Maths isgce revisión

​IGCSE​​Maths​​—​​Complete​​Revision​​Guide​​Year​​10​​Mock​​Prep​




​IGCSE​​MATHEMATICS​
​Complete​​Revision​​Guide​
​Year​​10​​Mock​​Examination​​Preparation​



📚
​ ​​How​​to​​Use​​This​​Guide​
​Each​​topic​​has​​four​​parts:​
📋
✏️
​ ​​Key​​Facts​​—​​the​​rules​​and​​formulas​​you​​MUST​​memorise​

🔥
​ ​​Worked​​Example​​—​​step-by-step​​model​​answer​
​ ​​Challenge​​Question​​—​​harder​​exam-style​​question​​to​​test​
​yourself​
✅​ ​​After​​each​​section:​​cover​​the​​examples​​and​​try​​to​​redo​​them​
​from​​memory!​



​ ame:​​________________________________​ ​Target​​Grade:​​_______​ ​Exam​​Date:​
N
​_______________​




​Cover​​the​​examples​​—​​then​​redo​​them​​from​​memory!​​Page​​1​

, ​IGCSE​​Maths​​—​​Complete​​Revision​​Guide​​Year​​10​​Mock​​Prep​



​SECTION​​1​​—​​Number​


🔢
​ ​ ​Indices​

📋
​ ​​Key​​Facts​​&​​Formula​ ✏️
​ ​​Worked​​Example​
​aᵐ​​×​​aⁿ​​=​​aᵐ⁺ⁿ​ ​Evaluate​​27^(2/3)​
​aᵐ​​÷​​aⁿ​​=​​aᵐ⁻ⁿ​ ​Step​​1:​​27^(1/3)​​=​​∛27​​=​​3​
​(aᵐ)ⁿ​​=​​aᵐⁿ​ ​Step​​2:​​3²​​=​​9​
​a⁰​​=​​1​ ​Answer:​​9​
​a⁻ⁿ​​=​​1/aⁿ​
​a^(1/n)​​=​​ⁿ√a​ ​ implify:​​(x³)²​​÷​​x⁴​
S
​a^(m/n)​​=​​(ⁿ√a)ᵐ​ ​=​​x⁶​​÷​​x⁴​​=​​x²​

🔥
​ ​​Challenge:​​If​​4^x​​=​​8,​​find​​x.​​(Hint:​​write​​both​​as​​powers​​of​​2)​



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​ ​ ​LCM​​and​​HCF​

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​ ​​Key​​Facts​​&​​Formula​ ✏️
​ ​​Worked​​Example​
​Use​​prime​​factor​​trees​ ​Find​​HCF​​and​​LCM​​of​​24​​and​​36​
​HCF:​​multiply​​COMMON​​factors​​(lowest​ ​24​​=​​2³​​×​​3​
​power)​ ​36​​=​​2²​​×​​3²​
​LCM:​​multiply​​ALL​​factors​​(highest​​power)​ ​HCF​​=​​2²​​×​​3​​=​​12​
​HCF​​×​​LCM​​=​​product​​of​​two​​numbers​ ​LCM​​=​​2³​​×​​3²​​=​​72​
​Tip:​​draw​​a​​Venn​​diagram​​of​​prime​​factors!​ ✓
​Check:​​12​​×​​72​​=​​864​​=​​24​​×​​36​​ ​

🔥
​ ​​Challenge:​​Three​​buses​​leave​​a​​station​​every​​8,​​12​​and​​20​​minutes.​​When​​do​​they​​next​​all​
​leave​​together?​



🔄
​ ​ ​Recurring​​Decimals​​to​​Fractions​

📋
​ ​​Key​​Facts​​&​​Formula​ ✏️
​ ​​Worked​​Example​
​Let​​x​​=​​the​​recurring​​decimal​ ​Convert​​0.272727...​​to​​a​​fraction​
​Multiply​​by​​10ⁿ​​where​​n​​=​​length​​of​​recurring​ ​Let​​x​​=​​0.272727...​
​block​ ​100x​​=​​27.272727...​
​Subtract​​to​​eliminate​​the​​recurring​​part​ ​99x​​=​​27​
​Solve​​for​​x​​and​​simplify​​the​​fraction​ ​x​​=​​27/99​​=​​3/11​

🔥
​ ​​Challenge:​​Convert​​0.583̄​​(0.5833...)​​to​​a​​fraction.​​Show​​all​​algebraic​​steps.​



​√​ ​Surds​

📋
​ ​​Key​​Facts​​&​​Formula​ ✏️
​ ​​Worked​​Example​
​√(ab)​​=​​√a​​×​​√b​ ​Simplify:​​3√8​​−​​√50​​+​​√18​
​√(a/b)​​=​​√a​​/​​√b​ ​=​​3×2√2​​−​​5√2​​+​​3√2​
​Simplify:​​find​​largest​​square​​factor​ ​=​​6√2​​−​​5√2​​+​​3√2​​=​​4√2​
​Add/subtract:​​like​​terms​​only​​(same​​surd)​



​Cover​​the​​examples​​—​​then​​redo​​them​​from​​memory!​​Page​​2​