Mathematics SL formula booklet - Edukraft

1 Mathematical studies SL: formula booklet 1 Published March 2012 International Baccalaureate Organization 2012 5045 Mathematics SL formula booklet For use during the course and in the examinations First examinations 2014 Diploma Programme Mathematics SL formula booklet 1 Contents Prior learning 2 Topics 3 Topic 1 Algebra 3 Topic 2 Functions and equations 4 Topic 3 Circular functions and trigonometry 4 Topic 4 Vectors 5 Topic 5 Statistics and probability 5 Topic 6 Calculus 6 Mathematics SL formula booklet 2 Formulae Prior learning Area of a parallelogram A bh= Area of a triangle 1()2= Abh Area of a trapezium 1()2= +Aa bh Area of a circle 2= Ar Circumference of a circle 2= Cr Volume of a pyramid 1(area of base vertical height)3= V Volume of a cuboid (rectangular prism) = V l wh Volume of a cylinder 2= Vrh Area of the curved surface of a cylinder 2= Arh Volume of a sphere 343= Vr Volume of a cone 213= Vrh Distance between two points 1 11(, ,)xyzand 2 22(, ,)xyz 2 22121 212()()()= + + d xxyyzz Coordinates of the midpoint of a line segment with endpoints 1 11(, ,)xyz and 2 22(, ,)xyz 1 2 1 21 2, , 222+++ x xy yz z Mathematics SL formula booklet 3 Topics Topic 1 Algebra The nth term of an arithmetic sequence 1(1)=+ nuu n d The sum of n terms of an arithmetic sequence 11( 2(1) )()22= + = +nnnnSu n duu The nth term of a geometric sequence 11 =nnuur The sum of n terms of a finite geometric sequence 11(1)(1)11 == nnnururSrr, 1 r The sum of an infinite geometric sequence 11uSr = , 1r< Exponents and logarithms logxaabxb= = Laws of logarithms logloglogcccabab+= logloglogcccaabb = loglogrccar a= Change of base logloglogcbcaab= Binomial coefficient ()!

2 !!rnrnrn = Binomial theorem 1()1 + = +++++ nnnnr rnnnab aaba bbr Mathematics SL formula booklet 4 Topic 2 Functions and equations Axis of symmetry of graph of a quadratic function 2( )axis of symmetry 2bf xaxbx cxa= ++ = Relationships between logarithmic and exponential functions lnexxaa= loglogaxxaa xa= = Solutions of a quadratic equation 2240,02bbacaxbx cxaa + += = Discriminant 24bac = Topic 3 Circular functions and trigonometry Length of an arc lr = Area of a sector 212Ar = Trigonometric identity sintancos = Pythagorean identity 22sin1cos += Double angle formulae 2 sinsin 2cos = 2222cossin2 cos1 1 2csios2n = = = Cosine rule 2 222coscababC=+ ; 2 22cos2abcCab+ = Sine rule sinsinsinabcABC== Area of a triangle 1sin2 AabC= Mathematics SL formula booklet 5 Topic 4 Vectors Magnitude of a vector 222123vv v= ++v Scalar product cos =vwvw 112 23 3 = + +vw v w vwvw Angle between two vectors cos =vwvw Vector equation of a line =+trab Topic 5 Statistics and probability Mean of a set of data 11niiiniifxxf=== Probability of an event A ()P( )()=nAAnU Complementary events P( ) P( ) 1 +=AA Combined events P() P( ) P( ) P() = + ABABAB Mutually exclusive events P() P( ) P( ) = +ABAB Conditional probability P() P( ) P( | )A BA BA = Independent events P() P( ) P( ) =ABA B Expected value of a discrete random variable X E( )P() = == xXxXx Binomial distribution ~ B ( , )P ()(1),0 , 1,,rnrnXnpXr pprnr == = Mean E( )=Xnp Variance V a r ( )(1)

3 Xnpp= Standardized normal variable =xz Mathematics SL formula booklet 6 Topic 6 Calculus Derivative of ()fx 0d()()()() limdhyfx h fxy fxf xxh + = = = Derivative of nx 1()()nnf xxf xnx = = Derivative of sinx ( ) sin( ) cosfxxf xx = = Derivative of cosx ( ) cos( )sinfxxf xx = = Derivative of tanx 21() tan()cosfxxf xx = = Derivative of ex () e() exxfxf x = = Derivative of lnx 1() ln()fxxf xx = = Chain rule ()=y gu, d dd()dddy yuu fxx ux= = Product rule d ddd ddy vuy uvuvx xx= =+ Quotient rule 2dddddduvvuuyxxyv xv = = Standard integrals 1d,11nnxxxC nn+= + + 1dln,0xx Cxx=+> sin dcosxxx C= + cos dsinxxx C=+ ed e= + xxxC Area under a curve between x = a and x = b dbaAyx= Volume of revolution about the x-axis from x = a to x = b 2 dbaVyx= Total distance travelled from 1t to 2t distance 21()dttvt t= Mathematics SL formula booklet 7