Summary
This topic covers the structure and calculation of numbers, including ordering integers, understanding the order of 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, 2.5
- Irrational Numbers — numbers that cannot be expressed as a fraction of two integers. Example: π, √2
- Order of Operations — rules that determine the sequence of operations in an expression. 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 that two or more numbers have in common. Example: HCF of 12 and 16 is 4
- Lowest Common Multiple (LCM) — the smallest multiple that two or more numbers share. Example: LCM of 6 and 10 is 30
- Powers — expressing a number as a base raised to an exponent. Example: 2^3 = 8
- Roots — the inverse operation of powers, finding a number that, when multiplied by itself a certain number of times, gives the original number. Example: √9 = 3
- Standard Form — a way of writing very large or very small numbers using powers of 10. Example: 4.2 x 10^5
Exam Tips
Key Definitions to Remember
- Integers are whole numbers, including negatives and zero.
- Rational numbers can be expressed as a fraction of two integers.
- Irrational numbers cannot be expressed as a fraction of two integers.
- Order of operations follows BIDMAS.
- Prime factors are the prime numbers that multiply to give the original number.
- HCF is the largest common factor of two numbers.
- LCM is the smallest common multiple of two numbers.
- Powers involve raising a number to an exponent.
- Roots are the inverse of powers.
- Standard form expresses numbers as A x 10^n.
Common Confusions
- Mixing up HCF and LCM.
- Incorrectly applying the order of operations.
- Confusing rational and irrational numbers.
Typical Exam Questions
- What is the HCF of 24 and 36? Answer: 12
- Write 0.00042 in standard form. Answer: 4.2 x 10^-4
- Simplify 2^3 x 2^2. Answer: 2^5 or 32
What Examiners Usually Test
- Ability to correctly order operations in complex expressions.
- Understanding of prime factorization and its applications.
- Conversion between standard form and ordinary numbers.
- Calculation of HCF and LCM using prime factors.