Advanced Math & Competition Math Course

Course Overview

This course is designed for students who aim to excel in advanced mathematics and prepare for North American and Canadian math competitions. It combines the rigorous curriculum of Singapore Math and American Math standards with specialized training for math competitions like the AMC (American Mathematics Competitions), CEMC (Canadian Mathematics Competition), and other national/international contests.

1. Key Focus Areas

Problem Solving Skills: Focus on the Singapore Math approach of model drawing and heuristic problem-solving methods.

Algebra & Geometry: Advanced concepts in algebra, including quadratic equations, inequalities, and geometricproofs. 

Number Theory: Introduction to concepts such as prime numbers, divisibility rules, and modular arithmetic. Trigonometry & Calculus (for higher grades): Prepare students for advanced calculus concepts, including limits, derivatives, and integrals. 

Critical Thinking: Emphasize logical reasoning, analytical skills, and creative problem-solving. 

Canadian & North American Math Competition Preparation:

Competition Strategies: Learn strategies for time management, multiple-choice tricks, and problem interpretation for competitions like AMC and CEMC. 

Past Competition Problem Practice: Work through previous math competition problems to understand the format, types of questions, and difficulty levels. 

Speed & Accuracy: Focus on solving complex problems within a limited timeframe, improving both speed and precision. 

Advanced Topics:

Combinatorics: Study advanced counting methods, permutations, combinations, and probability. 

Graph Theory: Introduction to graph theory and its applications in competition problems. 

Advanced Geometry: Study advanced topics in Euclidean and coordinate geometry, including conic sections and transformations.

Inequalities & Sequences: Learn advanced concepts related to mathematical inequalities, sequences, and series.

2. Course Breakdown by Section

Week 1-4:

Introduction to Advanced Algebra and Geometry

Solving Word Problems Using the Singapore Math Model

Basics of Number Theory and Divisibility

Introduction to Past Math Competition Questions (AMC, CEMC)

Week 5-8:

Advanced Problem Solving with Combinatorics and Probability

Speed Drills for Arithmetic and Algebra

Practice with Geometry and Trigonometry Problems

Mock Math Competitions

Week 9-12:

Focus on Past Competitions: AMC, CEMC, Math Olympiad

Advanced Topics: Inequalities, Sequences, and Graph Theory

Final Mock Competition and Review

One-on-One Feedback and Strategy Development

3.Test-Taking & Competition Strategies

Time Management: Learn to prioritize problems, identify easier vs. harder questions, and allocate time wisely. Efficient Problem Solving: Techniques for breaking down complex problems and solving them step-by-step. Handling Pressure: Build mental toughness and confidence for high-stakes exams and competitions.

4. Study Materials

Competition Papers: Provide access to previous AMC, CEMC, and other competition papers for practice. Advanced Math Workbooks: Singapore Math and American Math problem sets. Online Resources: Recommend apps and websites for additional math practice (e.g., AoPS for advanced problem

solving). 

5. Progress Monitoring & Assessments

Weekly Problem Sets: Regular homework to reinforce skills learned in class. Mock Competitions: Simulate real competition environments and assess student performance.

Individual Feedback: Provide personalized advice and strategies based on mock test performance