Mathematics Methods Year 11 formula sheet

1 2015/75002v2 Mathematics Methods Unit 1 and Unit 2 formula sheet (For use with Year 11 examinations and response tasks) Copyright School Curriculum and Standards Authority, 2015 This document apart from any third party copyright material contained in it may be freely copied, or communicated on an intranet, for non-commercial purposes in educational institutions, provided that the School Curriculum and Standards Authority is acknowledged as the copyright owner, and that the Authority s moral rights are not infringed. Copying or communication for any other purpose can be done only within the terms of the Copyright Act 1968 or with prior written permission of the School Curriculum and Standards Authority. Copying or communication of any third party copyright material can be done only within the terms of the Copyright Act 1968 or with permission of the copyright owners.

2 Any content in this document that has been derived from the Australian Curriculum may be used under the terms of the Creative Commons Attribution-NonCommercial Australia licence Disclaimer Any resources such as texts, websites and so on that may be referred to in this document are provided as examples of resources that teachers can use to support their learning programs. Their inclusion does not imply that they are mandatory or that they are the only resources relevant to the course. This document is valid for teaching and examining from 1 July 2015. Mathematics Methods 1 formula sheet UNIT 1 AND UNIT 2 3 3 2 2 Measurement Circle: C = 2 r = D, where C is the circumference, r is the radius and D is the diameter A = r 2, where A is the area Triangle: A = 1 bh, where b is the base and h is the perpendicular height Parallelogram: A = bh Trapezium: A= 1 (a + b)h, where a and b are the lengths of the parallel sides Prism: V = Ah, where V is the volume and A is the area of the base Pyramid: V = 1 Ah 3 Cylinder: S = 2 rh + 2 r 2, where S is the total surface area V = r 2h Cone: S = rs + r 2, where s is the slant height V = 1 r 2h Sphere.

3 S = 4 r2 V = 4 r 3 Mathematics Methods 2 formula sheet UNIT 1 AND UNIT 2 Functions and graphs Lines and Linear relationships For points()()112 2 and P x ,yQ x ,y Mid-point of and PQ: 1 21 222x xy yM,++ = Gradient of the line through and PQ: 2121yymxx = Equation of the line through P with slope m: ()11y y mx x = Parallel lines: 12mm= Perpendicular lines: 121mm= General equation of a line: 0ax by cymx c+ += = +or Quadratic relationships For the general quadratic equation 200axbx c, a+ += Completing the square: 22224bbaxbx ca xcaa + += + + Discriminant: 24bac = Quadratic formula : 242bbacxa = Graphs and Relations Equation of a circle: () ()222xayb r + = where,( )a,bis the centre and r is the radius Trigonometric functions Cosine and sine rules For any triangle ABC with corresponding length of sides a,b,c Cosine rule: 2 222 coscababC=+ Sine rule: sinsinsinab cABC== Area of : 1sin21()()()()2where AabCA ssasbscsabc== = ++ Mathematics Methods 3 formula sheet UNIT 1 AND UNIT 2 Circular measure and radian measure In a circle of radius r, for an arc subtending angle (radians) at the centre Length of arc: r = Length of chord: 122 sinlr = Area of sector: 212Ar = Area of segments: 212sin()Ar= Trigonometric functions.

4 (fundamentals) ( )sinsin = ( )coscos = ( )tantan = sincos2 += sosicn2 = 22sincos1 += Angle sum and difference identites ()sinsincoscossinABABA B = ()coscoscossinsinABA BA B = Counting and probability Combinations Number of combinations: ()n!rr!r!nn = (of objects taken from a set of distinct objects) Binomial expansion: ()11nnnnr rnnnxy xxyx yyr + =+++++ Binomial coefficients: ()()()( )11121nn nnrn!rr! n r !rr + == Probability Fundamentals of probability: ()( )()()() ( )( ) ()()() () ()( ) ()1complement ofor and PA PAPAPA BPA B PA PB PA BPABPA B PAPB|APBPA|B== = = + = == Conditional probability: ()()( )( )0PA BP B| AP APA = for Mathematics Methods 4 formula sheet UNIT 1 AND UNIT 2 Exponential functions Index laws: For a, b >0 and m,n real, 0()( )11mmmmnmnmnmnmmmnmna baba aaaaaaaaaa+ ====== For a > 0, m an integer and n a positive integer, ( )mmnmnnaa a== Arithmetic and geometric sequences and series Arithmetic sequences For initial term a and common difference d.

5 ()11nTand ,n=+ 11nnTTd,Ta+=+=where ()()212nnSan d= + Geometric sequences For initial term a and common ratio r: 11nnTrT ,Ta+==where 11nnTar,n = ()11nnarSr = 11 aS,rr =< Mathematics Methods 5 formula sheet UNIT 1 AND UNIT 2 Introduction to differential calculus Rates of change Difference quotient: () ( )fx h fxyxh + = Derivative (concept): ( )() ()0hfx h fxdyfxlimdxh + = = Computation of derivatives: ( ) = Anti-derivatives: ( )( )()111If then constantnnaxfxaxf xc,nn+ ==+ + Note: Any additional formulas identified by the examination writers as necessary will be included in the body of the particular question.