## CEMC Pascal, Cayley, Fermat Contests: Key Concepts

The Centre for Education in Mathematics and Computing (CEMC) Pascal, Cayley, and Fermat Contests are designed to challenge students' mathematical problem-solving skills. These contests cover various mathematical concepts and problem-solving strategies. Here are key concepts commonly encountered in the CEMC Pascal, Cayley, and Fermat Contests:

## 1. Number Theory:

### 1. Divisibility:

- Understanding rules of divisibility and applying them to problem-solving.

### 2. Prime Numbers:

- Identifying and working with prime numbers.

### 3. Modular Arithmetic:

- Solving problems involving modular arithmetic and congruences.

## 2. Algebra:

### 1. Equations and Inequalities:

- Solving equations and inequalities involving integers, fractions, and variables.

### 2. Functions:

- Understanding properties of functions and their graphical representations.

### 3. Polynomials:

- Factoring polynomials, polynomial operations, and solving polynomial equations.

- Applying methods to solve quadratic equations.

## 3. Geometry:

### 1. Euclidean Geometry:

- Understanding properties and theorems related to angles, triangles, circles, and polygons.

### 2. Coordinate Geometry:

- Applying coordinate geometry concepts to solve problems.

### 3. Transformation Geometry:

- Understanding transformations such as translations, rotations, reflections, and dilations.

## 4. Combinatorics:

### 1. Counting Principles:

- Understanding fundamental counting principles, including permutations and combinations.

### 2. Probability:

- Solving probability problems and understanding concepts like conditional probability.

## 5. Computation and Logic:

### 1. Number Systems:

- Working with different number systems, including binary and hexadecimal.

### 2. Logic and Reasoning:

- Solving problems involving logical reasoning, puzzles, and deductions.

## 6. Trigonometry:

### 1. Basic Trigonometric Ratios:

- Understanding and applying sine, cosine, and tangent ratios.

### 2. Trigonometric Identities:

- Using trigonometric identities to simplify expressions and solve equations.

## 7. Series and Sequences:

### 1. Arithmetic Sequences:

- Understanding and working with arithmetic sequences.

### 2. Geometric Sequences:

- Understanding and working with geometric sequences and series.

## 8. Calculus Concepts (Fermat Contest):

### 1. Limits and Continuity:

- Understanding the concept of limits and continuity.

### 2. Derivatives:

- Calculating derivatives and understanding their applications.

### 3. Integration:

- Understanding the concept of integration and applying integration techniques.

These key concepts are foundational for success in the CEMC Pascal, Cayley, and Fermat Contests. Students preparing for these contests should focus on developing a strong understanding of these mathematical topics and honing their problem-solving skills. Additionally, practicing with past contest papers and reviewing solutions can be valuable in familiarizing oneself with the contest format and refining problem-solving techniques.