Why Number?
On Foundation tier, the Number topic carries the largest weighting on the paper. Get fluent here and you've banked the easy marks before anything difficult comes along.
This deck covers the five skills you'll see every series: ordering, BIDMAS, primes & factors, powers and standard form.
Spec reference: AQA 8300, §3.1 Number.
Ordering numbers (N1)
To order a mixed list of fractions and decimals, convert everything to the same form first — usually decimals are easiest.
Convert: 1/4 = 0.25, 3/4 = 0.75. Now order: 0.25, 0.55, 0.6, 0.75.
Answer: 1/4, 0.55, 0.6, 3/4.
Common slip: assuming a fraction with bigger numbers is bigger overall. 7/8 < 9/10, even though 9 > 7.
BIDMAS / order of operations (N3)
Brackets, Indices, Division & Multiplication (left to right), Addition & Subtraction (left to right).
Brackets first: 80 ÷ 10 − 3 × 2
Division & multiplication: 8 − 6
Answer: 2.
Common slip: working strictly left to right ignores BIDMAS and gives 22.
Primes, factors & multiples (N4)
A prime number has exactly two factors: 1 and itself. So 1 is not prime. The first few are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
HCF = largest number that divides both. LCM = smallest number both go into.
60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 = 2² × 3 × 5.
For HCF/LCM with another number, do the same and combine.
Powers & roots (N6)
You should know by heart the squares from 1² to 15² (so up to 225) and the cubes 1³, 2³, 3³, 4³, 5³, 10³.
7² = 49, 2³ = 8
49 × 8 = 392.
Also useful: 1000 = 10³ and 1 million = 10⁶.
Standard form (N9)
Standard form is A × 10ⁿ where 1 ≤ A < 10 and n is an integer.
Move the decimal point right until you have a number between 1 and 10: 7.5. You moved 4 places, and the original was small, so n is negative: 7.5 × 10⁻⁴.
Common slip: writing 75 × 10⁻⁵ — looks the same, but A isn't between 1 and 10. No marks.
Five things to remember
1. Convert to the same form before ordering.
2. BIDMAS. Always BIDMAS.
3. 1 is not prime.
4. Squares to 15² and small cubes — memorise them.
5. Standard form: 1 ≤ A < 10.
That's the toolkit. Now go and try the practice paper.
Well done!
You finished this lesson. You worked hard and learned something new today. 🎉
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