Study Notes
This topic covers the structure and calculation of numbers, including ordering integers, understanding operations, and working with powers and roots.
- Integers — whole numbers that can be positive, negative, or zero. Example: -3, 0, 2
- Rational Numbers — numbers that can be expressed as a fraction of two integers. Example: 1/2, 2.5, 0.666...
- Irrational Numbers — numbers that cannot be expressed as a fraction of two integers. Example: π, √2
- Order of Operations — rules that define the sequence to solve expressions. Example: Brackets, Indices, Division, Multiplication, Addition, Subtraction (BIDMAS)
- Prime Factors — expressing a number as a product of its prime numbers. Example: 36 = 2 x 2 x 3 x 3
- Highest Common Factor (HCF) — the largest factor shared by two numbers. Example: HCF of 12 and 16 is 4
- Lowest Common Multiple (LCM) — the smallest multiple shared by two numbers. Example: LCM of 6 and 10 is 30
- Powers and Roots — powers are repeated multiplications, roots are inverse operations. Example: 2^3 = 8, √9 = 3
- Standard Form — a way to express large numbers using powers of 10. Example: 3.2 x 10^6
Exam Tips
Key Definitions to Remember
- Integers
- Rational Numbers
- Irrational Numbers
- Order of Operations
- Prime Factors
- Highest Common Factor
- Lowest Common Multiple
- Powers and Roots
- Standard Form
Common Confusions
- Mixing up rational and irrational numbers
- Incorrect order of operations
- Misidentifying prime factors
Typical Exam Questions
- What is the HCF of 12 and 16? Answer: 4
- Write 56,700,000 in standard form? Answer: 5.67 x 10^7
- Simplify 2^5 ÷ 2^3? Answer: 2^2
What Examiners Usually Test
- Ability to order and calculate with integers
- Understanding and applying the order of operations
- Identifying and using prime factors
- Calculating HCF and LCM
- Converting numbers to and from standard form