AS Double Mathematics - HELP

Name:AS DoubleMathematicsGreen BlockP1, P2, Stats MechTeacher: Ingrid Flynn

Checklist for Completed Assignments:o The assignment cover sheet has boxes ‘Done’ and ‘Ready’ ticked for every question,and none of these ticks are a lieo Each question is started on a new side of A4o Question numbers are written as a large title at the top of every page and underlinedtwice: e.g. “Question 1 ”.o All questions are in ordero Equals signs are all in a straight vertical line down the page (no snaking!)o All questions are written neatly and all working is showno Mistakes are boxed off neatly and scored outo Answers are underlined twice and checked (show it has been checked by ticking it)o All pages are stapled together in the top left cornerExample:Assignment TestYou will have an 30min assignment test on the day you hand in your assignment. There will be 5questions which are identical to the questions in the assignment. Therefore, everyone should passthis test.2

Your ExamsThe Pearson Edexcel Level 3 Advanced GCE in Mathematics consists of threeexternally-examined papers:Paper 1: Pure Mathematics 1 (*Paper code: 9MA0/01)Paper 2: Pure Mathematics 2 (*Paper code: 9MA0/02)Paper 3: Statistics and Mechanics (*Paper code: 9MA0/03)Each paper is: 2-hour written exam with calculator; 33.33% of the qualification; 100marks.To get an E you need an average of about 45% in the exams. To get an A grade youneed an average of roughly 85%.PURE (Paper 1 and Paper 2) Topic 1 – Algebra and functions Topic 2 – Coordinate geometry in the (x, y) plane Topic 3 – Sequences and series Topic 4 – Trigonometry Topic 5 – Proof Topic 6 – Exponentials and logarithms Topic 7 – Differentiation Topic 8 – Integration Topic 9 – Numerical methods Topic 10 – VectorsSTATISTICS (Paper 3, Section A) Topic 1 – Statistical sampling Topic 2 – Data presentation and interpretation Topic 3 – Probability Topic 4 – Statistical distributions Topic 5 – Statistical hypothesis testingMECHANICS (Paper 3, Section B) Topic 6 – Quantities and units in mechanics Topic 7 – Kinematics Topic 8 – Forces and Newton’s laws Topic 9 – MomentsNext Year’s Exams: Further Maths A Level (4 in total, each 1.5hr and 25%):Compulsory: Core Pure 1, Core Pure 2Options x2: Choose one from { FP1,FS1,FM1,D1} and {FP2,FS1,FM1,D1,FS2,FM2, FS1,D2}3

Your Teacher: Ingrid www.ingridflynn.weebly.comWarning: I am very strict with homework so don’t even bother trying to get away with not doing all of thework I set (which is a lot)! I am also very helpful I am (almost) always in room 3 or room 11 to givehelp if you need it.Your LessonsBRING THIS PACK TO EVERY LESSON PLEASEIn the first 3 half terms (about 19 weeks) we will study the course content, then for the next two halfterms (about 12 weeks) we will practice the techniques, consolidate your learning and prepare for theexams.Before each lesson you will have watched a video introducing a new topic. In total, this is usually aboutan hour’s work per week. In the lesson you will, for most of the time, be working rather than listening tome talk. You will be practicing basic mathematical skills and strengthening your understanding of thenew topic by working through exercises, together with developing your problem solving skills byattempting to solve complicated problems using the maths you have learned.CalculatorsYou need a calculator for this course. The recommended calculator is theCasio Fx-991ex Classwiz ( 22).Some doubles students choose to buy the Casio fx9860GII, an expensive but very goodgraphical calculator (around 70 from www.calculatorsdirect.co.uk) which is a hugeadvantage in the exams as it will solve all the equations for you, so you can check youranswers. Slightly better (same functions but colour screen and nicer graph sketcher) isthe Casio fx-CG20 (around 100). Please talk to me if you are worried about buying a calculator.Expectations. You will 1. Attend all lessons and contact me as soon as possible if a lesson needs to be missed. You will checkthe Absence Box when you return to catch up on any missed work2. Come to each lesson on time3. Work hard in lessons4. Hand in a complete, well presented assignment on last lesson of each week5. Prepare fully for the weekly assignment test by practising6. Ask for help if you need it, not wait for me to come to you and offer help7. If an assignment test is not passed, you will need to re-do the incorrect questions twice each andalso find two similar questions to do (for each incorrect question). These will be handed in with thenext assignment.AssignmentsYou will be set 1 assignment per week. It will always have the same format. You will have 9 hours ofmaths lessons per week, and are expected to do 9 hours of study out of lessons also in order to keep upwith the pace of the course. Some of you will complete the assignment in 2 hours. Some of you will take6 or 7 hours to complete it. It is your responsibility to make sure you start early enough to ensure youmeet the deadline.VideosEach week, you will be set videos to watch to introduce you to a new technique. As you watch the video,complete the associated pack pages then tick it off. Feel free to get ahead! Videos can be accessed using the QRcodes or on my website.4

WkWkbegins011/912345Pure: Simultaneous EquationsStatistics: Sampling18/9 Pure: Trigonometry: Radians measure and applicationStats: Measures of Location and Spread: Median and IQR of a listStats: Measures of Location and Spread: Mean and S.D of groupeddata (by hand)Stats: Measures of Location and Spread: Mean and S.D of groupeddata (using a calculator)Stats: Measures of Location and Spread: Mean and IQR of groupeddata (Interpolation)Stats: Measures of Location and Spread: Percentiles25/9 Pure: Trigonometry: Mini Trig EquationsPure: Trigonometry: Reciprocal Trig FunctionsPure: Trigonometry: Reciprocal Trig GraphsPure: Trigonometry: Pythagorean Trig Identities - ProofPure: Trigonometry: Using Trig Identities to Solve EquationsStats: Linear CodingStats: Combined mean2/10 Pure: Arithmetic Series and ProofPure: Geometric Series and ProofStats: Histograms: IntroStats: Histograms: Dimensions of Bars9/10 Pure: Binomial Expansion: FinitePure: Recurrence RelationPure: Sigma NotationStats: Probability: Venn Diagrams: UnionStats: Probability: Venn Diagrams: IntersectionStats: Venn Diagrams: Addition Rule16/10 Pure: Factor TheoremPure: Algebraic DivisionStats: Probability: Venn Diagrams: Given (Conditional Probability)Stats: Probability: Tree DiagramsStats: Probability: Tree Diagrams: Given (Conditional Probability)WkWkbegins630/107910Videos Half Term 1Videos Half Term 2Pure: Algebraic FractionsPure: Partial Fractions6/11 Pure: Proof by Contradiction and DeductionPure: Proof by ExhaustionStats: Probability: Mutually Exclusive and Independent EventStats: Statistical Distributions – DRVsStats: Statistical Distributions – Discrete uniform distribution20/11 Pure: Trigonometry – Compound Angle FormulaePure: Trigonometry – Double Angle FormulaeStats: Statistical Distributions – Binomial Distribution17/11 Stats: Hypothesis Testing – Binomial DistributionStats: Hypothesis Testing – Lower Tails TestStats: Hypothesis Testing – Upper Tails ü5

11124/12Pure: Exponentials and Logs – The BasicsPure: Exponentials and Logs – Sketching e x and lnxPure: Exponentials and Logs – Solving EquationsPure: Exponentials and Logs – gins131/1148/1Videos Half Term 3Stats: Hypothesis Testing – Critical Values - Lower Tail TestStats: Hypothesis Testing – Critical Values - Upper Tail TestStats: Hypothesis Testing – Critical Regions - Two Tail TestMins8816WatchPagebyü7374756

Pure Topic 1 – Algebra and functions Topic 2 – Coordinate geometry in the (x, y) plane Topic 3 – Sequences and series Topic 4 – Trigonometry Topic 5 – Proof Topic 6 – Exponentials and logarithms Topic 7 – Differentiation Topic 8 – Integration Topic 9 – Numerical methods Topic 10 – Vectors7

Pure - Simultaneous EquationsLinear and quadratic simultaneous equationsEquations and inequalities20 minWrite down the easier equationRearrange into y or x Sub that the harder equationSolve to find y (or x)Use the easy equation to find x (or y)Level 1Level 22 x 3 y 104 x y 202 x 3 y 104 x y 2 20Little sketch of what you’re finding:Little sketch of what you’re finding:8

Write down the easier equationRearrange into y or x Sub that the harder equationSolve to find y (or x)Use the easy equation to find x (or y)Level 32 x 3 y 104 x 2 y 2 20Little sketch of what you’re finding:9

Pure - TrigonometryRadian measure and its applications (TOOLS)17 minT Triangle AreaO Sector AreaO Arc LengthL Cosine RuleS Sine Rule10

11

Pure - TrigonometryGraphs of standard trig functionsand solving mini trig equationssin x sin x 323213 min0 x 3600 x 2π12

320 x 3602 tan x - 20 x 360cos x 13

Pure - TrigonometryReciprocal trig functions3 minWrite down the three reciprocal trig functionsSecant !(Sec !) Cosecant !Cotangent(Cosec !) (Cot !) Work out the value of this function:Sec 60 Top Tip for remembering which is which:Circle thefirst letter:sin xcos xtan xCircle thethird letter:cosec xsec xcot x14

Pure - TrigonometryReciprocal trig graphs13 miny cosec !y sec !y cot !15

Pure - TrigonometryPythagorean trig identities – proof6 minProve that:1 cot2 ! cosec2 !Divide through by sin2 !Prove that:tan2 ! 1 sec2 !Divide through by cos2 !16

Pure - TrigonometryUsing Pythagorean Trig Identities to Solve Equations 2 minThis is an example of using a pythagorean trig identity to solve an equation.Solve4!"# ! ! ! 9 !"# !"# 0 ! 36017

Pure - Arithmetic Seriesmin25What do all these terms add up to?Proof of the sum of an Arithmetic Series (to learn)18

Translate the information into maths using the two equations!19

Translate the following information1The 5th term is 112The 8th term is 73The sum of the first 8 terms is 124The sum of the first 18 terms is -25The 12th term is -176The sum of the first 9 terms is 157The 17th term is 918The sum of the first 52 terms is 5009The 11th term is 910The sum of the first 6 terms is -2020

Pure - Geometric Series and Proofmin172, 4, 8, 16, , 256, , 3276What do all these terms add up to?Proof of the sum of a Geometric Series (to learn)21

Translate the information into maths using the two equations!822

Translate the following information1The 5th term is 112The 8th term is 73The sum of the first 8 terms is 124The sum of infinite terms is -25The 12th term is -176The sum of the first 9 terms is 157The 17th term is 918The sum of infinite terms is 5009The 11th term is 910The sum of the first 6 terms is -2023

Pure: Binomial Expansion(a b )0(a b )1(a b )2(a b )3(a b )4(a b )7Finding the coefficientsMethod 1:Method 2:Method 3:24

(2 3x )4(1 x )7x 2 2 425

(2 px )4(1 2 x )nWhy is 0! 1? Where does the nCr formula come from?! Why is it called n ‘choose’ r? Watch thesevideos to find out!26

Pure: Recurrence RelationsThis is an example of how to interpretrecurrence relation notation6 minun 1 un 5, u1 427

Pure: Sigma Notation22 minI haven’t left you much room here sorry – you need to make notes on what the notation is telling youto do and how you would answer the problem but don’t attempt to copy out everything from thescreen! Just the key points to enable you to answer one of these questions.6 (2k 1)k 2142 (7r 2)r 104 2rr 210 3uk 4kun 1 un 5,u1 428

Pure: Algebraic Division4 minCopy the example!! ! !!! ! !!!!!"! ! !!!!!29

Pure: Algebraic Fractions4 minCopy the two examples:1) Simplify2) Simplify!! ! !!!!!!!!!!!! ! !!!!!!" !!!!!"30

Pure: Partial !!!! !!!16 minin partial fractions. Show the full method!!! ! !!"! !!!!! ! !!!!in partial fractions. Show the full method .continued on next page31

Pure - Partial Fractions Page 232

Pure - Algebraic Methods - ProofContradiction (Counter-example)8 minDefinition of proof by contradiction:Write down the proof that2 is irrationalIf !! is even then ! is even. Why is this true?33