IGCSE Math RevisionNumber: Edexcel IGCSE Maths (4MA1) knowledge organiser
Everything to know about number on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.
Key definitions
- Prime Factor Decomposition
- ‘Prime factor decomposition’ means writing a number as a product of prime numbers using powers.
- Standard Form
- Standard form writes a number as A × 10ⁿ where 1 ≤ A < 10.
- Upper and Lower Bounds
- A rounded measurement has a lower and upper bound — the range of true values it could really be.
- Surd Operations
- A surd is a root that can't simplify to an integer (e.g. √2). Rationalising means removing surds from a fraction's denominator.
Key formulas
| Indices | \(a^m\times a^n=a^{m+n},\) \(a^m\div a^n=a^{m-n},\) \((a^m)^n=a^{mn},\) \(a^0=1,\) \(a^{-n}=\tfrac1{a^n},\) \(a^{\frac mn}=(\sqrt[n]a)^m\) |
| Standard form | \(A\times10^n,\) \(1\le A<10,\ n\in\mathbb Z\) |
| Surds | \(\sqrt{ab}=\sqrt a\sqrt b,\) \(\frac{a}{\sqrt b}=\frac{a\sqrt b}{b},\) \(\frac1{c+\sqrt b}=\frac{c-\sqrt b}{c^2-b}\) |
| Percentage change | \(\frac{\text{new}-\text{original}}{\text{original}}\times100\%\) |
| Reverse percentage | \(\text{original}=\frac{\text{new}}{1\pm\frac r{100}}\) |
| Compound growth / decay | \(A=P\left(1\pm\tfrac r{100}\right)^n\) |
| Recurring decimal: \(x=0.\dot2\dot7\), then \(100x-x=27\), so \(x=\tfrac{27}{99}=\tfrac3{11}\) | |
| Bounds: a value to the nearest \(u\) lies in \([x-\tfrac u2,\ x+\tfrac u2)\); for \(a-b\) and \(a\div b\) use max with min | |
| Compound measures | \(\text{speed}=\frac{\text{distance}}{\text{time}},\) \(\text{density}=\frac{\text{mass}}{\text{volume}},\) \(\text{pressure}=\frac{\text{force}}{\text{area}}\) |
| Sets | \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\) |
Worked example
£4000 invested at 3.5% compound interest for 3 years — total value?
- 4000 × 1.035³ = £4434.87.
Common mistakes
- Reverse percentages: finding a percentage of the new amount
- Compound interest and depreciation done as simple interest
- Listing multiples when HCF is asked (and vice versa)
- Rounding to significant figures by counting from the decimal point
More on what examiners see students get wrong: Examiner Insights.
You should be able to…
- Identify factors, multiples and primes, and recognise square and cube numbers and their roots, such as finding all factors of 36 or the cube root of 64.
- Solve problems in context with fractions, such as finding a fraction of an amount or the original amount after a fraction has been spent.
- Convert between ordinary numbers and standard form, including very large and very small numbers, and order numbers written in standard form.
- Solve harder ratio problems, such as using a given difference between shares or combining two ratios into one.
- Convert between metric units of length, area, volume and capacity, such as cm² to m² and cm³ to litres, using scale factors correctly.
- Use Venn diagrams to count members of sets, find n(A ∪ B) and work out missing numbers in regions from given totals.
The printable sheet
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Other Edexcel IGCSE Maths (4MA1) topics: Algebra · Graphs, sequences and calculus · Geometry and trigonometry · Statistics and probability · All Edexcel IGCSE Maths (4MA1) organisers