Momentum Learning Contest Math Advanced Level 2
Welcome to our contest math summer camp, where we delve into more challenging mathematical concepts beyond typical school curriculum. Our program is designed to cultivate a deeper understanding of mathematical principles and enhance problem-solving abilities in students.
This camp is for students who want to improve their performance on higher level competitions such as AMC 10, AMC 12, AIME, National Level MATHCOUNTS.
Contest Math Advanced Level 2
- Prerequisite: AIME Qualifier or completion of CM500 or CM501
Fee: $1,099 - Homework: Throughout the camp sessions, the instructor will tackle various example questions. It’s crucial that students thoroughly review and actively engage with any unanswered questions from each session, every day of the camp.
Online
Advanced Level 2
Geometry
Instructor: Michelle Nal
Dates: July 22 – August 2 (M-F)
Time: 1 – 4:30PM CT
All instructional materials from the camp, including recorded sessions, will remain accessible for an additional three months following the conclusion of the camp. Zoom and Canvas platforms will be utilized for delivery and access to these resources.
Advanced Level 2 – Number Theory
Algebra
- Manipulating algebraic expressions and identities
- Graphing special functions
- Polynomials (Vieta formulas, Rational root theorem, Factor theorem)
- Complex numbers
- Sequences and series
Number Theory
- Basics: Divisibility, LCM/GCD, Factorization
- Decimals and number bases
- Modular arithmetic (Solving system of congruences, Chinese Remainder theorem)
- Powers of primes (Fermat’s little theorem, Euler’s totient function and Euler’s theorem)
- Solving simple Diophantine equations (Introduction to Pell-type equations)
Advanced Level 2 – Algebra
- Advanced System of Equations
- Algebraic Number Theory
- Identities, Manipulations
- Polynomials and Complex Numbers
- Vieta formulas
- Rational root theorem and factor theorems
- Four operations in the complex plane
- Functions
- Piecewise defined and periodic functions
- Absolute value; Floor function
- Logarithmic and exponential functions
- Graphing functions
Advanced Level 2 – Geometry
Geometry (Week 1)
- Similarity and congruence of triangles
- Circles; Cyclic quadrilaterals; Ptolemy theorem
- Power of a point
- Law of Sines; Law of Cosines
- Coordinates; Solid geometry
Geometry (Week 2)
- Mass Point Geometry
- Area
- Coordinate Geometry
Advanced Level 2 – Combinatorics
Combinatorics (Week 1)
- Principle of Inclusion and Exclusion
- Constructive Counting
- Recursion
- Recursive Sequences
- Fibonacci, Catalan Numbers
- Stirling Numbers of 1st and 2nd Kind
- Probability
- Geometric Probability
- Conditional Probability
Combinatorics (Week 2)
- Casework, Complementary, and Constructive counting
- Distribution and partition problems
- Counting by 1-1 correspondences
- Combinatorial identities (Pascal, Hockey Stick and Vandermonde identities
- Probability; geometric probability; conditional probability
FAQ
Will summer camp cover the same material as spring and fall semesters?
There could be some overlap in topic coverage. However, most of the questions addressed in the camp will differ from those in our spring/fall classes.
Mastering contest math concepts typically requires multiple reinforcement opportunities. Each subsequent encounter with the same topics not only deepens students’ understanding but also progressively enables them to apply these concepts independently. It is unrealistic to expect students to fully grasp a concept and proficiently apply it after being exposed to it only once or twice.
Will there be homework assigned daily?
During the camp sessions, the instructor will present various example questions. Initially, students will be given 2-3 minutes to attempt solving the question. Subsequently, the instructor will solve the question and discuss its implications. It’s typical for students not to fully solve the questions within the allotted time. Therefore, the homework is for students to review and actively tackle all questions they didn’t complete during each day’s camp session.
Remember: You cannot claim to know how to solve a question unless you independently work through it without assistance.
Note: $40 annual registration fee per student (Fall 2023 – Summer 2024)