Study Notes
Set notation is used to describe different groups of numbers, each with unique properties.
- Natural Numbers — numbers used for counting. Example: 1, 2, 3, 4, 5, 6...
- Prime Numbers — numbers that have only two factors: 1 and themselves. Example: 2, 3, 5, 7, 11
- Square Numbers — numbers that are the product of a natural number multiplied by itself. Example: 1, 4, 9, 16, 25
- Integers — whole numbers that can be positive, negative, or zero. Example: -5, -4, 0, 1, 2
- Rational Numbers — numbers that can be expressed as a fraction of two integers. Example: -13/4, 1/8, 2/3
- Irrational Numbers — numbers that cannot be expressed as a simple fraction. Example: π, √2, √3
- Real Numbers — all numbers on the number line, including rational and irrational numbers. Example: -5, 0, 1, π, √2
Exam Tips
Key Definitions to Remember
- Natural Numbers: numbers used for counting
- Prime Numbers: numbers with only two factors, 1 and themselves
- Square Numbers: numbers that are the product of a natural number multiplied by itself
- Integers: whole numbers, positive, negative, or zero
- Rational Numbers: numbers that can be expressed as a fraction
- Irrational Numbers: numbers that cannot be expressed as a simple fraction
- Real Numbers: all numbers on the number line
Common Confusions
- Confusing prime numbers with composite numbers
- Mixing up rational and irrational numbers
- Forgetting that zero is an integer
Typical Exam Questions
- What is a prime number? A number with only two factors: 1 and itself
- Give an example of a square number. 16 (since 4 x 4 = 16)
- Are all integers rational numbers? Yes, because they can be expressed as a fraction with a denominator of 1
What Examiners Usually Test
- Ability to identify different sets of numbers
- Understanding of the properties of each number set
- Application of set notation in solving problems