Mathematics SL formula booklet - segravesmath.weebly.com

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 b h u Area of a triangle 1()2 uAb h Area of a trapezium 1()2 Aa b h Area of a circle 2 SAr Circumference of a circle 2 SCr Volume of a pyramid 1(area of base vertical height)3 uV Volume of a cuboid (rectangular prism) u uV l w h Volume of a cylinder 2 SVr h Area of the curved surface of a cylinder 2 SArh Volume of a sphere 343 SVr Volume of a cone 213 SVr h Distance between two points 111( , , )x y zand 222( ,, )x y z 222121212()()() dxxyyzz Coordinates of the midpoint of a line segment with endpoints 111( , , )x y z and 222( ,, )x y z 121212, , 222 xx yy zz Mathematics SL formula booklet 3 Topics Topic 1 Algebra The nth term of an arithmetic sequence 1(1) nuund The sum of n terms of an arithmetic sequence 11(2(1) )()22 nnnnSunduu The nth term of a geometric sequence 11 nnuu r The sum of n terms of a finite geometric sequence 11(1)(1)

2 11 nnnu rurSrr, 1zr The sum of an infinite geometric sequence 11uSrf , 1r Exponents and logarithms logxaabxb Laws of logarithms logloglogcccabab logloglogcccaabb loglogrccara Change of base logloglogcbcaab Binomial coefficient !!!rnrnrn Binomial theorem 1()1 ! !nnnn r rnnna baa ba 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 lnexx aa loglogaxxaax a Solutions of a quadratic equation 2240,02bbacaxbx cxaa r z Discriminant 24bac' Topic 3 Circular functions and trigonometry Length of an arc lrT Area of a sector 212 ArT Trigonometric identity sintancosTTT Pythagorean identity 22sin1cosTT Double angle formulae 2 sinsin 2cosTT T 2222cossin2 cos1 1 2c sios2nTTTTT Cosine rule 2222coscababC.

3 222cos2abcCab Sine rule sinsinsinabcABC Area of a triangle 1sin2 AabC Mathematics SL formula booklet 5 Topic 4 Vectors Magnitude of a vector 222123vvv v Scalar product cosT v w v w 112233 v wv wv wv w Angle between two vectors cosT v wv w Vector equation of a line = +tr a b Topic 5 Statistics and probability Mean of a set of data 11ni iiniif xxf Probability of an event A ( )P( )( ) n AAn U Complementary events P( ) P( ) 1c AA Combined events P() P( ) P( ) P() ABABAB Mutually exclusive events P() P( ) P( ) ABAB Conditional probability P() P( ) P( | )ABAB A Independent events P() P( ) P( ) ABAB Expected value of a discrete random variable X E( )P()P xXxXx Binomial distribution ~ B( , )P()(1),0, 1,,rn rnXn pXrpprnr ! Mean E( ) Xnp Variance Var( )(1)Xnpp Standardized normal variable PV xz Mathematics SL formula booklet 6 Topic 6 Calculus Derivative of ( )f x 0d()( )( )( ) limdhyf x hf xyf xf xxho c Derivative of nx 1( )( )nnf xxf xnx c Derivative of sinx ( ) sin( ) cosf xxf xxc Derivative of cosx ( ) cos( )sinf xxf xxc Derivative of tanx 21( )tan( )cosf xxf xxc Derivative of ex ( ) e( ) exxf xf xc Derivative of lnx 1( ) ln( )f xxf xxc Chain rule ( ) y g u, ddd( )dddyyuuf xxux u Product rule ddddddyvuy uvuvxxx Quotient rule 2dddddduvvuuyxxyvxv Standard integrals 1d,11nnxx xCnn z 1dln,0xx C xx !

4 Sin dcosx xx C cos dsinx xx C e de xxxC Area under a curve between x = a and x = b dbaAy x Volume of revolution about the x-axis from x = a to x = b 2 GbaVy x Total distance travelled from 1t to 2t distance 21( ) dttv tt Mathematics SL formula booklet 7