Study Notes
Number theory involves understanding the properties and relationships of numbers, including divisibility, prime factorization, and congruence. It also covers modular arithmetic and its applications.
- Natural Numbers — Numbers used for counting, starting from zero. Example: 0, 1, 2, 3, 4, 5...
- Integers — All whole numbers, including positive, negative, and zero. Example: -3, 0, 4
- Prime Numbers — Numbers that have only two factors: 1 and themselves. Example: 2, 3, 5, 7
- Square Numbers — Numbers that are the product of a number multiplied by itself. Example: 1, 4, 9, 16
- Cube Numbers — Numbers that are the product of a number multiplied by itself twice. Example: 1, 8, 27
- Triangular Numbers — Numbers that can form an equilateral triangle. Example: 1, 3, 6, 10
- Rational Numbers — Numbers that can be expressed as a fraction of two integers. Example: 1/2, 3/4
- Irrational Numbers — Numbers that cannot be expressed as a simple fraction. Example: π, √2
Exam Tips
Key Definitions to Remember
- Natural Numbers: Counting numbers starting from zero.
- Integers: Whole numbers, positive, negative, or zero.
- Prime Numbers: Numbers with only two factors, 1 and themselves.
- Square Numbers: Numbers that are squares of integers.
- Cube Numbers: Numbers that are cubes of integers.
Common Confusions
- Confusing prime numbers with odd numbers.
- Misunderstanding the difference between rational and irrational numbers.
Typical Exam Questions
- From the list of numbers, write down a prime number? Example: From 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, the prime number is 83.
- Write 6.39 ✕ 10^-2 as an ordinary number? Answer: 0.0639
- Write down an irrational number between 3 and 4? Example: √10
What Examiners Usually Test
- Understanding of different types of numbers and their properties.
- Ability to identify prime, square, and cube numbers.
- Application of number theory concepts in problem-solving.