Number Revision Notes for IGCSE Maths
These comprehensive revision notes cover everything you need to know about number for the Cambridge IGCSE Mathematics 0580 examination. Written by Teacher Rig, each section includes key concepts, essential formulas, and practical exam tips to help you achieve your best grade.
Fractions, Decimals, and Percentages
These are three ways of expressing parts of a whole. To convert between them: fraction to decimal - divide numerator by denominator; decimal to percentage - multiply by 100; fraction to percentage - multiply by 100. Operations with fractions require common denominators for addition/subtraction, and you multiply numerators and denominators directly for multiplication.
Key Formulas
- Percentage = fraction x 100
- To add fractions: find common denominator
- To multiply fractions: multiply tops and multiply bottoms
Exam Tips
- Always simplify fractions to their lowest terms
- To divide by a fraction, multiply by its reciprocal
- Convert mixed numbers to improper fractions before calculating
Percentages
Percentage increase/decrease: find the percentage of the amount and add/subtract. Multiplier method: increase of r% uses multiplier (1 + r/100), decrease uses (1 - r/100). Reverse percentages: divide by the multiplier to find the original. Compound interest uses repeated multiplication.
Key Formulas
- Percentage change = (change / original) x 100
- Compound interest: A = P(1 + r/100)^n
- Reverse: original = final / multiplier
Exam Tips
- For reverse percentages, NEVER subtract the percentage from the final amount
- Compound interest multiplies by the same factor each year
- Simple interest is the same amount each year: I = PRT/100
Ratio and Proportion
Ratios compare quantities in the same units. To share an amount in a given ratio, find the total number of parts, then divide. Direct proportion: as one quantity increases, the other increases at the same rate (y = kx). Inverse proportion: as one increases, the other decreases (y = k/x).
Key Formulas
- Direct proportion: y = kx
- Inverse proportion: y = k/x
- To share in ratio a:b: first part = a/(a+b) x total
Exam Tips
- Always simplify ratios to smallest whole numbers
- For proportion questions, find k first using given values
- Ratios must be in the same units before simplifying
Standard Form
Standard form writes numbers as A x 10^n where 1 <= A < 10 and n is an integer. Large numbers have positive n, small numbers have negative n. To multiply: multiply the A values, add the powers. To divide: divide the A values, subtract the powers.
Key Formulas
- A x 10^n where 1 <= A < 10
- Multiply: (A x 10^m)(B x 10^n) = AB x 10^(m+n)
- Divide: (A x 10^m)/(B x 10^n) = (A/B) x 10^(m-n)
Exam Tips
- Adjust if A is not between 1 and 10 after calculation
- On a calculator, use the EXP or x10^x button
- Negative powers mean small numbers: 3 x 10^(-4) = 0.0003
Upper and Lower Bounds
When a measurement is rounded, the true value lies within a range. For a measurement rounded to the nearest unit, the bounds are +/- half a unit. For calculations with bounds: to maximise a sum, use upper bounds; to maximise a difference, use upper of first and lower of second; to maximise a product, use upper bounds; to maximise a quotient, use upper of numerator and lower of denominator.
Key Formulas
- Rounded to nearest n: bounds = value +/- n/2
- Max of a/b = upper(a) / lower(b)
- Min of a/b = lower(a) / upper(b)
Exam Tips
- The upper bound is NOT included (it would round up to the next value)
- For multiplication: max uses both upper bounds, min uses both lower bounds
- For subtraction: max uses upper minus lower, min uses lower minus upper
Revision Checklist
- I understand all key concepts in number
- I have memorised the essential number formulas
- I can apply these concepts to exam-style questions
- I have practised past paper questions on number
- I know the common mistakes to avoid in number questions
Frequently Asked Questions
What number topics are covered in IGCSE Maths?
The IGCSE 0580 syllabus covers number across both Core and Extended tiers. Key areas include fractions, decimals, and percentages. Key areas include percentages. Key areas include ratio and proportion.
How important is number in the IGCSE exam?
Number is a significant part of the IGCSE Mathematics exam, typically appearing in Paper 2 (non-calculator) and Paper 4 (calculator). Questions range from straightforward calculations to multi-step problems that combine number with other topics.
What are the most common mistakes in number?
Common mistakes include not showing full working, forgetting to state units, misreading the question, and rushing through calculations. For number specifically, make sure you understand the underlying concepts rather than just memorising procedures.
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