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.
Math Contract - Mrs. Samuel's Math Class Information
Delta Math - Teacher Code 435293
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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
Rational and Irrational Numbers
Identifying
https://www.mathsisfun.com/irrational-numbers.html - Notes, what is an irrational number
https://mathbitsnotebook.com/Algebra1/RatIrratNumbers/RNRatIrrat.html - Notes
https://www.mathwarehouse.com/arithmetic/numbers/rational-and-irrational-numbers-with-examples.php - 8 practice problems
https://www.brainpop.com/math/numbersandoperations/rationalandirrationalnumbers/quiz/ - practice problems
https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:irrational-numbers/x2f8bb11595b61c86:irrational-numbers-intro/e/recognizing-rational-and-irrational-numbers - practice problems
https://www.mathgames.com/skill/8.9-identify-rational-and-irrational-numbers - practice problems
https://www.ixl.com/math/grade-8/identify-rational-and-irrational-numbers - practice problems
Ordering
http://www.tangischools.org/cms/lib3/LA01001731/Centricity/Domain/3827/ordering%20rational-irrational%20numbers%208-21.ppt. lesson, opens in power point
Subsets
https://www.mathgoodies.com/lessons/sets/subsets - notes and practice problems
Writing Expressions
https://www.mathgoodies.com/lessons/vol7/expressions - examples and practice problems
http://www.math-aids.com/Algebra/Algebra_1/Basics/Writing_Variable.html create your own worksheet with answer key
https://learnzillion.com/lesson_plans/8809-read-and-write-algebraic-expressions-using-parentheses/ - video w/parentheses
IXL - 6th grade Y2 two operations- https://www.ixl.com/math/grade-6/write-variable-expressions-two-operations
IXL - 8th grade V2 - multi operations https://www.ixl.com/math/grade-8/write-variable-expressions-two-or-three-operations
IXL - Algebra I1 - https://www.ixl.com/math/algebra-1/write-variable-expressions
Equivalent Expressions
https://www.classk12.com/worksheets-grade-6-math/algebraic-expressions-ee/distributive-property-equivalent-expression/6148 - distributive property practice
IXL - 6th grade Y16 - https://www.ixl.com/math/grade-6/identify-equivalent-expressions
IXL - 6th grade Y17 - https://www.ixl.com/math/grade-6/identify-equivalent-expressions-ii
IXL - algebra I4 - https://www.ixl.com/math/algebra-1/identify-equivalent-linear-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)
Mixed Review - IXL J3
2 Step Equations - Basic
https://braingenie.ck12.org/subjects/81 - pick from
Solving Two-Step Equations by Dividing and Adding/Subtracting
Solving Two-Step Equations by Multiplying and Adding/Subtracting
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
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.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
http://www.algebra-class.com/solving-word-problems-in-algebra.html - notes/examples of solving inequality word problems *key words*
http://www.algebra-class.com/solving-word-problems-in-algebra-practice.html - notes/examples of solving inequality word problems
http://www.softschools.com/quizzes/algebra/applications_and_word_problems_with_inequalities/quiz4771.html - 8 question quiz, starting with statements and moving to word problems
https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-expressions/pre-algebra-greater-than-less-than/e/inequalities-in-one-variable-1 - 4 - 6th grade - one step practice problems
https://www.khanacademy.org/math/algebra-basics/alg-basics-linear-equations-and-inequalities/alg-basics-two-step-inequalities/e/interpretting-solving-linear-inequalities - 4 two-step practice problems
https://www.ixl.com/math/algebra-1/linear-inequalities-word-problems - IXL Algebra T4
https://www.mathsisfun.com/algebra/inequality-questions-solving.html - notes, examples, and then 10 practice problems at the very bottom
Set Building Notation and Interval Notation
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
https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/v/graphical-relations-and-functions - video - recognizing functions from graph
https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/v/recognizing-functions-example-2 - video - vertical line test
https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/e/recog-func-2 - 4 practice problems, recognizing function from graph
https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/v/functional-relationships-1 - video - recognizing function from table
https://www.khanacademy.org/math/algebra/algebra-functions/recognizing-functions-ddp/e/recognizing_functions - 4 practice problems, recognizing functions from tables
http://www.algebralab.org/practice/practice.aspx?file=Algebra1_12-1.xml - Question Group 1 - identifying functions practice problems
http://www.softschools.com/quizzes/algebra/identifying_functions_as_relations/quiz5586.html - Question Group 2 - Evaluating a function
Continuous - without interruption
Discrete - individually separate and distinct
https://www.shmoop.com/probability-statistics/discrete-continuous-data-exercises.html - practice problems on Discrete vs Continuous
Domain and Range on Continuous Graphs
https://www.khanacademy.org/math/algebra/algebra-functions/domain-and-range/v/domain-and-range-from-graphs - video on Domain and Range from Continuous Graph
IXL:
DD3 - Domain and Range of Absolute Value Functions: Graphs
FF2 - Domain and Range of Radical Functions: Graphs
https://www.khanacademy.org/math/algebra/algebra-functions/domain-and-range/e/domain_and_range_0.5 - 7 practice problems on Domain and Range
https://www.math-aids.com/Algebra/Algebra_1/Domain_Range/Graphs_Domain_Range.html - make your own worksheet with available answer key to practice on your own.
http://mrsportermath.weebly.com/uploads/3/7/6/4/37643183/1.4_hw.pdf - worksheet with answer key
Maximum and Minimum
https://www.khanacademy.org/math/algebra/algebra-functions/maximum-and-minimum-points/v/relative-minima-maxima - video on Maximum and Minimum
https://www.khanacademy.org/math/algebra/algebra-functions/maximum-and-minimum-points/v/identifying-relative-and-absolute-maxima-and-minima - video on Max and Minimum
https://www.khanacademy.org/math/algebra/algebra-functions/maximum-and-minimum-points/e/recognize-maxima-and-minima - practice problems on max and min
Transforming Linear Functions
IXL:
S.14 Complete a table and graph a linear function
S.15 Compare linear functions: graphs and equations
S.27 Transformations of Linear Functions
https://www.onlinemathlearning.com/transformation-linear-functions.html - notes and practice
https://study.com/academy/lesson/translating-reflecting-graphs-of-linear-functions.html - video
https://www.mathworksheets4kids.com/linear-function/transformation/function-shift-1.pdf - worksheet with answer key
https://www.mathworksheets4kids.com/linear-function/transformation/transformation-1.pdf - worksheet with answer key
https://www.mathworksheets4kids.com/linear-function/transformation/mcq-1.pdf - worksheet with answer key
https://quizizz.com/admin/quiz/5849d4f16a2c354d3825c806/transformations-of-linear-functions - Quizziz
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!
https://www.quia.com/ba/28820.html - adding and subtracting battleship game
https://www.superteachertools.us/jeopardyx/jeopardy-review-game.php?gamefile=409339#.WcE9bLKGPIV – adding and subtracting jeopardy
https://www.khanacademy.org/math/algebra2/arithmetic-with-polynomials/adding-and-subtracting-polynomials-review/e/adding-and-subtracting-polynomials-2 - practice problems
https://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=97 – use algebra tiles to model and solve adding polynomials
https://www.khanacademy.org/math/algebra/introduction-to-polynomial-expressions/adding-and-subtracting-polynomials/e/subtract-polynomials practice problems
http://www.mesacc.edu/~scotz47781/mat120/notes/polynomials/add_subtract/add_subtract_practice.html - practice problems
http://www.algebralab.org/practice/practice.aspx?file=Algebra1_10-1.xml - practice problems
IXL Algebra Z3 Add and Subtract polynomials using algebra tiles
Z4 Add and subtract polynomials
Z5 Add polynomials to find perimeter
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
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.
https://www.shmoop.com/video/solving-systems-of-equations-by-graphing - graphing video
https://www.shmoop.com/systems-equations-inequalities/graphing-method-exercises.html - 7 practice problems (you will need a sheet of graph paper)
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-by-graphing - U2 Solving using graphing- graphing on the computer
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-by-graphing-word-problems - U3 solving word problems using graphing
https://www.ixl.com/math/algebra-1/find-the-number-of-solutions-to-a-system-of-equations-by-graphing - U4 How many solutions using graph - graphing on the computer
https://www.khanacademy.org/math/algebra/systems-of-linear-equations/introduction-to-systems-of-linear-equations/e/graphing_systems_of_equations - graph and find the solution
http://www.algebra-class.com/graphing-systems-of-equations-practice.html - 2 practice problems, need graph paper, with worked out answers
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.
https://www.youtube.com/watch?v=kf-o_CcTKH8 - video
https://www.khanacademy.org/math/algebra/systems-of-linear-equations/solving-systems-of-equations-with-substitution/e/systems_of_equations_with_substitution - practice problems
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-using-substitution IXL U8 solving using substitution
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-using-substitution-word-problems - IXL U9 solving word problems
http://www.algebra-class.com/solving-systems-using-substitution.html - 2 practice problems with fully worked out answer key
https://www.shmoop.com/systems-equations-inequalities/substitution-method-exercises.html - 6 practice problems
https://www.mathgames.com/skill/8.67-solve-a-system-of-equations-using-substitution - practice
http://www.mathscore.com/math/practice/System%20of%20Equations%20Substitution/ - practice problems *with places to put your answers in as you go so you can check your understand for each step*
http://www.coolmath.com/algebra/12-2x2-systems-of-equations/02-solving-by-substitution-01 - examples with practice problems
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
https://www.shmoop.com/video/solving-systems-of-equations-by-elimination - video
https://www.youtube.com/watch?v=8kRG7jlBMAY&disable_polymer=true - video
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-using-elimination - U10 solving using elimination
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-using-elimination-word-problems - U11 solving word problems using elimination
https://www.khanacademy.org/math/algebra/systems-of-linear-equations/equivalent-systems-of-equations/v/king-s-cupcakes-solving-systems-by-elimination - video - solving word problem with elimination
https://www.khanacademy.org/math/algebra/systems-of-linear-equations/equivalent-systems-of-equations/v/how-many-bags-of-potato-chips-do-people-eat - video - solving word problem with elimination
https://www.khanacademy.org/math/algebra/systems-of-linear-equations/equivalent-systems-of-equations/e/systems_of_equations_with_elimination_0.5 - practice problems
http://www.coolmath.com/algebra/12-2x2-systems-of-equations/03-solving-by-elimination-addition-01 - example with practice problems
https://www.mathgames.com/skill/8.54-solve-a-system-of-equations-using-elimination - practice
https://campus.mangahigh.com/en-us/px/219/0/0 - game
http://www.softschools.com/quizzes/algebra/solving_systems_of_equations_by_elimination/quiz9291.html - multiple choice test
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
Extra Practice:
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-using-any-method U14 - solve using any method
https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-using-any-method-word-problems U15 - solve word problems using any method
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.
Practice - https://www.shmoop.com/linear-equations/piecewise-functions-exercises.html
Practice - https://mathbitsnotebook.com/Algebra1/FunctionGraphs/FNGTypePiecewisePractice.html
Quiz - https://quizizz.com/admin/quiz/5bb4fe6542fc46001a56cdd7/piecewise-functions-practice
Notes - https://www.mathsisfun.com/sets/functions-piecewise.html
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/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
Notes on Cross Canceling - https://www.purplemath.com/modules/units.htm
Notes on Cross Canceling - https://www.mathsisfun.com/measure/unit-conversion-method.html
https://www.thatquiz.org/tq/practice.html?convertunits - practice
https://www.ixl.com/math/grade-8/convert-rates-and-measurements-metric-units - practice
https://www.thoughtco.com/metric-to-metric-conversions-quiz-4052360 - practice
https://www.gusd.net/cms/lib/CA01000648/Centricity/Domain/1822/Act.%202.4%20Unit%20Cancellation.pdf - worksheet with answer key
Unit 5
Pulling out the GCF
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-polynomials-1-common-factors/a/taking-common-factors - notes with practice problems
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/gcf/gcf_practice.html - 6 practice problems with answers and complete solutions worked out if you get stuck
IXL: AA2 Factor out a monomial
AA4 Factor with leading coefficient of 1
http://www.algebralab.org/practice/practice.aspx?file=Algebra_Redden4A.xml practice problems
https://shamokinmath.wikispaces.com/file/view/Keystone+Algebra+1+-+Factoring+Out+GCF+Practice.pdf – printable worksheet with answer key
Factoring when the leading coefficient is 1
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-1/a/factoring-quadratics-leading-coefficient-1 - examples and practice problems
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-1/e/factor-quadratics-sp - practice problems
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-1/e/factoring_polynomials_1 - practice problems
IXL: AA4 Factor with leading coefficient of 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/
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-2/a/factoring-by-grouping - notes and practice problems
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-2/v/factoring-trinomials-by-grouping-4 factoring quadratics by grouping video
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-2/a/factoring-quadratics-leading-coefficient-not-1 - factoring by grouping notes and practice problems
https://www.khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-2/e/factoring_polynomials_by_grouping_1 - practice problems
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/grouping/grouping.html - multiple step by step examples
https://www.shmoop.com/polynomials/grouping.html - factor by grouping notes
https://cdn.kutasoftware.com/Worksheets/Alg1/Factoring%20By%20Grouping.pdf - printable worksheet with answer key
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/grouping/grouping_practice.html - practice problems with answers and step by step explainations
IXL - AA7
http://www.coolmath.com/crunchers/algebra-problems-factoring-by-grouping - practice problems
https://mathbitsnotebook.com/Algebra2/Polynomials/POGroupingPractice.html - practice problems with multiple choice answers
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