Integers — Edexcel International GCSE Mathematics A
1. Core Integer Definitions and Ordering ★☆☆☆☆ ⏱ 5 min
Integers follow standard place value rules, where each digit's value depends on its position (units, tens, hundreds, thousands etc.). When ordering integers: negative numbers are smaller the further they are from zero, while positive numbers are larger the further they are from zero.
Exam tip: Double-check the order of negative integers: a very common error is writing $-2$ before $-9$ when sorting from smallest to largest.
2. Operations with Directed Integers ★★☆☆☆ ⏱ 5 min
- Adding a negative number = subtracting a positive number: $3 + (-2) = 3 - 2 = 1$
- Subtracting a negative number = adding a positive number: $5 - (-3) = 5 + 3 = 8$
- Multiplying/dividing two numbers with the same sign gives a positive result
- Multiplying/dividing two numbers with different signs gives a negative result
3. Order of Operations (BIDMAS) ★★★☆☆ ⏱ 5 min
Exam tip: Never calculate left to right without following BIDMAS: this is one of the most common sources of avoidable mark loss in arithmetic questions.
4. Prime Numbers, Factors and Multiples ★★☆☆☆ ⏱ 5 min
- **Even number**: Integer divisible by 2 (ends in 0, 2, 4, 6, 8)
- **Odd number**: Integer not divisible by 2 (ends in 1, 3, 5, 7, 9)
- **Prime number**: Positive integer with exactly two distinct positive factors (1 and itself; 1 is not prime)
- **Factor**: Integer that divides another integer exactly with no remainder
- **Multiple**: Product of an integer and any positive whole number
Common Pitfalls
Why: Assuming larger digit values mean larger numbers for negative integers
Why: Treating subtraction of a negative as subtraction of a positive
Why: Misremembering the prime number definition as 'number only divisible by 1 and itself' without the 'exactly two distinct factors' requirement
Why: Ignoring BIDMAS order of operations
Why: Misapplying sign rules for multiplication of directed numbers