Ch.20 HW Review

Ch.21 Triangles

Thanks for everyone’s participation in class! Do not forget to turn in your HW by 4/11 night.

Look forward to meeting you all on 4/19! We will learn Ch.22 then!

lilijia Post in SAT math，

05
April
2020

Comments Off on SAT Math 4/5

Ch.20 HW Review

Ch.21 Triangles

Thanks for everyone’s participation in class! Do not forget to turn in your HW by 4/11 night.

Look forward to meeting you all on 4/19! We will learn Ch.22 then!

lilijia Post in AOPS_Counting_Probability，

05
April
2020

Comments Off on AoPS Number Theory Ch.8 Base Number System

**Lesson review**

- A
**numeral**is a representation of a number. **Base number systems****Base**(radix, or scale)

**Homework**

- p.142 Ex.8.2.1(a) (d)
- p.145 Ex.8.3.1(b), 8.3.2(c), 8.3.3, 8.3.6(a)(d)(g)
- p.148 Ex.8.4.2
- p.152 Ex.8.5.2(a)(c), 8.5.3(a), 8.5.4
- P158 Ex.8.6.2 (a,c,d,e), 8.6.4
- p160 Ex.8.23

- Ex. 8.6.2, please use a “smart” way to convert. For example, from 3^2 to 3, from 2^4 to 2, from n to n-1, try to think about the methods we explained in the class.
**Extra Resources**

- https://www.khanacademy.org/math/algebra-home/alg-intro-to-algebra/algebra-alternate-number-bases/v/number-systems-introduction
- https://www.youtube.com/watch?v=nEBKpX8JZ04
- https://www.youtube.com/watch?v=jxC7_0dqHT4
- https://www.mathsisfun.com/numbers/bases.html
- https://betterexplained.com/articles/numbers-and-bases/

***Another way to determine Perfect/Abundant/Deficient Number **

Thanks to Jason’s Daddy’s sharing!

for example, 300 = 2^2 × 3 × 5^2.

The **sum of **all positive divisors of 300

=**(4+2+1)x(3+1)x(25+5+1) **

=7x4x31=868 > 2 x 300.

Therefore 300 is abundant.

**See you next next Sunday!**

According to NCLS calendar, there is no school next week (4/12).

Please take care and stay healthy!

We are going to learn Ch.9 Base Number Arithmetic on 4/19.

lilijia Post in AOPS_Counting_Probability, AoPS_Number_Theory, SAT math，

04
April
2020

Comments Off on Free online class

Thanks to Jason’s Dad for sharing, here is the link to a free online math class: https://momentumlearning.org/free_classes/

- Session 1: Polynomials [Andrew Cai – Recorded Video]
- Session 2: Sequences and Series [Justin Yu]
- Session 3: Permutations and Combinations [Andrew Cai – Recorded Video]
- Session 4: Angle Chasing [Luke Robitaille – Recorded Video]
- Session 5: Similarity [Benjamin Wright – Recorded Video]
- Session 6: Number Theory

Session 1 Recording: https://youtu.be/AW0qmIKH_Yc

Session 3 Recording: https://www.youtube.com/watch?v=I-tNKk-WqpM

Session 4 Recording: https://www.youtube.com/watch?v=UptxaTDsBLE

Session 5 Recording: https://www.youtube.com/watch?v=y9S676d7UNM

Enjoy and have fun!

lilijia Post in AoPS_Number_Theory，

30
March
2020

Comments Off on AoPS_Number Theory_ Ch.7 Algebra with Integers

** Lesson Review**

- A generalized form of a group of numbers is an algebraic expression common to all of the numbers in the group.
- Parameters: the variables that dictate the values of generalized expressions
- Algebraic factorization

**Homework**

p.136-137

- Ex. 7.10 to 7.13
- Ex. 7.16, 7.17
- Ex. 7.20 to 7.23
- Ex. 7.27

Sorry that the connection from my laptop to my “Tiny Blackboard” failed to work today☹ However, we had great fun playing Kahoot! I will redesign more Kahoot! Game in our future class.

Please remember to turn in the weekly homework by each Saturday night at 10:00 pm in Google Classroom. Next week we will learn Ch.8 Base Number Systems. Take care and see you then!

lilijia Post in SAT math，

30
March
2020

Comments Off on SAT Math Ch.20 Angles

Lesson review

**Lesson Review: **

1. Ch. 18 Complex Number + Ch. 19 Absolute Value HW review

2. Ch. 20 Angles

- Exterior Angle Theorem: x = a+b
- Parallel lines
- Vertical angles (congruent)

- Alternate interior angles (congruent)

- Corresponding angles (congruent)

- Same side interior angles (supplementary)

- Polygons
- the sum of interior angles = 180°(n-2)

- the sum of exterior angles = 360°

**Homework: **

1. Chapter 20 Exercise (Page 166-169)

2. In Google Classroom – Classwork, please type the # of questions in the Chapter Exercise that you made mistakes, or the ones that you would love Ms. Li to explain in our next class. Due 4/4 Saturday 11:59 pm.

**Other Resources:**

- https://www.mathsisfun.com/geometry/parallel-lines.html
- https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/sum-of-interior-angles-of-a-polygon
- https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/sum-of-the-exterior-angles-of-convex-polygon

We played the Kahoot! game today in class. It’s great fun! And I am so happy to see someone used “I love math” as her nickname 😛 Yes, I believe passion can lead you to learn math well!

Due to the property of the online class, I have decided to cancel our Midterm Exam (but we will keep our Final Exam at the end of the semester). Next week we are going to learn Ch. 21 Triangles. See you then!

lilijia Post in AoPS_Number_Theory，

23
March
2020

Comments Off on AoPS_Number Theory_Ch.6 Special Numbers

**Lesson Review**

- A Mersenne prime: 2^p-1 (p: prime number)
- A Fermat prime: 2^2n +1 (n: nonnegative integer)
- Twin primes: a pair of primes that differ by 2
- n factorial: n!=n(n-1)(n-2)…2*1
- a palindrome: an integer that reads the same forward as it does backward.

**Homework**

- p.109 Ex. 6.2.1, 6.2.2
- p.113 Ex. 6.3.2 to 6.3.5, 6.3.7
- p.115 Ex. 6.4.4 (6.4.1 classwork)
- p.118 Ex. 6.5.1 to 6.5.3
- p.120 Ex. 6.26*

**Other Resources**

- https://mathworld.wolfram.com/TwinPrimes.html
- https://byjus.com/maths/perfect-numbers/
- https://www.mathsisfun.com/definitions/palindromic-numbers.html
- https://nrich.maths.org/2574

**Something Else**

Please join our Google Classroom (Code: mtl4kzb). Students should turn in the weekly homework by each Saturday night at 10:00 pm.

Take care and look forward to seeing you all next Sunday. We will learn Ch.7 Algebra with Integers.

lilijia Post in SAT math，

23
March
2020

Comments Off on SAT-Math Chapter 18,19

**Lesson Review:**

1. Chapter 18 Complex Number

2. Chapter 19 Absolute Value

**Homework: **

1. Join Google Classroom (Class code: yzdaetx)

2. Chapter 18+19 Exercise (Page 154-155, 159-161)

Please type the # of questions in the Chapter Exercise that you made mistakes, or the ones that you would love Ms. Li to explain in our next class. Due 3/28 Saturday 11:59 pm.

**Other Resources:**

- https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:complex/x2ec2f6f830c9fb89:complex-num/a/intro-to-complex-numbers
- https://www.khanacademy.org/math/arithmetic/arith-review-negative-numbers/arith-review-abs-value/a/intro-to-absolute-value
- https://www.khanacademy.org/math/algebra-home/alg-absolute-value/alg-absolute-value-equations/v/absolute-value-equations

It’s great working with all of you today. I appreciate everyone’s participation in the Zoom activities! Next week we are going to learn Ch. 20 Angles. See you then!

lilijia Post in AoPS_Number_Theory，

16
March
2020

Comments Off on AoPS_Number Theory_Ch.5 Divisor Problems

**Lesson Review**

- formula to find the t (n) number of positive divisors of a positive number n
- A proper divisor of a positive integer is any divisor of other than. itself
- Any positive perfect square has an odd number of positive divisors;
- If m and n are any two positive integers such that gcd(m,n)=1, then t(mn)=t(m)*t(n)
- product of the positive divisors of a positive integer n: Pn=N^(t(n)/2)

**Homework**

- P.92 Ex 5.2.1(e)(f)(i)(l); 5.2.3
- P.98 Ex 5.3.1, 5.3.4, 5.3.7, 5.3.9
- P.101 Ex 5.4.3, 5.4.4, 5.4.6
- P.104 Ex 5.17
- P.105 Ex 5.21, *5.26, *5.27

**Other Resources**

- https://www.math.upenn.edu/~deturck/m170/wk2/numdivisors.html
- http://mathonline.wikidot.com/the-number-of-positive-divisors-of-an-integer
- https://www.youtube.com/watch?v=Be5fd7h4aQo
- https://www.youtube.com/watch?v=IeyVdRHOPzc

Ch.5 is not easy. If you have any questions, please feel free to reach out and Ms. Li will be happy to help. Remember to turn in your homework by next Sat night, so that I can grade and give it back to you before our class. Next week, we will spend some time discussing the leftover problems in Ch.5.

Take care and look forward to learning Ch. 6 with all of you next Sunday.

lilijia Post in SAT math，

16
March
2020

Comments Off on SAT-Math Chapter 17: Synthetic Division

**Lesson Review:**

1. Chapter 16 HW review (see pictures attached)

2. Chapter 17 Synthetic Division(see pictures attached)

**Homework: **

1. Corrections of Chapter 16 Exercise

2. Chapter 17 Exercise (Page 150-151)

**Other Resources:**

lilijia Post in AoPS_Number_Theory，

08
March
2020

Comments Off on AoPS_Number Theory_Ch 4 Prime Factorization

**Lesson review:**

- factor tree
- prime factorization
- rational numbers
- lowest form (reduced form) vs. unreduced form
- gcd (a,b)
- lcm [a,b]
- ab = gcd (a,b)*lcm [a,b]
- gcd(a
*c*,b*c*) =*c*gcd (a,b) - lcm [a
*c*,b*c*] =*c*lcm [a,b]

**Homework:**

- P.68 Ex.4.2.1 (b) (k) (p)
- P.71 Ex.4.3.2, 4.3.4
- P.74 Ex.4.4.1 (b) (f), 4.4.2 (b) (d)
- P.77 Ex.4.5.1 (d) (e) (g) (h)
- P.79 Ex.4.6.1, 4.6.5
- p.83 Ex.4.7.1
4.7.4*to* - * bonus: p.86 Ex. 4.36, 4.37, 4.38, 4.39

**Other Resources:**