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  • Summer 2022
Tokyo Math - Math Tutoring for Students in Tokyo, Japan

Ryuto's Learning


Summer Topics
Linear equations
​Graphing lines and inequalities
Linear inequalities
Systems of equations
Distance-Rate-Time problems

Mixture problems
Combined rates problems
Pythagorean Theorem
Quadratics
  • Standard form
  • Factored form
  • Vertex form
  • Completing the square
  • Word problems
Simplifying Radicals​
Other Topics in Algebra 2:
Trigonometry
Complex numbers
Sequences and series
Rational equations
​Absolute value equations
​Radians
Vocabulary
y-intercept
x-intercept
Roots
Solutions
Zeros
​Factors
​FOIL
Variable
​Coefficient
Constant
Term
​Vertex
Axis of symmetry
Hypotenuse
​Pythagorean triple

​Geometry

Textbook Links


Chapter 1
https://www.emsisd.com/cms/lib/TX21000533/Centricity/Domain/4688/Topic%201.pdf

Chapter 2
https://www.emsisd.com/cms/lib/TX21000533/Centricity/Domain/4688/Topic%202.pdf

Chapter 3
https://www.emsisd.com/cms/lib/TX21000533/Centricity/Domain/4688/Topic%203.pdf

Chapter 4
https://www.emsisd.com/cms/lib/TX21000533/Centricity/Domain/4688/Topic%204.pdf
Chemistry
​
Syllabus from another Pre-AP Chemistry class

https://www.fusd1.org/site/handlers/filedownload.ashx?moduleinstanceid=7344&dataid=12057&FileName=Pre-AP%20Chemistry%20Syllabus.pdf

Chemistry Notes
https://znotes.org/docs/cie-igcse-chemistry-0620-znotes.pdf

Youtube playlist of chemistry videos by Tyler Dewitt:
https://www.youtube.com/user/tdewitt451/playlists

Periodic Table of Elements
​ptable.com/
physical_and_chemical_properties_and_changes.pdf
File Size: 16107 kb
File Type: pdf
Download File


Homework
 August 16

Completing the square (try #10 and 15)
cdn.kutasoftware.com/Worksheets/Alg2/Quadratic%20Equations%20By%20Completing%20the%20Square.pdf

Systems of equations (try #17 and 18)
cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Two%20Equations.pdf

Special right triangles (try #3, 5, 7, 8)
Hint: You will need to find the length of the common side of the two triangles first using the special right triangle ratios for 45-45-90 and 30-60-90 triangles.
cdn.kutasoftware.com/Worksheets/Geo/8-Multi-Step%20Special%20Right%20Triangles.pdf

August 15

​Here is a PDF for today's assessment.  If you really get stuck on a problem, just skip it and we will review the concepts tomorrow. 
ryuto_assessment_8-15-18.pdf
File Size: 214 kb
File Type: pdf
Download File


August 14

​Print out and practice the second page until you can write out all the answers in less than 2 minutes
www.emathacademy.com/sat-math-formulas.html

Combined rates
​cdn.kutasoftware.com/Worksheets/Alg1/Work%20Word%20Problems.pdf

August 13

Graphing systems of linear inequalities (try #2, 4, 6, 8. 10, 12)
cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Inequalities.pdf

Review of linear equations (try all odd problems)
Hints:
  • For questions 1-5, turn the equations into y = mx + b form by getting y by itself.
  • For #7-13, standard form is Ax + By = C
  • For 15-21: first identify or find the slope of each equation.  Then plug in y, m, and x into y = mx+b to find what b is.  Lastly, convert it into standard form, which is Ax + By = C.
  • Some of these skills are new, so try them the best you can on your own, and if you have a lot of trouble, we can look at them together during the next lesson.
​cdn.kutasoftware.com/Worksheets/Alg2/Review%20Linear%20Equations.pdf

Intro to trigonometry video (we'll discuss this more later)
www.youtube.com/watch?v=VRz2d5yedsg&t=183s

August 12

Do this yet again (It'll be really good to be automatic with these formulas!) - Quadratics formulas (print out and fill in page 2 of the PDF on the link)
www.emathacademy.com/sat-math-formulas.html
​
Pythagorean Theorem Worksheet​
pythagoren_theorem_problems.pdf
File Size: 116 kb
File Type: pdf
Download File

Introduction to radians video
www.youtube.com/watch?v=cgPYLJ-s5II

August 11

Do this again - Quadratics formulas (print out page 2 of the PDF on the link, fold back on the dotted line, fill out each part and check your answers)
www.emathacademy.com/sat-math-formulas.html

Circles, circumference, and areas video
www.youtube.com/watch?v=O-cawByg2aA

Circles Worksheet
Hint: use the formulas below if needed to help answer the questions (this should be review from your math classes)
  • C=2πr
  • C=πd
  • d=2r
  • A=πr^2
​cdn.kutasoftware.com/Worksheets/Geo/11-Circumference%20and%20Area%20of%20Circles.pdf

August 10

Graphing factored form video
www.youtube.com/watch?v=EV57jv7JKCs

Graphing factored form (try problems #13 to 20 on page 1 and 2)
Hint:
  • x-intercepts are when y = 0 and x = p or q
  • x value of vertex: (p+q)/2
  • min/max value means what is the height at the vertex
  • y-intercept is when x = 0
​www.eatoncommunityschools.org/userfiles/23/Classes/5310/factoring%20&%20intercept%20form%20-%20graphing%20parabolas.pdf?id=15573

Quadratics formulas (print out page 2 of the PDF on the link, fold back on the dotted line, fill out each part and check your answers)
www.emathacademy.com/sat-math-formulas.html

August 9

Write the equation for the parabola in vertex form (Do the Protect the Castle worksheet)
There is also a video that shows the answers on the link, but try the questions on your own first and watch the video to check your answers.
www.emathacademy.com/math-worksheets.html

​
Graphing the vertex form
Hint: the way to find the x-intercepts is to solve for x by using the reverse order of PEMDAS for 0 = a(x-h)^2 + k.  (Subtract k first, etc.)
vertex_form_hw.pdf
File Size: 46 kb
File Type: pdf
Download File


August 8

​This is an assessment on about half of the concepts we have looked at.  I will post the other half on a different day.  Do all the problems on your own and without a calculator.  Do your best and if you don't know how to answer a question after giving it a good try, just move on to the next problem.
ryuto_assessment_8-8-18.pdf
File Size: 97 kb
File Type: pdf
Download File


August 7

​Simplifying radicals video
www.youtube.com/watch?v=yTnovf2jjlE

Simplifying radicals with variables video
www.youtube.com/watch?v=yHFYs_NQS4M

Simplifying radicals with variables video (another example)
​www.youtube.com/watch?v=F8wr7BXrPkM

Simplifying radicals worksheet (try problems #1, 2, 7, 8, 9, 10, 11, 12, 13, 14, 20, 25)
cdn.kutasoftware.com/Worksheets/Alg1/Simplifying%20Radicals.pdf

August 6

Mixture problems video example 1
www.youtube.com/watch?v=cxxdTshrM3k

Mixture problems video example 2
www.youtube.com/watch?v=9nQmEQk09ko

Mixture problems worksheet
Hint: Use the table to the right to help set up the problems.  The video links above used the same process, but set up the problems in just a slightly different way.  The math was the same, though.
cdn.kutasoftware.com/Worksheets/Alg1/Mixture%20Word%20Problems.pdf
Picture
This is the table we used to set up mixture problems.

Day 1

Intro to the vertex form of quadratics video
www.youtube.com/watch?v=_QqhuLixNEk

Graphing the vertex form of a quadratic video
www.youtube.com/watch?v=7QMoNY6FzvM

Vertex form of quadratics (try problems #15, 17, 19)
​cdn.kutasoftware.com/Worksheets/Alg2/Vertex%20Form%20of%20Parabolas.pdf

​Systems of equations (try #7, 8, 9, 10)
​cdn.kutasoftware.com/Worksheets/Alg1/Systems%20of%20Equations%20Word%20Problems.pdf

Day 2
​
Special right triangle video
www.youtube.com/watch?v=nVTtSE5nv7c

Special right triangles (page 1 only)
Hint: remember the ratios for a 30-60-90 triangle is x : x√3 : 2x (small leg : longer leg : hypotenuse)
and for a 45-45-90 triangle is is x : x : x√2 
​cdn.kutasoftware.com/Worksheets/Geo/8-Special%20Right%20Triangles.pdf

Graphing the vertex form of a quadratic (try problems #16, 18, 20)
cdn.kutasoftware.com/Worksheets/Alg2/Vertex%20Form%20of%20Parabolas.pdf

More with quadratics (try #12, 14, 15, 17)
​cdn.kutasoftware.com/Worksheets/Alg2/Properties%20of%20Parabolas.pdf

Day 3

​Distance Rate Time problems (try all odd problems)
cdn.kutasoftware.com/Worksheets/Alg2/Distance%20Rate%20Time%20Word%20Problems.pdf

​Completing the Square (try problems #2, 4, 6, 7, 16) 
​cdn.kutasoftware.com/Worksheets/Alg2/Quadratic%20Equations%20By%20Completing%20the%20Square.pdf

Day 4

Solving linear inequalities video
www.youtube.com/watch?v=0X-bMeIN53I

Solving linear inequalities (try problems #1, 3, 5, 7, 9, 11)
​cdn.kutasoftware.com/Worksheets/Alg1/Multi-Step%20Inequalities.pdf

Properties of Parabolas (try problems #8, 10, 12, 14)
cdn.kutasoftware.com/Worksheets/Alg2/Properties%20of%20Parabolas.pdf

July 30

Pythagorean Theorem Calculations

pleasanton.k12.ca.us/avhsweb/kiyoi/Algebra_Powerpoints/Pythagorean_Theorem.pdf

Pythagorean Theorem Word Problems (Answers are on the link below)
There are 4 problems on the first page.  Press "Next" to access the last 4 problems.  Please do all 8 problems.
betterlesson.com/lesson/resource/2998807/pythagorean-theorem-word-problems-pdf

Answers to the Questions Above
betterlesson.com/lesson/resource/2999040/key-pythagorean-theorem-word-problems-pdf

July 26

Mixture Problems (problems #1, 2, 5, 6, 7, 9, 11, 12)
​https://cdn.kutasoftware.com/Worksheets/Alg2/Mixture%20Word%20Problems.pdf

​
Solving Quadratics by Factoring (#1, 3, 5, 7, 9, 17)
cdn.kutasoftware.com/Worksheets/Alg2/Quadratic%20Equations%20By%20Factoring.pdf

Watch a proof of the Pythagorean Theorem
https://www.youtube.com/watch?v=r382kfkqAF4

July 24

Solving by completing the square (Problems #1, 3, 5, 8, 10, 15, 17)
​https://cdn.kutasoftware.com/Worksheets/Alg2/Quadratic%20Equations%20By%20Completing%20the%20Square.pdf
​
Practice proving the quadratic formula by completing the square (make sure you can do it in less than 3 minutes)

Review: Systems of Equations

http://imathworksheets.com/equation-worksheets/system-word-problems-1.pdf

Answers for the worksheet above can be found here (click on "View Answers" for worksheet 1):
http://imathworksheets.com/algebra-worksheets-page/systems-of-equations/elimination/word-problems/

July 23

Watch the video on how to solve distance - rate - time problems
https://www.youtube.com/watch?v=yCSAcjXO4tU

Distance Rate Time Problems (#7, 10)
https://cdn.kutasoftware.com/Worksheets/Alg1/Distance%20Rate%20Time%20Word%20Problems.pdf

Solving using the Quadratic Formula (#15 and 16)
Hint: If all the terms aren't all on one side, move them to one side so it is equal to 0 first.
https://cdn.kutasoftware.com/Worksheets/Alg2/Quadratic%20Formula.pdf

Properties of Parabolas (Page #9, 11, 13 only)
https://cdn.kutasoftware.com/Worksheets/Alg2/Properties%20of%20Parabolas.pdf

​Video on Galileo's discoveries of gravity's law (only watch from 27:00 until 33:40, but you can watch more if you want)
https://www.youtube.com/watch?v=8mve0UoSxTo

July 20 (weekend homework)

Properties of Parabolas (Page 1 only)
https://cdn.kutasoftware.com/Worksheets/Alg2/Properties%20of%20Parabolas.pdf

Watch the video on how to solve distance - rate - time problems
https://www.youtube.com/watch?v=yCSAcjXO4tU

Distance Rate Time Problems (# 2, 3, 5, 8, 9, 10)
https://cdn.kutasoftware.com/Worksheets/Alg1/Distance%20Rate%20Time%20Word%20Problems.pdf

Video on Galileo's discoveries of gravity's law (only watch from 27:00 until 33:40, but you can watch more if you want)
https://www.youtube.com/watch?v=8mve0UoSxTo

Solving using the Quadratic Formula (#1, 3, 7, 13, 15)
Hint: If all the terms aren't all on one side, move them to one side so it is equal to 0 first.
https://cdn.kutasoftware.com/Worksheets/Alg2/Quadratic%20Formula.pdf

​
Factoring Trinomials (#9, 11, 13, 15, 17)
https://cdn.kutasoftware.com/Worksheets/Alg1/Factoring%202.pdf

July 19

Properties of Parabolas (Page 1 only)
https://cdn.kutasoftware.com/Worksheets/Alg2/Properties%20of%20Parabolas.pdf

Factoring Trinomials (Even problems only)
https://cdn.kutasoftware.com/Worksheets/Alg1/Factoring%202.pdf

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