GCSE Maths - AQA 8300

GCSE Maths - AQA 8300Here is a detailed explanation of the entire syllabus. I have linked to Corbett maths videos where possible, and added some extra notes.If you want some questions on any topic, click on the Corbett maths link, then on "videos on worksheets". Using the number of the video you should be able tofind it in the list along with "practice questions" and "textbook exercise" (unfortunately these don't currently exist for ALL videos but it is nearly complete!).Answers to practice questions and textbook exercises are available here: ers/Online resources are constantly updating, so if this is not quite up-to-date I apologise!The first section relates to material for both FOUNDATION and HIGHER tiers.The second section relates to material JUST for Higher Tier.Good Luck!Section 1 - Foundation and HigherUsing a calculator - video 352NUMBERDescriptororder positive and negative integers,decimals and fractionsNotesBe particularly careful with place valueuse the symbols , , , , , This includes representing inequalities on a number line, and listingALL integers (whole numbers) that satisfy an inequality "is equal to" "is not equal to" "is less than" "is greater than" "is less than or equal to" "is greater than or equal to"LinksPlace value - video 222Ordering numbers - video 221Ordering negatives - video 208Ordering decimals – video 95Ordering fractions/decimals/percentages –video 131Ordering Fractions – video 144

apply the four operations, includingformal written methods, to integers,decimals and simple fractions (properand improper), and mixed numbers – allboth positive and negativeMake sure you have methods that you understand for longmultiplication and long division (including dealing with decimals). Ifthese are NOT the "traditional" methods then you may not alwaysget method marks so make sure your work is clear.Remember your rules for multiplying and dividing negative numbers,and make sure you can add/subtract negatives.For fractions:Addition/Subtraction: make sure you have a common denominator(deal appropriately with mixed numbers)Multiplication: change mixed numbers to topheavy, multiply topsand multiply bottomsDivision: change mixed numbers to topheavy, flip the secondfraction and multiplyAddition (column method) - video 6Subtraction (column method) - video 304Multiplication (times tables) - video 204aMultiplication (grid method) – video 199Multiplication (column method) – video 200Multiplication (last digit) - video 201Multiplication by 10, 100 etc - video 202Multiplication by powers of 10 - video 203Multiplication of decimals - video 204Short division – video 98Division with remainders – video 103Adding decimals – video 90Subtracting decimals – video 91Dividing decimals by integers – video 93Dividing by decimals – video 92Multiplying decimals – video 94Fractions of shapes – video 143Equivalent fractions – video 135Simplifying fractions – video 146Improper to mixed numbers – video 139Mixed numbers to improper – video 140Adding/subtracting fractions – samedenominator – video 132Adding/subtracting fractions – differentdenominators – video 133Multiplying fractions – video 142Dividing fractions – video 134Negatives in real life (temperature) - video 209Adding/subtracting negatives - video 205Multiplying negatives - video 206Dividing negatives - video 207Place value and operations - video 222aunderstand and use place value (eg whenworking with very large or very smallnumbers, and when calculating withdecimals)You should be happy with place value, especially when doing columnaddition/subtraction.You are expected to have knowledge and understanding of termsused in household finance, for example profit, loss, cost price, sellingprice, debit, credit, balance, income tax, VAT and interest rate.Questions will be give in some sort of context.Dividing by powers of 10, 100, 1000 – video 99Dividing by powers of 10 – video 100

recognise and use relationships betweenoperations, including inverse operations(eg cancellation to simplify calculationsand expressions)use conventional notation for priority ofoperations, including brackets, powers,roots and reciprocalsuse the concepts and vocabulary ofprime numbers, factors (divisors),multiples, common factors, commonmultiples, highest common factor, lowestcommon multiple, prime factorisation,including using product notation and theunique factorisation theoremYou need to understand how to do the inverse (opposite) of a givenoperation.You may well have referred to this as BIDMAS or BODMAS1Remember the "reciprocal" of x is /x.A prime number has EXACTLY two factors, so 1 is NOT a prime!When doing prime factorisation (using a factor tree) you may beasked to write a number as a product of prime factors written inindex form. This means using powers and writing (for example) 36 22 x 32 rather than 2 x 2 x 3 x 3Reciprocals – video 145Reciprocal graph - video 346Order of operations (BIDMAS) - video 211Multiples - video 220Factors - video 216Lowest common multiple - video 218Highest common factor - video 219Prime numbers - video 225Product of prime Factors - video 223Product of primes and HCF/LCM - video 224Remember that you can find HCF and LCM by listing, but for largernumbers it is often a good idea to draw a Venn diagram of factors.The HCF is the product of all the prime numbers in the middleintersection, the LCM is the product of all the prime numbers in thediagram.apply systematic listing strategiesFor example, list all the different meals that a customer can choosefrom a given menu.This may well include making a list or producing a table or diagram.Sample space diagrams - video 246Listing all outcomes - video 253use positive integer powers andassociated real roots (square, cube andhigher), recognise powers of 2, 3, 4, 5You should KNOW all square numbers up to 152 225This means recognising these square numbers (eg 169 132)You should know that 1000 103 and 1 million 106You have to be able to calculate with roots, and with integer indicesSquare numbers - video 225Squaring a number - video 226Square roots - video 227Cube numbers - video 212Cubing a number - video 213Cube roots - video 214Indices – video 172Calculate exactly with fractions and withmultiples of ie work with fractions rather than recurring decimalsMake sure you know what it means when it says "give your answerexactly", or give your answer exactly as a multiple of "

calculate with and interpret standardform A 10n,where 1 A 10 and n is an integerwork interchangeably with terminatingdecimals and their corresponding7fractions (such as 3.5 and /2 or 0.375and 3/8)identify and work with fractions in ratioproblemsinterpret fractions and percentages asoperatorsThis can be with or without a calculatorMake sure you know which button is the "standard form" button onyour calculator (may look like x10 )You need to be able to interpret your calculator display when theanswer is give in standard formYou need to be able to add, subtract, multiply and divide numbers instandard from with and without a calculatorAddition/subtraction: probably easiest to write them "normally", dothe calculation then convert back to standard fromMultiplication: multiply the numbers, add the powersDivision: divide the numbers, subtract the powersAlways make sure that your final answer is written correctly instandard formThis includes ordering fractions and decimalsYou may want to do this by converting to decimals, or writing asfractions with the same denominator (or numerator)Standard form - video 300Standard form (Addition/Subtraction) - video 301Standard form (multiplication) - video 302Standard form (division) - video 303Decimals to fractions – video 123Decimals to fractions (calc) – video 124Fractions to decimals – video 127Fractions to decimals (calc) – video 128For example, share a fraction in a given ratioeg find 25% of a value, or find 3/4 of a valueIncrease or decrease by a fractionThis includes using a multiplier for percentage problemsFind a fraction of a value – video 137Find the original value if you know a fraction– video 138Increase/decrease by a fraction – video 141use standard units of mass, length, time,money and other measures (includingstandard compound measures) usingdecimal quantities where appropriateYou need to know and use metric conversion factors for length,area, volume and capacity.So.1km 1000m, 1m 100cm, 1cm 10mm1kg 1000g, 1g 1000mg31 litre 1000ml 1000cmImperial/metric conversions will be given in the question.Drawing conversion graphs – video 151Interpreting conversion graphs – video 152Calculations with time - video 322Metric and Imperial Units - video 347Metric units (length) - video 349aMetric units (mass) - video 349bMetric units (capacity) - video 349cMetric to imperial (length) - video 349dMetric to imperial (mass) - video 349eMetric to imperial (capacity) - video 349festimate answers check calculationsusing approximation and estimation,including answers obtained usingtechnologyThis includes evaluation of results obtained. For example, explainingwhy a given answer MUST be an over (or under) estimate.

round numbers and measures to anappropriate degree of accuracy (eg to aspecified number of decimal places orsignificant figures)use inequality notation to specify simple error intervals due totruncation or roundingeg if x 15.1 (1 decimal place) then 15.05 x 15.15This includes appropriate rounding for questions set in context.Also, you need to know not to round values during intermediatesteps of a calculation.apply and interpret limits of accuracyRounding (nearest whole number) - video 276Rounding (nearest 10) - video 277aRounding (nearest 100) - video 277bRounding (1dp, 2dp) - video 278Rounding (significant figures) - video 279You need to demonstrate that you understand the maximum andminimum values that a value COULD take, if you have anapproximate value and information as to how it has been rounded.Upper and lower bounds – video 183NotesIt is expected that answers will be given in their simplest formwithout an explicit instruction to do so.LinksForming algebraic expressions - video 15Algebraic notation - video 19Unfamiliar formulae will be given in the question.See the Appendix for a full list of the formulae that you NEED tolearn!This also includes identities ( )This can be assessed both directly and indirectlySubstitution - video 20- collecting like terms- multiplying a single term over a bracket (expanding)- taking out common factors- simplifying expressions involving sums, products and powers,including the laws of indicesCollecting like terms - video 9Dividing algebraic terms - video 11Multiplying algebraic terms - video 18Expanding brackets - video 13Laws of indices – video 174Negative indices – video 175Factorising – video 117ALGEBRADescriptorUse and interpret algebraic notation,including: ab in place of a b 3y in place of y y y and 3 y a2 in place of a a, a3 in place of a a a,a2b in place of a a ba /bin place of a b coefficients written as fractions ratherthan as decimals bracketssubstitute numerical values intoformulae and expressions, includingscientific formulaeunderstand and use the concepts andvocabulary of expressions, equations,formulae, inequalities, terms and factorssimplify and manipulate algebraicexpressions by: