Summary
The topic covers the structure and calculation of numbers, including ordering integers, understanding operations, and working with prime numbers, factors, multiples, powers, roots, and standard form.
- 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, 0.75
- 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 or more numbers. Example: HCF of 12 and 16 is 4
- Lowest Common Multiple (LCM) — the smallest multiple shared by two or more numbers. Example: LCM of 6 and 10 is 30
- Powers — repeated multiplication of a number by itself. Example: 2^3 = 2 x 2 x 2
- Roots — the inverse operation of powers. Example: √9 = 3
- Standard Form — a way to express large numbers using powers of ten. 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 (HCF)
- Lowest Common Multiple (LCM)
- Powers and Roots
- Standard Form
Common Confusions
- Mixing up HCF and LCM
- Incorrect order of operations
- Misplacing the decimal in standard form
Typical Exam Questions
- What is the HCF of 18 and 24? Answer: 6
- Convert 0.00042 to standard form. Answer: 4.2 x 10^-4
- Simplify 2^3 x 2^2. Answer: 2^5
What Examiners Usually Test
- Ability to order and calculate with integers and rational numbers
- Understanding and applying the order of operations
- Finding HCF and LCM using prime factorization
- Converting between standard form and ordinary numbers