Algebra Resource Page
PH Chapter 1 Tools of Algebra
Solution Sets, Answer Keys, and additional printed resources
Photo below is pg 43, Section 1.6 of PH. In some 2004 student editions a DIFFERENT problem is listed for #97!
Writing Expressions and equations: from words to math Handout SB 13 as well as chart for English expressions and how to write them as an algebraic expression
Basics of exponents review SB 89PA
Chp 1 TEST SOLUTIONS ARE HERE Note: do 5 problems for each problem you missed on the test so that you understand those types of problems. You’ll notice that the test solutions guide has an answer page which lists exactly what section and example matches the test problem and what HW problems are suitable to practice that skill/concept.
Chp 1.1 Using variables pg 6-8
Chp 1.1 Translating words to math (algebraic expressions or equations) videos
Words to equations with Mario Translating Sentences into Equations - YouTube 2 minutes
Translating words to equations with Mash up Math TRANSLATING WORDS INTO ALGEBRAIC EXPRESSIONS! - YouTube 8 minutes
Translating words into inequalities Translating Words to Inequalities - YouTube 6 minutes by Victoria Miles
Translating words into symbols and numbers with Richard at Art of Problem Solving: (Word Problems Part 1: https://www.youtube.com/watch?v=mSg1mgCHmX0&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=10)
Translating words into symbols and numbers with Richard at Art of Problem Solving: Word Problems Part 2 https://www.youtube.com/watch?v=KVblB5EJ4Pw
Translating words into symbols and numbers with Richard at Art of Problem Solving: (Word Problems Part 3: https://www.youtube.com/watch?v=vNPWFe3zL4w&list=PLqiSsHAcyf9fcLxIYtr0mQfqyOOtLJmJ1&index=12)
Setting up equations from word problems AND equations with fractions with Prof Rob Bob (46 minutes— lots of sample problems) https://www.youtube.com/watch?v=ROGk0lJBipU
Chp 1.2 Order of Operations and basic exponents pg 12-15
Chp 1.3-1.4 Rational Numbers and Operations with Positive and Negative Integers, absolute value pg 20-31
Chp 1.3 & 1.4 Adding
Chp 1.5-1.6 Subtracting, Multiplying and dividing with negatives, matrices, reciprocals pg. 34-44 excludes example pages
Chp 1.5 Videos
“keep, change, change” refers to this is a memory trick for changing subtraction to adding a negative. Here’s a math rap explaining this HERE from Scam Squad.
Chp 1.6 Videos on division and reciprocals
Why is division is multiplying by a reciprocal? This is why video— a bit like a proof: Why is dividing the same as multiplying by a reciprocal? from Mathispower
Chp 1.7-1.8 Distributive Property and properties of real numbers pg 50-58
Chp 1.7 Videos: Division is multiplying by a reciprocal
AoPs Introduction to “Distributive Property” Prealgebra Video
The Distributive Property with Integers MooMooMath and Science
On distributing a negative: https://www.youtube.com/watch?v=CmeYAjbu264)
Chp 1.6 Videos on division and reciprocals
Why is division is multiplying by a reciprocal? This is why video— a bit like a proof: Why is dividing the same as multiplying by a reciprocal? from Mathispower
Chp 1.9 Graphing Data on the Coordinate Plane (scatter plots and correlation) pg 62-65
Additional examples and problems from B.A. Algebra Structures and Methods — PDF of 2.5, 2.7, 2.8, 2.9 HERE
2.5 Distributive Property and Factoring problems
2.7 Consecutive Integer Problems
2.8 Reciprocals
2.9 Division is multiplying by a reciprocal
PH Chapter 2 Solving Equations
Solution Sets, Answer Keys and Video Resources
Chp 2.2, 2.3, 2.4 page 83-85, 89-90, 98-101 Solving Two-step equations including with variables on both sides of the equation. (Even though the edge of some pages aren’t showing up, none of the assigned problems are missing.)
Video Resources for solving multi-step equations
Solving two step equations by Magic of Math
Solving Equations by combining like terms by Magic of Math
Solving Equations with Distributive property by Math is Simple
Handout: The Distributive Property Handout SB 67, 68 & 70a
Chp 2.5 107, 108 and 109. d=rt motion problems
Video Resources for Chp 2.5 Videos (motion in same direction)
A —Traveling in the same direction video from My Math Source
B - another video example Mr. Kumar’s explanation of how to figure out how to define the variables is really good. (8 minutes)
C -Traveling in the same direction problem video with Mario - similar to example 2 on page 168 of Orange textbook (Alg 1 Structures and Methods) (often the distance both objects travel is the
Chp 2.6-2.7 Transforming Formulas and Measures of Central Tendency pg 113-123
Video Resources for Chp 2.6
Measures of Central Tendency: Math with Mr. J playlist Mean, Median, Mode, Range
Stem and Leaf Plots
review 3 minute video by MySecretMathTutor
Stem and leaf plot video -3 minutes by Moo Moo Math and Science
More advanced stem and leaf plot 13 minute video
Chp 2 Practice Test answers pg 128 - uploaded at 12:40 Monday 10/23
PH Chapter 3
Solution Sets, Answer Keys, and Video Resources
Here’s a full play list of videos on inequalities. (The chapter sections don’t perfectly line up with ours though) from ssgurg9s
Chp 3-1 Inequalities and their graphs, pg 136-9
Video resources for 3-1
12 minute video on graphing inequalities on a number line — includes clearing fractions: https://www.youtube.com/watch?v=EE2qWIyjKD0 12 minute video by Mike Devor
Short review of how to graph inequalities on the number line, here’s a 3 minute video from Moo Moo Math and Science
Chp 3-2 Solving Inequalities using addition and subtraction pg 142-5
Video resources for 3-2
Art of Problem Solving Pre-algebra Chp 5.5 Basics of Inequalities Part 1
Art of Problem Solving Pre-algebra Chp 5.5 Basics of Inequalities Part 2
Art of Problem Solving Pre-algebra Chp 5.5 Solving Linear Equalities
Art of Problem Solving Pre-algebra Chp 5.5. Solving Linear Equalities Word Problem
Chp 3-3 Solving Inequalities using multiplication and division pg 149-151
Video resources for 3-3
Chp 3-4 Multi-step inequalities pg 153-160 (I believe that the AoPs videos for 3-2 probably have examples of multi-step inequalities)
Video resources for 3-4 Multi-step inequalities
Video resources for 3-5 compound inequalities
How to solve and graph compound inequalities Mario Math Tutoring 12 minutes
Chp 3-6 Absolute Value Equations and Inequalities pg 169-173
Video resources for 3-6 absolute value equations
How to conceptualize an absolute value inequality on the numberline and then solve for x with Mario
Short absolute value inequality graphing video from ssgurgs9
Here’s a simple series of six videos that will walk you through how to solve these absolute value equations and inequality problems from Mario’s Math Tutoring. I recommend you take notes and pause the video to try subsequent example problems.
Chp 3 Chapter Review pp. 175-177
PH Chapter 4 Proportions (and percents and probability)
Solution Sets, Answer Keys
Chp 4-1 Ratio and Proportion pp 185-188
Video resources: unit rates & dimensional analysis
Unit Rates | Solving Unit Rate Problems - Link fixed 1/15 4:25 Monday Math with Mr. J
Solving Unit Rate Word Problems | Math with Mr. J
Converting from miles/hr to feet/second is called unit conversion or dimensional analysis
Solving proportions with cross products Math Antics Proportions video (10 minutes)
Word Problems with proportions. How to set up a proportions when reading word problems? Richard from AoPs sets up proportion (equal ratios are called proportions) (Note at minute 6 he “clears” the fraction by multiplying by 2 so he doesn’t have to have a fraction in the numerator.) He calls method 1 finding an equivalent ratio “scaling it up by a factor of _____”
Chp 4-2 Proportions and Similar Figures 192-195 (within in this pdf, scroll past the 4-1 pages)
Video resources
9 minute video on corresponding parts in similar polygons: https://www.youtube.com/watch?v=aG7KcNNoe5I )
Similarity and measurement (11 minutes) if you need more examples from Organic Chemistry Tutor
Watch Angle basics from Math Antics (7 minutes)
What does congruent mean? Watch Don’t Memorize' 3 minute “What are Congruent Figures”
Similar vs. Congruent— what do these words mean? Watch Math Mashup 6 minutes
Chp 4-3 Proportions and Percent Equations pp 200-203
Video resources: Percent basics (review from math 7 and pre-algebra):
Converting fractions to percents and vice versa Introduction to percent with Richard from AoPs converting fractions into percents and percents into fractions without a calculator
There are three basic types of percent problems - watch Richard of AoPs review how to solve these three basic problems.
What is this percent of that? Example What is 30% of 120?
What percent of this is that? What percent is 88 of 33?
This is that percent of what number? 42 is 150% of what number?
Dr. Dan video #50 : How to translate the sentence into an equation https://www.youtube.com/watch?v=hYv63oei9Vo (28 minutes) These are GREAT videos.
Dr. Dan video #51: https://www.youtube.com/watch?v=50cCWoIKon8 (28 minutes) These are GREAT videos
Chp 4-4 Percent of Change pp 207-209 (within in this pdf, scroll past the 4-3 pages)
Video resources
Percent Increase or Decrease (McD 7.6) Art of Problem Solving Percent Change or Increase or Decrease video part 1
Chp 4-5 Probability: theoretical, experimental, odds in favor pp 210, 214-217
Video resources
Theoretical and Experimental Probability Math Antics Probability
Odds in favor and odds against: What are odds?
How to figure out odds if you’re given the odds “Odds with Shaq”
Chp 4-6 Probability of compound events and sampling pp 222-225
Video resources
PH Chapter 5 Graphs & Functions
Solution Sets, Answer Keys, Video Resources
Chp 5-1 Relating Events to their Graphs pg 237-40
Video resources- none
Chp 5-2 Relations and Functions (What’s a function?) pg. 241-6 (scroll past section 5.1 in the pdf)
Video resources
Magic of Math What is a Function?
Overview of function notation 10 minute video by Kevin Dorey https://www.youtube.com/watch?v=lVUeWKIiypM )
Function Notation 4 minute Mario math tutor video https://www.youtube.com/watch?v=e0EdFGpcvc (do problem 2 before he does it).
How to determine if an equation or set of data represents a function? Four methods: here
More advanced examples f(g+2)=blah blah https://www.youtube.com/watch?v=8wYVB7Jgo40 by Math WOEs
Chp 5-3 Functions, Rules, Tables and Graphs pg 249-253
Video resources
Magic of Math Is this a Function or just some other relation?
Magic of Math - 5 Ways to write a function
Bonus Magic of Math Does the Table represent a linear or non-linear function?
Bonus Magic of Math What’s the Domain and Range of the Function
Magic of Math How to Graph Absolute Value Functions (they make a V)
Chp 5-4 Writing a Function Rule pg 256-9 (scroll past section 5.3 in the pdf) - think Mr. Function Fox
Video resources
How to write a function rule using addition and subtraction with Mr. J
How to write a function rule from input - output tables Mario Math Tutor
How to write a function rule from a table Organic Chemistry Tutor
Writing a linear function from a table (Mario Math Tutor)
Writing a function from a table in y= mx + b form (Org. Chem Tutor)
Chp 5-5 Direct Variation pg 261-267 y = kx straight line through the origin
Direct Variation Video options y = kx
(Math 8 chp 8.5, Algebra 1 PH 5-5 and BA chp 8.9, and some Math 7 Chp 5)
11 minute video by Victoria Miles: https://www.youtube.com/watch?v=fVGQIOrVXls
Prof Rob Bob https://www.youtube.com/watch?v=Ps_YRWPdkfk&list=PLGbL7EvScmU7ZqJW4HumYdDYv12Wt3yOk&index=40 (Remember to take notes and after he does one problem, pause the video and do the other problems with him.)
Direct variation word problems with Joann https://www.youtube.com/watch?v=0Oloi4o7MhE
Video with Joann https://www.youtube.com/watch?v=G6Dt0z1osKI (“Algebra I #12.5a, Direct Variation and Constant of Variation”)
Word problems direct variation -Video with Joann https://www.youtube.com/watch?v=ZQgjSvM8_1I
PENTAGON: Watch Direct variation word problem example with Mario Direct Variation Word Problem Example - YouTube
Chp 5-6 Describing Number Patterns - Arithmetic Sequences 256-9 (scroll past section 5.3 in the pdf)
Video resources
Magic of Math Arithmetic Sequences
PH Chapter 6 Linear Equations and their Graphs
Online Graphing Calculator: Desmos.com/calculator
Solution Sets, Answer Keys, and additional printed resources plus videos for each topic
Chp 6-1 Videos
Equation of a line, slope intercept form, functions, perpendicular lines & horizontal lines Math Antics Basics of Linear Functions
How to graph a line when you have an equation in y = mx + b or slope-intercept form. WATCH this video.
Mario’s Math Tutoring on equation of the horizontal and vertical lines
Math Antics Slope and Distance of a line (slope = RISE / RUN or change in y over change in x or )
How to calculate slope. Richard reminds us what slope is and how to find it (10 minutes). https://www.youtube.com/watch?v=5z6IduhkeF0
Richard walks us through positive and negative slopes, slope of a horizontal line is zero (y=some number), vertical line has an undefined slope, steepness of slope, what does a line with a slope of 1 look like? (10 minutes) https://www.youtube.com/watch?v=Nl0AAmARm18
Chp 6-2 Slope Intercept Form pages 294-297 and additional problems from pg 293-96 including check understanding #5, #54, 55, 57a
Chp 6-2 Slope Intercept Form Videos
Equation of a line, slope intercept form, functions, perpendicular lines & horizontal lines Math Antics Basics of Linear Functions
What is the equation of a horizontal line? of a vertical line? Mario’s Math Tutoring on equation of the horizontal and vertical lines
Chp 6-3 Standard Form Investigation pg 298 & Standard Form pg 301-303, pg 299 check understanding and 301-303 23-2, 46-54ish pg 299-303 additional graphs
Chp 6-4 Point Slope Form pg 306-9, Problems 1-11 graphs for 6-4 and page 307-309 equations of the line for problems 10-30
Chp 6-4 Point Slope Form Videos
Richard of AoPs explains what Point-slope form means and can do for us (9 minutes) https://www.youtube.com/watch?v=xa_QG-dZEjo
Mario’s math intro to point-slope form (2 minutes) — pause the video and try to do problem 2 before Mario does it. https://www.youtube.com/watch?v=SqFj06Y3tl4
Optional additional video: Organic chem tutor intro to Point-Slope Form https://www.youtube.com/watch?v=XzG-fi__hsU
All three equation formats: Review Video of Slope intercept form, standard form and point-slope form: 32 minutes by Organic Chem Tutor
Chp 6-5 Parallel and Perpendicular lines Videos
Chp 6-6 Scatter Plots and Equations of Lines pg 320-4 and Page 319 #1 & 2, 318 check skills you need 1-2, 319 check undertanding 1roblems 1-11 graphs for 6-4
Chp 6-6 Videos
What is a scatter plot? How to make it? Magic of Math video- do the problems when the instructor tells you to do so! https://www.youtube.com/watch?v=hKNFn2E2biw
Additional videos on basics of scatter plots and correlation a) 24mathGuy https://www.youtube.com/watch?v=lL7q-DBvacg b) Joann Video https://www.youtube.com/watch?v=lA6yDZcnWvs
Video: Models Magic of Math video https://www.youtube.com/watch?v=hNUV2sH3tPA&list=PLIa7w81Zp_7wXewiDi95QAMSUcTxd0k3h&index=5
Predictions with lines of fit Magic of Math video https://www.youtube.com/watch?v=D2FGViDqDAo&list=PLIa7w81Zp_7wXewiDi95QAMSUcTxd0k3h&index=5
Mathcation video (10 minutes) https://www.youtube.com/watch?v=zLxRcUX_oMQ
Optional more advanced videos r as a correlation coefficient https://www.youtube.com/watch?v=-Y-M9aD_ccQ
Chp 6-7 Graphing Absolute Value Equations pg 327-30, and page 327-329 prob 1-3, 28-31, 42
Chp 6 Chp Review pg 331-333
PH Chapter 7
Solution Sets, Answer Keys,
Chp 7-1 AND back of book graphs for all of chp 7 solutions
Chp 7.2-7.3 Solutions (see first link for most graphs)
Chp 7.4-7.5 Solutions (see first link for additional graphs not shown here)
VIDEO RESOURCES
Video resource playlist for the entire chapter is here. The section numbers are incorrect but the titles show you what the content is.)
PH Chp 7.1 Solving Systems of Equations using graphing (method 1 of 3)
Solve Linear systems of Equations by Graphing (video from ssgurgs9)
PH Chp 7.2 Solving Systems of Equations using Substitution (method 2 of 3)
Solving Systems of Equations by Substitution (video from ssgurgs9)
PH Chp 7.3 Solving Systems of Equations using Addition and Subtraction aka Elimination Method (method 3 of 3)
Solving Systems of Equations by Elimination or using Addition and Subtraction (video from ssgurgs9)
Solving Systems of Equations using Multiplying first then using elimination (video from ssgurgs9)
PH Chp 7.4 Applications of Linear Systems (Solving Systems of Equations in real world)
Linear Systems with no solution, or infinite solutions, and real world problems (video from ssgurgs9)
PH Chp 7.5 Graphing Inequalities in two variables on a coordinate plane (not systems yet) — shaded area above or below lines
Graphing Inequalities on a coordinate plane (from ssgurgs9)
PH Chp 7.6 Graphing Systems of Linear Inequalities
Graphing Systems of Linear Inequalities (video from ssgurgs9)
Mashup Math on Graphing Systems of Linear Inequalities or another by Mario
PH Chapter 8 Exponents and Exponential Functions
Solution Sets, Answer Keys, and video resources
Overview of exponents - Video Resources
Introduction to exponents — 10-minute video to review how exponents work: Intro to Exponents by Math Antics
Overview of basic exponent laws: Laws of Exponents from Math Antics: https://www.youtube.com/watch?v=LkhPRz7Hocg Write these rules down (again— you should already have them in your notes) NOTE- broken link was fixed on 1/19/21
AoPs What are the exponent rules? Deriving the exponent rules. Then, can we use exponent rules to make a problem easier to solve? “Same Base Exponent Rules” at 5:10 try to solve the problem, then watch Richard the math wiz solve it.
AoPs Sample Exponent Rule problem. Stop the video at 0:15, write down the problem and use your exponent rules (aka Laws of Exponents) to solve the problem. Hint: write these in terms of the same base. Then watch Richard the math wiz solve it. Then look at problems 2.19a,b,c in AoPs Prealgebra text p. 71. Do those problems and check your answers.
Chp 8-1 Zero and Negative Exponents pg. 394-99
Videos for Zero and Negative Exponents
Zero exponents Math Antics video explains patterns: x to 0 power is? and how to “undo” exponents and roots https://www.youtube.com/watch?v=S3IEeCyUWWA
AoPs What does 3 to the zero power mean? “Zero as an Exponent”
AoPs “Negative exponents Introduction” After watching this video, turn to page 78-9 in AoPs Prealgebra text and do problems 2.28-2.30. Check your answers in the text on pages 80-82
Bonus: AoPs “Reciprocals and negative exponents” Pause the video at 1:38 and do the problem then watch Richard’s solution. (Reciprocal of a reciprocal returns the original number)
Bonus: AoPs “Exponent Rules with Negative Exponents” Pause the video at 0:20 and try to simplify the expressions so you can compare them. Afterwards, watch Richard solve the problem. After watching this video, turn to page 79 in AoPs Prealgebra text and do problems 2.31-2.35 then check your answers on pages 82-86
Chp 8-2 Scientific Notation pg 402-4
Videos Resources
Scientific Notation What is it? Math Magic video: https://www.youtube.com/watch?v=7Mi3cZwixIA&list=PLIa7w81Zp_7wQivt4auzylmrZUlE7UrE2&index=28
Scientific Notation - how to add, subtract, multiply and divide in scientific notation Math Magic “How to Perform Operations in Scientific Notation . . . How to Add, Subtract, Multpliy & Divide”
Chp 8-3 Multiplying powers with the same base (a^m)(a^n) = a^m+n (scroll down for 8-3)
Videos
Can I multiply exponents with different bases? NO— at least not the way you can with the same base Video with Mr. J
Chp 8-4 Powers of Powers (a^m)^n = a^(mn) pg 413-16 AND pg 411 Powers of Powers Investigation
Videos
Power of a Power with Mr. J
Chp 8-5 Division Properties of Exponents pg 420-423
Videos for dividing exponents with the same base
Chp 8-6 Geometric Sequences pg 427-9
Video Resources
Mario Math Tutor - Explicit Formula for Geometric Sequences
Chp 8-7 Exponential Functions pg 432-5
Video on Exponential Growth Functions (exponents above 1) from ssgurgs9
Chp 8-8 Exponents and Exponential Functions pg 441-5
Video on Exponential Decay Functions (exponents below 1) from ssgurgs9
Chp 8 Review pg 447-9
PH Chapter 9 Polynomials and Factoring
Solution Sets, Answer Keys, Video Resources
Chp 9-1 Classifying, Adding and Subtracting Polynomials pages 459-61
Chp 9-1 Video options
How to add and subtract Polynomial Expressions Organic Chemistry Tutor
What’s this degree nonsense? Organic Chemistry Tutor (don’t fret about this part. Just remember to make the term with the highest exponent first or the “leading term”).
Additional examples and problems from Algebra: Structure and Methods (BA): Read BA Section 4-2 Adding and subtracting Polynomials pg 146-147 and 4-3 Multiplying Polynomials
Chp 9.2 Multipying Monomials and polynomials and factoring pages 463-6
9.2 Video Options
Watch how to use a Prime Factorization Tree + Venn diagram to find GCF example is GCF of 24 & 36
How to find GCF of monomials (Khan Academy) or Mario Math Tutor
Chp 9.3 Multiplying Binomials (and trinomials) pg 469-472- draw the swoopies ;) to keep track of which terms you’re multiplying
Video resources for 9.3— a sort of different way to keep track of what you’re multiplying
FOIL (first, outer, inner, last) is a mnemonic that works for binomials 6 minute Prof. Dave FOIL video
Chp 9.4 Multiplying Special Cases pg 475-480 (square of a binomial)^2 = perfect square trinomial and difference of squares a^2-b^2 = (a+b)(a-b)
Videos on Perfect Square Trinomials: Factoring Perfect Square Trinomials which are really Squares of Binomials in disguise (a + b)^2 = a^2 + 2ab + b^2 or (a-b)^2 =
Videos on Difference of Squares (a-squared - b-squared)
Difference of Squares
Watch Mario factor some difference of squares problems: https://www.youtube.com/watch?v=Up8Zllvii90
Watch Richard from AoPs factor some difference of squares problems. https://www.youtube.com/watch?v=rXzcW0WTeWs & Basic Difference of Squares problems with Richard from AoPs. Using difference of squares factorization to solve problems.
Math is visual Difference of Squares video https://www.youtube.com/watch?v=3X2Pp2FOwCY
Walk through simple difference of squares problems and harder ones with ProfRobBob’s 15 minute video— sometimes you aren’t done factoring after one set of difference of squares. Sometimes there’s a second difference of squares lurking in the factors. Written explanation of difference of squares problems
Slightly harder Difference of Squares and another short video with slightly harder problems
1st Look for a GFC (greatest common factor)
Look for a difference of squares OR a squares of binomials
You might need to simplify and them combine like terms
This AoPs video is showing how we can use difference of squares to solve interesting word Math Counts problems. It gets especially cool when he gets to minute 9. Here’s another Math Counts video — jump to minute 4:32 —showing how recognizing a difference of squares can help you solve problems quickly
Here are the missing check understandings for some early chp 9 (9.2-9.5s approximately)
Chp 9.5 Factoring regular trinomials (x ² +bx +c or -c) with coefficient of 1 for quadratic term pp 481-485
Video Resources for regular quadratic trinomials
Factoring Regular trinomials x ² +bx +c from Mash up math where a =1
DIAMOND & BOX METHOD
Using the diamond/box method with Mario (3 minutes)
If you need a refresher, you can watch this 2 minute diamond and box method video https://www.youtube.com/watch?v=GV9lppYweQ8 )
Diamond Method and Box Method (aka Corner Piece method) https://www.youtube.com/watch?v=cvaW5p0vSzw with Diana Hang 2 minutes
Another sample problem using the diamond and box method https://www.youtube.com/watch?v=ekvAgTdTCCg with Diana Hang 2 minutes
The “SPLIT METHOD” : https://www.youtube.com/watch?v=JlxV8qFPq7I byMath Mashup 8 minutes
Chp 9.6 Factoring regular trinomials (ax^2 + bx +c) with any coefficient for quadratic term pp 486-489
Video Resources for regular quadratic trinomials
Sort of GUESS AND CHECK method AoPs Factoring Quadratics Part 1 10 minutes - guess and check,
MAGIC X method: this builds on the diamond method but for quadratic coefficients which are greater than 1: Review how to factor quadratic equations by watching 9 minute video with Nancy Pi. She uses the diamond method and then adds a quick step she calls magic x for ax^2 +bx+c
Chp 9.7 Factoring special cases difference of squares and perfect square trinomials (a² +or - 2ab+b²) pp 490-495
Video Resources for Factoring: special cases SoBs = PST and Difference of Squares
Remember to first look for Greatest Common Factors- Factoring Monomials from a Polynomial
Factoring Polynomials Difference of Squares
Factoring Perfect Square Trinomials which are really Squares of Binomials in disguise (a + b)² = a² + 2ab + b² or (a-b)² = a² - 2ab + b²
Richard from AoPs shows us how to squares of binomials 10 minutes
Review of both special cases from ssgurgs9
PENTAGON — THIS IS NOW INCLUDED UNDER ALGEBRA 2 Chp 9.8 Factoring by grouping pp 496-502 and test taking strategies
Mario of factoring by grouping when you have four terms and by Organic Chem Tutor
Chp 9 Chapter Review pp 503-506
Here’s our full collection of factoring quadratic expressions and solving quadratic equations videos
Remember polynomials are monomials added together
Difference of Squares
Watch Mario factor some difference of squares problems: https://www.youtube.com/watch?v=Up8Zllvii90
Watch Richard from AoPs factor some difference of squares problems. https://www.youtube.com/watch?v=rXzcW0WTeWs & Basic Difference of Squares problems with Richard from AoPs. Using difference of squares factorization to solve problems.
Math is visual: Difference of Squares video https://www.youtube.com/watch?v=3X2Pp2FOwCY
Walk through simple difference of squares problems and harder ones with ProfRobBob’s 15 minute video— sometimes you aren’t done factoring after one set of difference of squares. Sometimes there’s a second difference of squares lurking in the factors. Written explanation of difference of squares problems
Slightly harder Difference of Squares and another short video with slightly harder problems
1st Look for a GFC (greatest common factor)
Look for a difference of squares OR a squares of binomials
You might need to simplify and them combine like terms
This AoPs video is showing how we can use difference of squares to solve interesting word Math Counts problems. It gets especially cool when he gets to minute 9. Here’s another Math Counts video — jump to minute 4:32 —showing how recognizing a difference of squares can help you solve problems quickly
Factoring Perfect Square Trinomials which are really Squares of Binomials in disguise (a + b)^2 = a^2 + 2ab + b^2 or (a-b)^2 =
Factoring 4 terms by grouping
Mario 2 minutes https://www.youtube.com/watch?v=VYUhUeeD_Z0
Factoring quadratic trinomials
DIAMOND & BOX METHOD
Using the diamond/box method with Mario (3 minutes)
If you need a refresher, you can watch this 2 minute diamond and box method video https://www.youtube.com/watch?v=GV9lppYweQ8 )
Diamond Method and Box Method (aka Corner Piece method) https://www.youtube.com/watch?v=cvaW5p0vSzw with Diana Hang 2 minutes
Another sample problem using the diamond and box method https://www.youtube.com/watch?v=ekvAgTdTCCg with Diana Hang 2 minutes
The “Split method” : https://www.youtube.com/watch?v=JlxV8qFPq7I byMath Mashup 8 minutes
Sort of guess and check method AoPs Factoring Quadratics Part 1 10 minutes - guess and check,
Magic x method: this builds on the diamond method but for quadratic coefficients which are greater than 1: Review how to factor quadratic equations by watching 9 minute video with Nancy Pi. She uses the diamond method and then adds a quick step she calls magic x for ax^2 +bx+c
Art of Problem Solving - Factoring to solve Q. E. part 1
Summary of many different ways to factor polynomials: Summary of 4 types of factoring polynomials with Mario
Factoring Techniques videos from Prof. Rob Bob
Factoring Monomials from a Polynomial
Factoring Polynomials Difference of Squares
Factoring Polynomials Sum Difference of Cubes
Factoring Quadratic Trinomial x^2+bx+c Polynomial
Factoring Quadratic Trinomial ax^2+bx+c
Solving Quadratic Functions
Solving quadratic equations by completing the square (Algebra 12.2)
Prof Rob Bob (20 minutes) https://www.youtube.com/watch?v=oKT-N1xL0Ig
https://www.youtube.com/watch?v=prx_Bf2hakw&t=198s (Nancy Pi?)
AoPs Completing the Square Part 1 https://www.youtube.com/watch?v=x2CfgdwogoA
AoPs Completing the Square Part 2 https://www.youtube.com/watch?v=hUQXfU2lEAw
Organic Chem Tutor https://www.youtube.com/watch?v=C206SNAXDGE
completing the square video Math Mash up 8 minutes https://www.youtube.com/watch?v=ypNXI75IjqI
Solving quadratic equations using quadratic formula (Algebra 12.3)
Song mnemonic device (tune of Pop Goes the Weasel) https://www.youtube.com/watch?v=VOXYMRcWbF8
AoPs Using the Quadratic Formula Part 1 https://www.youtube.com/watch?v=mvmk9tfpUfE
AoPs Using the Quadratic Formula Part 2 https://www.youtube.com/watch?v=Tuuzi1ILubA
Watch Mario demonstrate how to use the quadratic formula to solve quadratic equations https://www.youtube.com/watch?v=sthnDdr6klY
The Discriminant = what’s under the radical sign in the quadratic equation = b-squared - 4ac (Algebra 12.4)
What is the Discriminant? with Richard from AoPs 6 minutes https://www.youtube.com/watch?v=SKFhXIv42N4
The Discriminant 3 minute video from Organic Chem Tutor https://www.youtube.com/watch?v=6fU9ZgwbU74
The Discriminant -a longer video 25 minutes from Math & Science.com https://www.youtube.com/watch?v=VzKKgVXLvJo
Song- rap Mr. 2Pi https://www.youtube.com/watch?v=cjZpGM7veW4 — key vocab: discriminant, imaginary
Another playlist for quadratic equations (disregard chapter numbers as they don’t line up with our textbook) from ssgurgs9
PH Chapter 10
Solution Sets, Answer Keys, and additional printed resources
Chp 10 quiz solutions - note to self, remove after a week
Chp 10-1 to 10-2 Quadratic Graphs and Functions
Chp 10-3 to 10-4 Estimating Square Roots and Solving Quadratic Equations p517-35
Chp 10-5 to 10-6 Est Sq Roots, Solving Quadratic Eq p517-35
Chp 10-7 to 10-8 Quadratic Formula, Discriminant
Chp 10-9 to Chp Review Choosing Linear, Quadratic or Exponent Model p559-72
Video Resources
Review of Solving Square Roots
Square Root introduction part 1 by Art of Problem Solving
Square Root intro part 2 by Art of Problem Solving
Square Roots - non-integer square roots (such as what is the square root of 2?)
Square Root of a product by Art of Problem Solving
Sum of Square Roots — beware common errors! sums and products are different! by Art of Problem Solving
Simplifying Square Roots Part 1 by Art of Problem Solving
Simplifying Square Roots Part 2 by Art of Problem Solving before you watch this video, review divisibility rules
Simplifying radical expressions by Mario’s Math Tutoring A different method for evaluating radical expressions by breaking down the radican into it’s prime factors Simplifying Radicals Easy Method by Mario’s Math Tutoring
10.5 Factoring to Solve Quadratic Equations
10.6 Completing the Square - Solving quadratic equations by completing the square (BA Algebra 12.2)
Prof Rob Bob (20 minutes) https://www.youtube.com/watch?v=oKT-N1xL0Ig
https://www.youtube.com/watch?v=prx_Bf2hakw&t=198s (Nancy Pi?)
AoPs Completing the Square Part 1 https://www.youtube.com/watch?v=x2CfgdwogoA
AoPs Completing the Square Part 2 https://www.youtube.com/watch?v=hUQXfU2lEAw
Organic Chem Tutor https://www.youtube.com/watch?v=C206SNAXDGE
completing the square video Math Mash up 8 minutes https://www.youtube.com/watch?v=ypNXI75IjqI
10.7 Solving quadratic equations using quadratic formula (also BA Algebra 12.3)
Song mnemonic device (tune of Pop Goes the Weasel) https://www.youtube.com/watch?v=VOXYMRcWbF8
AoPs Using the Quadratic Formula Part 1 https://www.youtube.com/watch?v=mvmk9tfpUfE
AoPs Using the Quadratic Formula Part 2 https://www.youtube.com/watch?v=Tuuzi1ILubA
Watch Mario demonstrate how to use the quadratic formula to solve quadratic equations https://www.youtube.com/watch?v=sthnDdr6klY
The Discriminant = what’s under the radical sign in the quadratic equation = b-squared - 4ac (Algebra 12.4)
What is the Discriminant? with Richard from AoPs 6 minutes https://www.youtube.com/watch?v=SKFhXIv42N4
The Discriminant 3 minute video from Organic Chem Tutor https://www.youtube.com/watch?v=6fU9ZgwbU74
The Discriminant -a longer video 25 minutes from Math & Science.com https://www.youtube.com/watch?v=VzKKgVXLvJo
Song- rap Mr. 2Pi https://www.youtube.com/watch?v=cjZpGM7veW4 — key vocab: discriminant, imaginary
PH Chapter 11
Solution Sets, Answer Keys
Chp 11-1
CHp 11-5 to 11-6 Solving Rad Exp and Graphing Sq Root Functions p607-19
Video Resources
11.1 Radical Expressions - simplifying expressions with a radical sign
Simplifying Square Roots Part 1 by Art of Problem Solving
Simplifying Square Roots Part 2 by Art of Problem Solving before you watch this video, review divisibility rules
Simplifying radical expressions by Mario’s Math Tutoring A different method for evaluating radical expressions by breaking down the radican into it’s prime factors Simplifying Radicals Easy Method by Mario’s Math Tutoring
11.2 Pythagorean Theorem
Art of Problem Solving Pythagorean Theorem part 1
Art of Problem Solving Pythagorean Theorem part 2
Art of Problem Solving Pythagorean Triples
11.3 Distance and Midpoint Formula
Art of Problem Solving - the distance formula
Mario Distance Formula for finding length of a diagonal line on a coordinate plane
Midpoint of a line formula by Math Mashup
Midpoint of a line formula by Organic Chem tutor
PH Chapter 12
Solution Sets, Answer Keys,
Chp 12-1 to 12-2 Inverse Variation Grph Rational Functions p 636-51
Chp 12-3 to 12-4 Simplifying Rational Expressions & 12-4 Multiplying and Dividing them
Video Resources
12.1 Intro to Inverse variation compared to direct variation (not tested)
Is this direct variation or inverse variation? Mario 6 minutes
12.3 Simplifying Rational Expressions, aka algebraic fractions
(BA Algebra 6.1) 14 minute video with Nancy Pi and take notes https://www.youtube.com/watch?v=i7w_aRlVagU then try to do one of the problems before she does so pause the video.
12.4 Multiplying and Dividing Rational Expressions, aka, Algebraic Fractions Using Factoring
Dividing fractions that have quadratic expressions in them which requires factoring with Brian M. dividing fractions with quadratic expressions (aka dividing rational expressions) Brian also shows you the educated guess and check method of factoring a quadratic expression
Fractional Equations method #2 solve as proportion —> cross multiplication (Also BA Algebra chp 7.4) Prof Rob Bob video (but he doesn’t go into fractions that need to be factored first as in example 3. You’ll need to read the book for that. https://www.youtube.com/watch?v=De5ghpLlkUQ&list=PLGbL7EvScmU7ZqJW4HumYdDYv12Wt3yOk&index=32
12.6 Adding and Subtracting Rational Expressions, aka algebraic fractions (fractions with variables and polynomials in the denominator)
Easy version by Math and Science adding and subtracting algebraic fractions (fractions with variables and polynomials part 1)
7 minute video from Mario on Adding and Subtracting Algebraic fractions and a longer 10 minute video here
Bonus video- -what if I have TRINOMIALS IN THE DENOMINATOR?! 7 minutes by Brian McLogan (can I factor first??)
Cumulative Review of Most Algebra Principles
Review sample Algebra 1 final exam problems with Mario -1 hour 80 problems covering 33 types of problems
Math 8 Video Resources
Corresponds to Greenie & KIN
GREENIE page #5 - Solving Equations with Fractions review
GREENIE page #6 - Solving Two step equations - use clearing decimals by multiplying by a factor of ten
GREENIE page #10 Graphs and Functions - Using a Table to graph a function and Determining if a relation is a function
How to determine if an equation or set of data represents a function? Four ways to determine if an equation or set of ordered pairs represents a FUNCTION here
Input & Output Tables Math Antics Video about functions inputs & output table
GREENIE page #11 Graphs and Functions - Equations, Tables and Graphs DIRECT VARIATION
(What kind of variation are these functions? Are they straight lines which pass through the origin? What’s the name of that kind of variation? Hint: y=kx)
Video resources Direct Variation Take notes on video — Direct Variation intro with Organic Chemistry Tutor
More advanced Direct variation word problems with Joan
Math 8 4.3 What does similar mean? How is that different from congruent? Video Similar v. congruent (Math 8 chp 4.3)
Using proportions to find missing measurements in similar figures short video. Here’s a longer one (11 minutes) if you need more examples from Organic Chemistry Tutor (Math 8 chp 4.3)
Greenie #25 Geometric Relationships: Angle Relations
Angle basics from Math Antics and Angle Review (vertical, complementary, supplementary etc ) w/ Ms. Merkins https://www.youtube.com/watch?v=M7ToxgRvKx0&list=PLJM2N9UmkFqhRi05TkVVWbGTNMYLQvide&index=5
Lines & Angles Rap 3 minutes by Go Noodle & Angle Names by Tutoring hour 5 minutes
Richard from AoPs explain straight angles (a.k.a. a straight line) https://www.youtube.com/watch?v=EjTaOODJTVg
After Richard writes the supplementary angles problem on the board, pause the video and try to draw a picture of the problem. Unpause. Then try to write an equation before he does. Then once he’s written the equation, pause the video and YOU solve for “c” and then figure out the measurement of each angle before he does. Then watch him and correct your work.
Do the same when he writes the vertical angle problem on the board.
Supplementary & complementary angles from Mr. J
Greenie #26 Geometric Relationships: Parallel and Perpendicular Lines
Angles & Parallel lines: Richard from AoPs solve problems involving angles and parallel lines Try pausing the video when he starts to do a problem and and see if you can draw it out, write the equation and solve it. Unpause after you do each step to see if you are on the right track.
Harder supplementary angle problems with variables and equations
Much more complicated angles when there are parallel lines with a transversal cutting across two parallel lines with Mario
Another sample of finding angles when parallel lines are cut by a transversal https://www.youtube.com/watch?v=uOrXWJQ8vWA&list=PLCqwggKH0w8b3J9_iGeax3huTLTBxl-iS&index=2
GREENIE page #34 Measurement and Geometry: Volume of Triangular Prisms, Cylinders