## Sunday, March 13, 2016

### Division M2 session on March 13, 2016

 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: Thinking in terms of equations Generalizing distributive property to arbitrary operators. Homework: Download PDF Note: There are some hints in the end of the file. Try to solve first without looking at them. Notes: You can access video resources at: https://www.artofproblemsolving.com/videos/prealgebraVideos related to today's session are the first four videos of chapter 1.

### Division M1 session on March 13, 2016

 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: Avoiding unnecessary computations.  Working out the problems step-by-step. Using mathematical vocabulary e.g. commutative property in explaining solution. Identity for addition. Homework: Read Section 1.1 and 1.2. Watch all of the videos for Section 1.1, 1.2, and 1.3 from https://www.artofproblemsolving.com/videos/prealgebra Solve all of the exercises and problems from Section 1.1 and 1.2 Notes: You can download the handout for Section 1.1 and 1.2 from http://aops-cdn.artofproblemsolving.com/products/prealgebra/exc1.pdf

## Thursday, March 10, 2016

### Feb 28, 2016—Math Contest

No classes—students participated in Math Contest. The winners were announced on March 6th:

M2: Basir, Omar
M1: Bilal M, Abdur-Rafay
E:   Abiha

### Division M1 session on March 6, 2016

 Instructor: Mr. Isa Hafalir, Mr. Zia Hydari Attendance: AbdulRafay, Adeel, Bilal, Remy, Sohaib, Areej Handout: Problems Solved in Class: MOEMS Volume 3 p. 73: 3C, 3D, and 3E MOEMS Volume 3 p. 74: 4D, 4E From the contest on Feb 28th:  1, 2, 4, 5, and 6. Concepts: Mean, median, mode. Percent change. Area. Congruent shapes. Student Difficulties: Homework: MOEMS Volume 3 p. 75 (all problems from Set 10 Olympiad 5). Due date is March 20th. Notes: