M2: https://goo.gl/17XRbN
Postscript: AMC 8 Prep Sessions during Fall 2016
Instructor:
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Mr. Ahmed Hefny
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Attendance:
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Adan, Omar, Areej
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Handout:
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Pre-Algebra Chp 2
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Problems Solved in Class:
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Chosen exercises from chapter 2
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Concepts:
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* Definition of exponent
* Properties of exponent:
- Not commutative
- Not associative (default order is top to bottom)
- Does not distribute over addition
- Distributes over base multiplication (ab)^c = a^c * b^c
- 1 is a "right identity" element.
* (a+b)^2 = a^2 + b^2 + 2ab. It can be proven using distributive property.
* Negative powers.
* 0th Power.
* Powers of 0.
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Student Difficulties:
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. Students still have difficulties using variables to prove general statements.
. A problem that took un expected long time is showing that:
(2a+2b)^m = 2^m (a+b)^m
Students had trouble figuring out that this is a simple application of distributive properties.
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Homework:
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· Chapter 2: Please watch teh videos and make sure you can solve example problems.
. Solve exercises: 2.1.2, 2.1.5, 2.1.9, 2.2.6, 2.2.10, 2.2.11, 2.4.6
. Solve review exercises: 2.45, 2.50. 2.76
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Notes:
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Instructor:
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Mr. Zia Hydari
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Attendance:
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AbdulRafay, Sohaib, Abiha, Abdul
Qadir, Adeel, Rami, Kamal
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Handout:
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Problems Solved in Class:
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Problems illustrating the
distributive property
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Concepts:
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Operators, distributive property
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Student Difficulties:
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Using variables to prove
properties e.g. if the operator “@” is defined as:
a @ b = 2a + 2b
and I asked students to prove that
“@” is commutative, the students used specific numbers to create examples but
did not use variables to construct a general proof.
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Homework:
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·
Read
Section 1.1, 1.2, and 1.3
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Watch
all of the videos for Section 1.1, 1.2, and 1.3 from https://www.artofproblemsolving.com/videos/prealgebra
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If
you need more help, please watch the following videos and work through the
online exercises at:
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Solve
all of the exercises and problems from Section 1.1, 1.2, and 1.3
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Solve
problem 1.71 on page 51. Then solve these additional items:
1.
Does
multiplication distribute over “@”?
2.
Does
addition distribute over “@”?
3.
Does
“@” distribute over addition?
4.
Does
“@” distribute over multiplication?
HINT: First, try to solve on your
own; then use the hint below. Recall that problem 1.71 in the book defines the
operator “@” as:
a @ b = 2a + 2b
Part 1 asks if the following is
true: a ( b @ c) = ab @ ac
Part 2 asks if the following is
true: a + (b @ c) = (a + b) @ (a +
c)
Part 3 asks if the following is
true: a @ (b + c) = (a @ b) + (a @ c)
Part 4 asks if the following is
true: a @ bc = (a @ b) (a @ c)
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Notes:
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Instructor:
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Mr. Zia Hydari
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Attendance:
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AbdulRafay, Sohaib, Abiha
(Abdul Qadir?, Adeel?, Rami?,
Kamal?)
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Classwork:
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Problems illustrating the
distributive property
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Homework:
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All problems from Section 1.3
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Instructor:
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Mr. Isa Hafalir
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Attendance:
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AbdulRafay, Abiha, Rami
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Classwork and Homework
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In the first half, we did Pre-Algebra book Section 1.3 and exercises 1.3.5 to 1.3.11 were assigned as
homework.
In the second half, we went over
Set 10 Olympiad 5 and Set 11 Olympiad 1.
5 questions in Set 11 Olympiad 2
were assigned as homework.
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Instructor: | Mr. Ahmed Hefny |
Attendance: | Ayan, Adan, Areej, AbdulRafay, Bilal, Baseer, Omar |
Handout: | Pre-Algebra Chapter 1 |
Problems Solved in Class: | * Probability problems: throwing a die and drawing from a deck of cards. * Disproving false statements about properties of operators: commutative and associative properties of subtraction, addition distributes over multiplication. |
Concepts: | [Session 1] A brief introduction to probability:* Probability and statistics are two opposite inference paths; probability tells us, given knowledge about a random process, how to answer questions related to samples from that process. [Ex: what is the probability of getting 3 heads in a row if I throw a fair coin three times ?]. Statistics tells us, given a sample from the random process, how to gain knowledge about that process. [Ex: Given a sample of 10000 voters, how much is the American community biased towards Republicans ?] * Basic probability laws and the conditions for their correctness: Let A and B be two conditions (usually called events) - P(A) = # of outcomes that satisfy A / # of all possible outcomes [Assuming all outcomes are equally likely] - P(A and B) = P(A)P(B) [iff A and B are independent] - P(A and B) = P(A)P(B|A) [P(B|A) is the probability of B happening given that A happened. P(B|A) = P(B) iff A and B are independent]- P(A or B) = P(A) + P(B) [iff A and B are disjoint i.e. A and B cannot happen together]- P(A or B) = P(A) + P(B) - P(A and B) [This is the same inclusion-exclusion principle for counting the union of two sets] [Session 2] Pre-algebra: - Commutative property- Associative property - Distributive property - Disproving a property by a counter-example - Negation vs subtraction. Negation is a unary operator (takes one number) and gives its negative. Subtraction is a binary operator (takes two numbers) and returns the difference. They happen to use the same symbol '-' but they are different things. |
Student Difficulties: |
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Homework: |
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Notes: | You can access video resources at: https://www.artofproblemsolving.com/videos/prealgebra Videos related to today's session are the first four videos of chapter 1. |
Instructor: | Mr. Zia Hydari |
Attendance: | AbdulRafay, Sohaib, Abiha, Abdul Qadir (not present: Adeel, Rami, Kamal) |
Handout: | Pre-Algebra http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf |
Problems Solved in Class: | All exercises from section 1.2. |
Concepts: | Commutative, associative, and identity for addition operator |
Student Difficulties: |
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Homework: |
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Notes: | You can download the handout for Section 1.1 and 1.2 from http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf |