9



Inequalities

Inequality Key Words

6th/7th Grade Review

IXL:

  • K1 - Graph inequalities

  • K2 - Write inequalities from graphs

http://www.algebra-class.com/solving-inequalities.html - notes on direction of arrow

http://www.softschools.com/math/algebra_1/graphing_inequalities/graphing_inequalities_on_number_line/ - graphing on a number line practice

Solving Inequalities - Review

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/multi-step-inequalities/v/multi-step-inequalities-3 - video, variables on both sides

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/multi-step-inequalities/v/multi-step-inequalities-2 - video, variables on both sides and parentheses

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/multi-step-inequalities/e/linear_inequalities - 4 practice problems

http://www.softschools.com/quizzes/algebra/solving_equations_and_inequalities/quiz9301.html - practice solving equations and inequalities

IXL:

  • K8 Solve two-step inequalities

  • K9 Graph solutions to two-step inequalities

  • K 10 Solve advanced inequalities

  • K11 Graph solutions to advanced inequalities **have to solve and graph


Inequality Word Problems

Compound Inequalities

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/multi-step-inequalities/v/multi-step-inequalities-2 - video on OR

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/compound-inequalities/v/compund-inequalities-2 - video on AND

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/compound-inequalities/e/compound_inequalities - practice problems

https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/compound-inequalities/v/compound-inequalities-4 - video, compound, no solution

https://www.ixl.com/math/algebra-1/solve-compound-inequalities

https://www.sporcle.com/games/dianaburnham08/solving-compound-inequalities 11 - question quiz

http://www.algebralab.org/practice/practice.aspx?file=Algebra1_6-3.xml - 9 question quiz

http://www.coolmath.com/crunchers/algebra-problems-solving-inequalities-3 - practice problems, must do on paper

IXL:

  • K12 Graph compound inequalities

  • K13 Write compound inequalities from graph

  • K14 Solve compound inequalities

  • K15 Graph solutions to compound inequalities **solve and graph

https://www.quia.com/rr/521133.html?AP_rand=1774613553 - Who Wants to be a Millionaire? game

http://www.algebra-class.com/compound-inequalities.html - notes

http://www.softschools.com/math/algebra/inequalities/solving_inequality_disjunctions/ - create your own worksheet to work on solving OR compound inequalities (be sure to click "show answers" button before generating so you have a way to check your answers - remember you don't have to print it out, you just need a piece of paper to solve them on)

http://www.softschools.com/math/algebra/inequalities/solving_inequality_conjunctions/ - create your own worksheet to work on solving AND compound inequalities (be sure to click "show answers" button before generating so you have a way to check your answers - remember you don't have to print it out, you just need a piece of paper to solve them on)

Unit 2

Slope

https://campus.mangahigh.com/en-us/px/238/0/0 - 10 finding slope problems from graphs

https://www.mathgames.com/skill/8.32-find-slope-from-two-points - find slope from 2 ordered pairs

https://www.mathgames.com/skill/8.41-find-the-slope-of-a-graph - find slope from graphs

https://www.quia.com/rr/79713.html - Who Wants to be a Millionaire? finding slope

https://www.quia.com/rr/149651.html - Rags to Riches Game - finding slope

http://www.crctlessons.com/slope-game.html - Basketball Game - finding slope

http://www.xpmath.com/forums/arcade.php?do=play&gameid=86 - Halo Slope Game

IXL:

  • S2 Find the slope of a graph

  • S3 Find the slope from 2 points

  • S4 Find the missing coordinate using slope

https://www.mangahigh.com/en-us/math_games/algebra/straight_line_graphs/find_the_x_and_y_intercepts_of_lines - 10 questions finding x and y intercepts

https://www.quia.com/rr/379720.html - Rags to Riches - finding slope and y-intercept

http://www.superteachertools.us/jeopardyx/jeopardy-review-game.php?gamefile=640030#.WjQeElWnHIV - Jeopardy Game

http://www.crctlessons.com/slope-intercept-game.html - slope intercept basketball game

https://www.quia.com/cz/43443.html?AP_rand=1840812885 - graph by using slope intercept form

https://www.quia.com/cb/79602.html?AP_rand=688862906http://www.quia.com/cb/79602.html?AP_rand=688862906 - point slope form jeopardy

IXL:

  • S5 Slope intercept form: find the slope and y-intercept

  • S6 Slope intercept form: graph an equation

  • S7 Slope intercept form: write an equation from a graph

  • S8 Slope intercept form: write an equation

  • S9 Slope intercept form: write an equation from a table

  • S10 Slope intercept form: write an equation from a word problem

  • S11 Linear equation: solve for y

  • S12 Write linear functions to solve word problems

  • S15 Write equation in standard form

  • S16 Standard form: find x and y intercepts

  • S17 Standard form: graph an equation

  • S20 Point Slope form: graph an equation

  • S21 Point Slope Form: write an equation

  • S22 Point Slope Form: write an equation from a graph

Parallel and Perpendicular Lines

These lines are Parallel. If you look at the slope, they are the same in each equation. Parallel lines MUST have the same slope

These lines are perpendicular. Look at the slopes. They are opposite reciprocals of each other.

-3/2 is the opposite reciprocal of 2/3


http://www.math-play.com/slope-intercept-basketball/slope-intercept-basketball_html5.html - Basketball game - slope intercept with perpendicular lines

https://www.quia.com/rr/35674.html - Who Wants to be a Millionaire? with parallel and perpendicular lines

https://campus.mangahigh.com/en-us/px/254/0/0 - test your skills with this game - parallel

https://jeopardylabs.com/play/parallel-perpendicular-lines-and-slope - jeopardy with parallel and perpendicular

IXL: S23 slope of parallel and pependicular lines

S24 write an equation for a parallel or perpendicular line

Unit 3

Functions

Vocabulary -

Relation - pairs of input and output values

Function - is a relation in which each input is paired with exactly one output

Domain - inputs

Range - outputs

Function Notation - f(x) - read as "f of x"

IXL:

  • Q1 - Relations: go between tables, graphs, mapping, and lists

  • Q2 - Domain and Range of Relations

  • Q3 - Identify independent and dependent variables

  • Q4 - Identify Functions

  • Q5 - Identify Functions using vertical line test

  • Q7 - Evaluate a function


Continuous - without interruption

Discrete - individually separate and distinct


Transforming Linear Functions

Stretch and Shrink.pdf
Translations.pdf

R-Value and Line of Best Fit

Correlation between 2 sets of data, means that they are connected in some way. EX: as the temperature increases, the number of ice creams sold increases. When our data is shown in a scatter plot as below, we can describe it using Correlation Coefficient or the R-Value.

R-Value (aka: Correlation Coefficient) is the number from -1 to 1 that tells how close the data is to forming a straight line, how much it correlates.


R-Values from 0-0.5 are weak/low 0.51-.99 are strong/high 1 is perfect

Steps on the graphing calculator:

  • Press Stat

  • #1: Edit

  • Enter your x values in L1

  • Enter your y values in L2

  • Press Stat

  • Move the cursor right to Calc

  • #4:LinReg (ax+b) --a stands for slope

  • Scroll down to Calculate, hit enter

  • Write down the equation from the information given

  • Write down the r

  • Ignore the r^2 this year :)

If your calculator doesn't have an r-value:

  • Press 2nd

  • Press 0 (zero)

  • Scroll down to DiagnosticOn

  • Press Enter

  • Press Enter

  • When it says DiagnosticOn Done, go back at do Stat, Calc, #4 again

If you delete a list (L1 or L2):

  • Press Stat

  • #5: Set Up Editor

  • Enter

and the lists will return :)

IXL: KK.11 Calculate correlation coefficients (use the calculator to solve, if you get it wrong, it will tell you the formula to use but we are using the calculator to solve so you don't need the formula)

KK.10 Match correlation coefficients to scatter plots

KK.13 Find the equation of a regression line (use the calculator to solve)


Types of Equations


Linear

Linear functions are those whose graph is a straight line. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. a is the constant term or the y intercept.

Identifying Linear from Graphs - there is always a constant rate of change. Here are two examples:


To Determine the Zeros (aka: x-intercept, solutions, roots) graph the equation and see where it crosses the x axis or set the equation equal to zero and solve.

Polynomials

https://www.symbaloo.com/mix/mrkingsmathlinks?searched=true – polynomial “music video”

http://www.softschools.com/math/algebra/polynomials/classifying_polynomials/ - classifying leading coefficient, degrees, and number of terms practice (3 question practice)

http://www.softschools.com/quizzes/algebra/identifying_polynomial_or_not_polynomial/quiz4373.html - Identifying polynomial or not polynomial 10 question quiz

http://www.softschools.com/quizzes/algebra/monomial_or_polynomial/quiz4322.html - naming Monomials vs Polynomials 10 question quiz

IXL - Algebra Z1 Polynomial vocabulary


Adding and Subtracting Polynomials

This topic is a review from 6th grade and 7th grade! We just called it combining like terms. Remember that the sign in front of a number belongs with that number!

Multiplying Polynomials

https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/multiplying-polynomials-by-monomials/v/multiplying-monomials-by-polynomials - multiplying monomial by polynomial video

https://www.mangahigh.com/en-us/math_games/algebra/simplifying_algebra/product_of_any_two_binomials - game!!

https://www.quia.com/rr/69387.html?AP_rand=1206402933 – who wants to be a millionaire

https://www.quia.com/rr/79717.html - Who wants to be a millionaire

http://www.softschools.com/math/algebra/polynomials/multiplying_binomials_using_foil_method/ Multiplying Binomials using FOIL method quick video

http://www.softschools.com/quizzes/math/multiplying_polynomials/quiz2003.html - 10 questions

https://jeopardylabs.com/play/multiplying-polynomials6 - Jeopardy

IXL – Algebra Z6 Multiplying a polynomial by a monomial

Z7 Multiply two polynomials using algebra tiles

Z8 Multiply two binomials

Z9 Multiply two binomials: special cases

Z10 Multiply polynomials

Exponent Rules

Exponent Rules in no particular order:

https://www.khanacademy.org/math/in-eighth-grade-math/exponents-powers-1/laws-exponents/v/exponent-rules-part-1 - Exponent Rules Intro Video

https://www.khanacademy.org/math/in-eighth-grade-math/exponents-powers-1/laws-exponents/v/exponent-rules-part-2 - Exponent Rules Video in Problems

https://www.khanacademy.org/math/in-eighth-grade-math/exponents-powers-1/laws-exponents/v/exponent-properties-involving-quotients - Exponent Rules Video with Dividing

https://www.khanacademy.org/math/in-eighth-grade-math/exponents-powers-1/laws-exponents/v/exponent-properties-4 - Video

http://www.math-play.com/Exponents-Jeopardy/exponents-jeopardy-math-game_html5.html - quick Jeopardy game with evaluating exponents, solving with exponents and exponents with fractional bases

https://www.quia.com/rr/180013.html - Product Rule Game

https://www.quia.com/ba/53930.html - Exponent Rules Battleship Game

http://www.learnalberta.ca/content/mejhm/index.html?l=0&ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.EXPO&lesson=html/object_interactives/exponent_laws/use_it.html - Exploring Laws of Exponents Digging Game

http://www.mathopolis.com/questions/q.php?id=751&site=1&ref=/algebra/negative-exponents.html&qs=751_2024_2025_2026_752_2027_3147_3148_3149_3150 – 10 question practice on negative exponents

https://www.symbaloo.com/mix/mrkingsmathlinks?searched=true – exponent rules “music video”

IXL –

https://www.ixl.com/math/algebra-1/exponents-with-integer-bases - Exponents with integer bases (basic review)

https://www.ixl.com/math/algebra-1/exponents-with-decimal-and-fractional-bases - Exponents with decimal and fractional bases

https://www.ixl.com/math/algebra-1/negative-exponents - Negative Exponents

https://www.ixl.com/math/algebra-1/multiplication-with-exponents - Multiplication with exponents

https://www.ixl.com/math/algebra-1/division-with-exponents - Division with exponents

https://www.ixl.com/math/algebra-1/multiplication-and-division-with-exponents - multiplication and division with exponents

https://www.ixl.com/math/algebra-1/power-rule - power rule

https://www.ixl.com/math/algebra-1/evaluate-expressions-using-properties-of-exponents - mixed review

https://www.ixl.com/math/algebra-1/identify-equivalent-expressions-involving-exponents - identify equivalent expressions involving exponents


Quadratic Equations

To Determine the Zeros (aka: x-intercept, solutions, roots) graph the equation and see where it crosses the x axis, since it is Quadratic - there will be 2 answers.

Exponential Graphs

(for Algebra 1) is a curved graph that doesn't touch zero. It's going to come close but it won't ever touch.

Identifying Exponential Function from table, there is always a common ratio that is either being multiplied or divided.

b can also be called the growth or decay factor. If b is greater than one - then its growth. If b is between 0 and 1 - then its decay.

Cubic -

the x is to the third power. The third difference in a table is the same.

To Determine the Zeros (aka: x-intercept, solutions, roots) graph the equation and see where it crosses the x axis, since it is Cubic - there will be 3 answers.

Absolute Value

Identifying Types of Equations:

https://www.youtube.com/watch?v=vLkOL-yqj60&disable_polymer=true Using Tables to Identify Linear, Exponential, or Quadratic Functions Video

IXL:

CC Identify linear and exponential function from graphs

CC1 Identify linear, quadratic, and exponential functions from graphs

CC Identify linear and exponential functions from tables

CC2 Identify linear, quadratic and exponential function from tables

https://d3jc3ahdjad7x7.cloudfront.net/DJaSNx3YQHzb3nyn6P9fjjOA6bfWFQ1nmUmcA7N7sVdABVZs.pdf - notes with answered questions


Writing Exponential Equations from Word Problems

Unit 3

Exponential Growth and Decay


https://www.youtube.com/watch?v=_1R51sCYCoQ - video with examples of both growth and decay

IXL - X5 - Exponential growth and decay: word problems *I like the practice BUT it doesn't have you write the equation which is necessary - so make sure you write and use an equation to solve


Is it Exponential Growth or Decay using Equations?

Exponential Decay - the number raised to the x has to be less than 1

Exponential Growth - the number raised to the x has to be more than 1

Notice in the example below - it doesn't matter what a is as long as b is greater than 1

Line Regression or Line of Best Fit - is a straight line that best represents the data on a scatter plot. This line may pass through some of the points, none of the points, or all of the points. The equation for the line is written in slop-intercept form.


Unit 4

Systems of Equations

A "system" of equations is a set or collection of equations that you deal with all together at once.

Does this ordered pair work for the system? IXL U1

3 main ways to solve: graphing, substitution, and elimination

Using Graphing - graph both equations on the same coordinate system. The solution to the system will be in the point where the two lines intersect.

If the equation(s) aren't in point-slope form, you will first have to turn them into point-slope form before graphing as shown in the picture to the right.

Using Substitution: solving for one variable (look for one that has the coefficient of 1 or -1). Then plug into the other equation. Once you solve the the variable, plug your answer into the equation to find the other variable.

Using Elimination - Use elimination when you are solving a system of equations and you can quickly eliminate one variable by adding or subtracting your equations together.

Above - both equations have the same coefficient and since they are opposite we add.

Right - the equations don't have the same coefficient so you need to come up with common equations first

Special Cases - No Solution and Infinite Solution

https://www.shmoop.com/systems-equations-inequalities/elimination-method-exercises.html - 6 practice problems including 1 with fractions, whole number answers, no solution, and infinite solution.

https://www.quia.com/cz/43456.html?AP_rand=1270533692 - game - Identify the solution of the given graphs. For no solution enter "no solution" and for infinite solutions enter "infinite solutions"

REVIEW

Piecewise Functions

Are functions that have restrictions or domains

Evaluate Piecewise Functions Graphically

f(-5) means x=5. Go to x=-5 and go straight down or up till you reach a line. In this case it would be y=-7

f(-1) means x=-1 and since there are 2 dots where x=-1, one of the circles is open which means that it can't be equal. The other is a closed circle, which means it can equal and that y value is 2

f(0)=-5. Look at x=0 , the line that crosses across x=0 (the y-axis) crosses at y=-5

Evaluate Piecewise Functions

You can graph them to see where the f(x) is or you can look at each of the domains separately and then look at the equation that it relates to and solve equation if needed.

f(6) is not less than 3 (the first one), it isn't equal to 3 (second one), it greater than 3 (third one). So, use the equation that relates to the third one -(x-4)^2. Evaluate f(6)= -(x-4)^2 = -(6-4)^2 = -(2)^2 = -4. So f(6)=-4

f(-2) is not less than -2 (the first one), it is less than or equal to -2 (the second one). Use the second equation and evaluate for f(-2)=x+2 = f(-2)=-2+2 = f(-2)=0. So f(-2)=0

Graphing Piecewise Functions

Graph the first equation, start at y=4 and go down one to the right 1 since the slope is -1.

The constraints for the first equation is -5<or =x < or=1, which means the starting point is -5 and the ending point is 1. Anything to the left of -5, delete. Anything to the right of 1, delete. Since they are both equal to, they need to be closed circles on both sides of the line.

Graph the second equation f(x)=1, which is horizontal at y=1. The starting point is x=1 and the end is x=4.

Then put the two graphs on the same coordinate plane.

As you can see on the left side, graph, f(x)=-5 which is a horizontal line at y=-5. Because it says -6<x<-1, it is going to have an open starting point at -6 and a open ending point at -1.

For the second equation, start at -6, rise 2 run to the right 1, repeat several times. Looking at the domain, it says -1<x<6, which means that it is going to be an open circle at x= -1 and an open circle at x=6.

We can also do piecewise functions with quadratics. Make a table so you can graph the quadratic, using the starting and ending points as points on your table.

Example of Floor and Ceiling Rounding

Graphing Inequalities with 2 Variables

Step 1: Write as equation

Step 2: Graph the boundary line (write it in slope intercept form or make a table)

Step 3: Pick a point on the graph to test. Plug it into the inequality, if it is true - color the side of the point. If it is false - color the opposite side.

Everything colored is a solution.

Notice the dotted line - it is for < or >. The solid line is for when they include being equal to.

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphing-linear-inequalities-in-two-variables-example-2 - video how to graph a 2 variable linear inequality

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphing-linear-inequalities-in-two-variables-3 - video how to write a 2 variable linear inequality from a graph

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/e/graphing_inequalities_2 - practice problems - graphing

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/e/graphs_of_inequalities - practice problems - writing the inequality from graph

https://cdn.kutasoftware.com/Worksheets/Alg1/Graphing%20Linear%20Inequalities.pdf – printable practice problems with answer key

https://www.ixl.com/math/algebra-1/graph-a-two-variable-linear-inequality - IXL Graphing - T3

https://www.ixl.com/math/algebra-1/does-x-y-satisfy-the-inequality - IXL does this ordered pair satisfy inequality - T1

https://www.ixl.com/math/algebra-1/linear-inequalities-solve-for-y - IXL solving an inequality for y - T2

https://www.ixl.com/math/algebra-1/linear-inequalities-word-problems - IXL - word problems - T4

https://mathbitsnotebook.com/Algebra1/Inequalities/IQGraphingPractice.html - mix review practice problems

https://www.quia.com/rr/79715.html?AP_rand=1238564056 – Who Wants to be a Millionaire? Game

https://www.mangahigh.com/en-us/math_games/algebra/inequalities/inequalities_on_graphs - Game

https://www.mangahigh.com/en-us/math_games/algebra/inequalities/inequalities - game

Systems of Inequalities

1) Graph the first inequality (dotted or solid line?)

2) Test a point and color the correct side to shade above or below

3) Graph the second inequality

4) Test a point and color the correct side

5) The solution region is the one colored in with both colors or both shading

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/v/graphical-system-of-inequalities – video – graphing systems of inequalities

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/a/graphing-inequalities-x-y-plane-review - notes

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/graphing-inequalities/e/graphing_systems_of_inequalities_2 - practice problems - graphing systems of inequalities

https://www.ixl.com/math/algebra-1/is-x-y-a-solution-to-the-system-of-inequalities - IXL - is the a solution to a system of inequality – T5

https://www.ixl.com/math/algebra-1/solve-systems-of-linear-inequalities-by-graphing - IXL - practice problems – T6

http://www.algebra-class.com/graphing-systems-of-inequalities-practice.html - 3 practice problems

Word Problems

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/v/constructing-two-variable-linear-inequality-word-problem - video - word problem

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/v/interpreting-visual-linear-inequality-word-problem - video - word problem

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/e/modeling-constraints - practice word problems

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/e/modeling-systems-of-linear-inequalities - practice word problems

https://www.khanacademy.org/math/algebra/two-variable-linear-inequalities/modeling-with-linear-inequalities/e/compare-expressions-with-unknown-variables-word-problems - practice word problems

http://simplifyingradicals2.blogspot.com/2014/03/systems-of-linear-equations-game-on.html - Desmos Game

Conversion

This is the resource that will be available for testing:

Examples

Unit 5

Pulling out the GCF

Factoring when the leading coefficient is 1

Factoring when the leading coefficient isn’t 1

http://www.algebra-class.com/factoring-a-trinomial.html - notes

https://www.ck12.org/book/CK-12-Algebra-II-with-Trigonometry-Concepts/section/5.2/ - video example of the other method (that was not taught in class) with 20 problems at the end (you can use these problems and solve them using my guess and check method or the other method taught in the video)

Factoring by Grouping

from http://muchobene.com/15-grouping-factoring/

Graphing Quadratics /Vertex Form

https://www.khanacademy.org/math/algebra/quadratics/vertex-form-alg1/e/graphing_parabolas_1 - practice problems

https://www.khanacademy.org/math/algebra/quadratics/vertex-form-alg1/e/graphing-quadratics-in-vertex-form-warmup practice problems

https://quizizz.com/admin/quiz/5802351dab98727c4ff85d48 - quiz on quadratics

https://cdn.kutasoftware.com/Worksheets/Alg2/Vertex%20Form%20of%20Parabolas.pdf - vertex form questions - printable

Graphing - IXL BB1 - Characteristics of quadratics

IXL BB2 - Completing table for quadratic

BB3 Transformations of Quadratics

BB4 Graph quadratic in vertex form

Reading Graph

Looking at graph and stating

  • vertex (bottom or top most point)

  • axis of symmetry (the x value of the vertex)

  • domain (inputs, x values, left to right)

  • range (inputs, y values, top to bottom)

  • minimum - if concave up, vertex (no max)

  • maximum - if concave down, vertex (no min)

  • zeros/roots/solutions - are all x intercepts

  • y- intercept

  • concave up - U (smiley)

  • concave down - n (frown)


When using the quadratic formula, you should be able to solve it by hand, although if you get to answers that are too hard to find the square root, you may use a calculator

Must knows for Quadratic Unit

  • Reading graph - stating the vertex, axis of symmetry, domain, range, minimum, maximum, zeros/roots/solutions/x-intercepts, y-intercept, concave up or down

  • Solving quadratics

  • Word Problems - check out this website - it is amazing - https://www.algebra-class.com/problems-involving-quadratic-equations.html

  • Comparing quadratic equations (for heights or distances)

  • Movement compared to the parent graph - right/left, up/down, concave up/down, wider (vertical shrink) or skinnier (vertical stretch)

  • Graphing quadratics in standard form by using a table or from vertex form or from factored answers (ie: (x+5)(x-13)

  • How many possible zeros and a sketch of what that would look like

  • Foiling

  • Order of operations

  • Factoring quadratics (trinomial)

  • From standard form - find the zeros, max or min, vertex, y-intercepts

  • Finding axis of symmetry from graph or standard form equation