Mathematics

Back to Notes | Phys­ics | Math­em­at­ics | Eng­lish | Eco­nom­ics

How to study maths: a quick guide

  • Prac­tise reg­u­larly and prac­tise with com­mit­ment. Go over the work you did at school at night, and try to do the exer­cises set, and maybe find oth­er chal­len­ging exer­cises to do as well.
  • Make sure you know the basics before mov­ing on to more advanced top­ics. In par­tic­u­lar, make sure you can read­ily recall for­mu­las and tech­niques.
  • Before exams, do some past papers in the spe­cified time lim­it. That will give you a feel as to what to expect in the real thing.
  • Don’t spend too much time on one ques­tion in the exam. If you can’t do it, move on to the next ques­tion, and go back later.
  • For Exten­sion 2 stu­dents, don’t worry if you can’t do every ques­tion. At least give each ques­tion a go, and you should find that your suc­cess rate will gradu­ally improve.
  • Ask if you need help!

Extension 2 Resources

Resource Type
Fort Street High School 2003 Tri­al
Con­tains ques­tions and fully worked solu­tions.
Exam
Fort Street High School Com­plex Num­bers Assess­ment Task
Con­tains ques­tions on com­plex num­bers and fully worked solu­tions.
Exam
Integ­ra­tion (Exten­sion 2)
Con­tains notes and com­mon examples on the top­ic of integ­ra­tion.
Notes
Con­ics
Con­tains notes and com­mon examples in selec­ted areas of con­ic sec­tions.
Notes

Extension 1 Resources

Resource Type
Fort Street High School 2003 Tri­al
Con­tains ques­tions and fully worked solu­tions.
Exam
Fun­da­ment­al Lim­it
Proves the fun­da­ment­al lim­it, and provides examples of its use.
Notes
Inequa­tions (Exten­sion 1)
Shows step-by-step examples of how to solve more dif­fi­cult inequal­it­ies.
Notes
Para­met­ric Equa­tions and the Para­bola
Provides com­plete dis­cus­sions and proofs of chan­ging from para­met­ric to cartesian equa­tions, equa­tions of tan­gents and nor­mals, inter­sec­tions of tan­gents and nor­mals, focal chords, chord of con­tact, and com­monly tested prop­er­ties of para­bolas.
(old ver­sion)
Notes
Poly­no­mi­als
Sum­mar­ises remainder and factor the­or­ems, rela­tion­ship between the roots and approx­im­a­tion of roots.
(old ver­sion)
Notes
Tri­go­no­met­ric Equa­tions
Dis­cusses trans­form­a­tions, t-res­ults and gen­er­al solu­tions.
Notes

2-Unit Resources

Resource Type
Circle Geo­metry
Provides defin­i­tions and com­mon circle prop­er­ties. Labelled dia­grams included.
Notes
Cir­cu­lar Func­tions
Sum­mar­ises radi­an meas­ure, arcs, sec­tors, seg­ments and simple sin and cos curves.
Notes
Expo­nen­tial and Log­ar­ithmic Func­tions
Dis­cusses dif­fer­en­tial and integ­ral cal­cu­lus involving expo­nen­tial and log­ar­ithmic func­tions.
Notes
Geo­metry
Provides a com­plete sum­mary of lines, types of angles, con­cur­rent and par­al­lel lines, prop­er­ties of poly­gons, tests for con­gru­ency, inter­cept prop­er­ties, sim­il­ar tri­angles and the the­or­em of Pythagoras.
Notes
Inequa­tions
Dis­cusses axioms, square roots and abso­lute val­ues.
Notes
Integ­ra­tion
Sum­mar­ises approx­im­a­tion meth­ods, and def­in­ite and indef­in­ite integ­rals.
Notes
Log­ar­ithms and Indices
Out­lines the laws of log­ar­ithms, indices, change of base and the con­ver­sion between index and log­ar­ithm forms.
Notes
Basic Arith­met­ic and Algebra
Dis­cusses the real num­ber sys­tem, fac­tor­isa­tion, quad­rat­ics and surds.
Notes
Prob­ab­il­ity
Dis­cusses ter­min­o­logy used in prob­ab­il­ity, mutu­ally exclus­ive and inde­pend­ent events and the use of dia­grams.
Notes
Quad­rat­ic Equa­tions
Provides details of roots of quad­rat­ics, com­plet­ing the square, quad­rat­ic for­mula and inequal­it­ies.
Notes
Rela­tions and Func­tions
Defines com­monly used func­tions and terms, and sum­mar­ises odd and even func­tions, graphs, straight lines, para­bolas, circles, semi-circles, expo­nen­tials, hyper­bolas and regions.
Notes
Tri­go­no­metry
Sum­mar­ises ratios, spe­cial angles, elev­a­tion and depres­sion, sine rule, cosine rule, area of a tri­angle, graphs of trigno­met­ric func­tions, iden­tit­ies and 3-D trigno­metry.
Notes

Year 10 Resources

Resource Type
Circle Geo­metry
Dis­cusses prop­er­ties of chords, angles and tan­gents, and lists sev­er­al import­ant proofs.
Notes
Poly­no­mi­als and Log­ar­ithms
Sum­mar­ises curve sketch­ing, poly­no­mi­al defin­i­tions, remainder and factor the­or­ems, dif­fer­ent graphs, func­tion nota­tion, inverse func­tions, log­ar­ithmic laws and graphs of log­ar­ithmic and expo­nen­tial func­tions.
Notes
Quad­rat­ics
Dis­cusses quad­rat­ic equa­tions, para­bolas, con­cav­ity, solu­tions to quad­rat­ics, fac­tor­isa­tion, com­plet­ing the square, quad­rat­ic for­mula, as well as dif­fer­ent types of graphs, includ­ing straight lines, para­bolas, expo­nten­tials, hyper­bolas and circles.
Notes
Yearly Exam Notes
Provides notes on surds, rates and vari­ations, sur­face area and volume and con­sumer arith­met­ic.
Notes

General Resources

Resource Type
Areas and Volumes
Out­lines the for­mu­las used to cal­cu­late the areas and volumes of com­mon shapes and solids. Dia­grams giv­en.
Notes
Maths Corner 1: Stick Tree
Provides an ana­lys­is of the dimen­sions of a fractal tree, where each branch divides into two, each half the length of the par­ent branch.
Art­icle
Maths Corner 2: Infin­ity
Explains the con­found­ing and often bewil­der­ing concept of infin­ity, and briefly touches on the rules for oper­a­tions with infin­ity and transfin­ite num­bers. Just how many infin­it­ies are there?
Art­icle