Eexel Level 3 Avne GCE in Mthemtis (9MA0) Two-yer Sheme of Work Stuents stuying A Level Mthemtis will tke 3 ppers t the en of Yer 13 s inite elow. All stuents will stuy Pure, Sttistis n Mehnis. A level Mthemtis Pper 1: Pure Mthemtis 33%, 2 hours, 100 mrks Any pure ontent n e ssesse on either pper Pper 2: Pure Mthemtis 33%, 2 hours, 100 mrks Pper 3: Sttistis n Mehnis 33%, 2 hours, 100 mrks Setion A: Sttistis (50 mrks) Setion B: Mehnis (50 mrks)
Yer 1: AS Mthemtis pure ontent Pure Mthemtis 1 Alger n funtions Algeri expressions si lgeri mnipultion, inies n surs Qurti funtions ftorising, solving, grphs n the isriminnts Equtions qurti/liner simultneous Inequlities liner n qurti (inluing grphil solutions) e Grphs ui, qurti n reiprol f Trnsformtions trnsforming grphs f(x) nottion 2 Coorinte geometry in the (x, y) plne Stright-line grphs, prllel/perpeniulr, length n re prolems Cirles eqution of irle, geometri prolems on gri 3 Further lger Algeri ivision, ftor theorem n proof The inomil expnsion 4 Trigonometry Trigonometri rtios n grphs Trigonometri ientities n equtions 5 Vetors (2D) Definitions, mgnitue/iretion, ition n slr multiplition Position vetors, istne etween two points, geometri prolems 6 Differentition Definition, ifferentiting polynomils, seon erivtives Grients, tngents, normls, mxim n minim 7 Integrtion Definition s opposite of ifferentition, inefinite integrls of x n Definite integrls n res uner urves 8 Exponentils n logrithms: Exponentil funtions n nturl logrithms
Yer 1: AS Mthemtis pplie ontent Sttistis n Mehnis Setion A Sttistis 1 Sttistil smpling Introution to smpling terminology; Avntges n isvntges of smpling Unerstn n use smpling tehniques; Compre smpling tehniques in ontext 2 Dt presenttion n interprettion Clultion n interprettion of mesures of lotion; Clultion n interprettion of mesures of vrition; Unerstn n use oing Interpret igrms for single-vrile t; Interpret stter igrms n regression lines; Reognise n interpret outliers; Drw simple onlusions from sttistil prolems 3 Proility: Mutully exlusive events; Inepenent events 4 Sttistil istriutions: Use isrete istriutions to moel rel-worl situtions; Ientify the isrete uniform istriution; Clulte proilities using the inomil istriution (lultor use expete) 5 Sttistil hypothesis testing Lnguge of hypothesis testing; Signifine levels Crry out hypothesis tests involving the inomil istriution Setion B Mehnis 6 Quntities n units in mehnis Introution to mthemtil moelling n stnr S.I. units of length, time n mss Definitions of fore, veloity, spee, elertion n weight n isplement; Vetor n slr quntities 7 Kinemtis 1 (onstnt elertion) Grphil representtion of veloity, elertion n isplement Motion in stright line uner onstnt elertion; suvt formule for onstnt elertion; Vertil motion uner grvity 8 Fores & Newton s lws Newton s first lw, fore igrms, equilirium, introution to i, j system Newton s seon lw, F = m, onnete prtiles (no resolving fores or use of F = μr); Newton s thir lw: equilirium, prolems involving smooth pulleys 9 Kinemtis 2 (vrile elertion) Vrile fore; Clulus to etermine rtes of hnge for kinemtis Use of integrtion for kinemtis prolems i.e. r v t, v t
Yer 2: Remining A Level Mthemtis pure ontent Pure Mthemtis 1 Proof: Exmples inluing proof y eution* n proof y ontrition 2 Algeri n prtil frtions Simplifying lgeri frtions Prtil frtions 3 Funtions n moelling Moulus funtion Composite n inverse funtions Trnsformtions Moelling with funtions* 4 Series n sequenes *exmples my e Trigonometri, exponentil, reiprol et. Arithmeti n geometri progressions (proofs of sum formule ) Sigm nottion Reurrene n itertions 5 The inomil theorem Expning ( + x) n for rtionl n; knowlege of rnge of vliity Expnsion of funtions y first using prtil frtions 6 Trigonometry Rins (ext vlues), rs n setors Smll ngles Sent, osent n otngent (efinitions, ientities n grphs); Inverse trigonometril funtions; Inverse trigonometril funtions Compoun* n oule (n hlf) ngle formule e R os (x ± α) or R sin (x ± α) f g Proving trigonometri ientities Solving prolems in ontext (e.g. mehnis) 7 Prmetri equtions Definition n onverting etween prmetri n Crtesin forms Curve skething n moelling *geometri proofs expete
8 Differentition e Differentiting sin x n os x from first priniples Differentiting exponentils n logrithms Differentiting prouts, quotients, impliit n prmetri funtions. Seon erivtives (rtes of hnge of grient, infletions) Rtes of hnge prolems* (inluing growth n kinemtis) 9 Numeril methos* Lotion of roots *see Integrtion (prt 2) Differentil equtions Solving y itertive methos (knowlege of stirse n owe igrms) Newton-Rphson metho Prolem solving 10 Integrtion (prt 1) *See Integrtion (prt 2) for the trpezium rule Integrting x n (inluing when n = 1), exponentils n trigonometri funtions Using the reverse of ifferentition, n using trigonometri ientities to mnipulte integrls 11 Integrtion (prt 2) 12 e f Integrtion y sustitution Integrtion y prts Use of prtil frtions Ares uner grphs or etween two urves, inluing unerstning the re is the limit of sum (using sigm nottion) The trpezium rule Differentil equtions (inluing knowlege of the fmily of solution urves) Vetors (3D): Use of vetors in three imensions; knowlege of olumn vetors n i, j n k unit vetors
Yer 2: Remining A Level Mthemtis pplie ontent Sttistis n Mehnis 1 Regression n orreltion Chnge of vrile Setion A Sttistis Correltion oeffiients Sttistil hypothesis testing for zero orreltion 2 Proility Using set nottion for proility Conitionl proility Questioning ssumptions in proility 3 The Norml istriution Unerstn n use the Norml istriution Use the Norml istriution s n pproximtion to the inomil istriution Seleting the pproprite istriution Sttistil hypothesis testing for the men of the Norml istriution 4 Moments: Fores turning effet 5 Fores t ny ngle Resolving fores Frition fores (inluing oeffiient of frition µ) 6 Applitions of kinemtis: Projetiles 7 Applitions of fores Equilirium n sttis of prtile (inluing ler prolems) Dynmis of prtile 8 Further kinemtis Constnt elertion (equtions of motion in 2D; the i, j system) Vrile elertion (use of lulus n fining vetors r n r t given time)