Module 1
Negative numbers & sequences
Quick-reference revision notes for parents.
1.1 Ordering negative numbers
On a number line, numbers get smaller as you go left and larger as you go right. Think of temperature: −10°C is colder (smaller) than −2°C.
−7 < −3 (−7 is smaller)
−1 > −4 (−1 is bigger)
0 > −5
1.2 Adding and subtracting
When two signs sit next to each other they combine into one. This is the bit students get wrong most often.
| What you see | What it becomes |
|---|---|
| + (−) | subtract |
| − (−) | add |
| + (+) | add |
| − (+) | subtract |
5 + (−3) = 5 − 3 = 2
7 − (−4) = 7 + 4 = 11
−6 + 2 = −4
−3 − 5 = −8
Don't confuse −3 − 5 (which is −8) with −3 − (−5) (which is +2). The brackets matter.
1.3 Multiplying and dividing
One simple rule: same signs → positive, different signs → negative. Works for both × and ÷.
−4 × 3 = −12
−5 × −2 = +10
−20 ÷ 4 = −5
−18 ÷ −6 = +3
"Same signs, smiley face. Different signs, frowny face." Same → positive, different → negative.
1.4 Arithmetic sequences
An arithmetic sequence adds (or subtracts) the same amount each time. That amount is called the common difference.
Example: 3, 7, 11, 15, 19... has a common difference of +4.
Finding the nth term
- Find the common difference (d)
- Start your formula as dn + something
- Work out the "something" by checking term 1
Common difference = 4, so start with 4n.
When n = 1: 4(1) = 4, but the first term is 3, so subtract 1.
nth term = 4n − 1
Check with n = 2: 4(2) − 1 = 7 ✓
1.5 Other sequences
Not every sequence adds the same amount. Worth recognising the common types.
Quick reference
- Two minuses next to each other become a plus
- Same signs (× or ÷) → positive
- Different signs (× or ÷) → negative
- nth term formula = (common difference × n) + adjustment