Mathematical studies SL formula booklet - Edukraft

1 Mathematical studies SL formula booklet 1 Published March 2012 International Baccalaureate Organization 2012 5042 Mathematical studies SL formula booklet For use during the course and in the examinations First examinations 2014 Diploma Programme Mathematical studies SL formula booklet 1 Contents Prior learning 2 Topics 3 Topic 1 Number and algebra 3 Topic 2 Descriptive statistics 3 Topic 3 Logic, sets and probability 4 Topic 5 Geometry and trigonometry 5 Topic 6 Mathematical models 6 Topic 7 Introduction to differential calculus 6 Mathematical studies SL formula booklet 2 Prior learning Area of a parallelogram A bh= , where b is the base, h is the height Area of a triangle 1()2 Abh= , where b is the base, h is the height Area of a trapezium 1()

2 2= +Aa bh, where a and b are the parallel sides, h is the height Area of a circle 2= Ar, where r is the radius Circumference of a circle 2= Cr, where r is the radius Distance between two points 11(, )xy and 22(, )xy 22121 2()()= + d xxyy Coordinates of the midpoint of a line segment with endpoints 11(, )xy and 22(, )xy 1 21 2, 22++ xxyy Mathematical studies SL formula booklet 3 Topics Topic 1 Number and algebra Percentage error AEE100%vvv = , where Ev is the exact value and Av is the approximate value of v The nth term of an arithmetic sequence 1(1)=+ nuu n d The sum of n terms of an arithmetic sequence 11[ 2(1) ]()22nnnnSu n duu= + = + The nth term of a geometric sequence 11 =nnuur The sum of n terms of a geometric sequence 11(1)(1)

3 11nnnururSrr == , 1 r Compound interest 1100knrFVPVk = + , where FV = future value, PV = present value, n = number of years, k = number of compounding periods per year, r% = nominal annual rate of interest Topic 2 Descriptive statistics Mean of a set of data 1kiiifxxn== , where 1 == kiinf Interquartile range 31 IQRQQ= Mathematical studies SL formula booklet 4 Topic 3 Logic, sets and probability Truth tables p q p pq pq pq pq pq T T F T T F T T T F F F T T F F F T T F T T T F F F T F F F T T Probability of an event A number of outcomes in P( )total number of outcomesAA= Complementary events P( ) 1 P( ) = AA Combined events P() P( ) P( ) P()ABABAB = + Mutually exclusive events P() 0AB = Independent events P() P( ) P( )ABA B = Conditional probability P()P( | )P( )ABABB = Mathematical studies SL formula booklet 5 Topic 5 Geometry and trigonometry Equation of a straight line ;0= + + +=ymxc axbyd Gradient formula 2121 = yymxx Sine rule sinsinsin==abcABC Cosine rule 22 22 222cos.

4 Cos2+ =+ =bcaabcbcAAbc Area of a triangle A= 1sin2abC, where a and b are adjacent sides, C is the included angle Area of the curved surface of a cylinder 2= Arh, where r is the radius, h is the height Surface area of a sphere 24 =Ar, where r is the radius Area of the curved surface of a cone A= rl, where r is the radius, l is the slant height Volume of a pyramid 1,3 VAh=where A is the area of the base, h is the vertical height Volume of a cuboid = V l wh, where l is the length, w is the width, h is the height Volume of a cylinder 2= Vrh, where r is the radius, h is the height Volume of a sphere 343= Vr, where r is the radius Volume of a cone 213= Vrh, where r is the radius, h is the vertical height Volume of a prism V = Ah, where A is the area of cross-section, h is the height Mathematical studies SL formula booklet 6 Topic 6 Mathematical models Equation of the axis of symmetry for the graph of the quadratic function 2yaxbx c= ++ 2= bxa Topic 7 Introduction to differential calculus Derivative of axn 1()()nnf xaxf xnax = = Derivative of a sum 11(), ()()()nmnmf xaxg xbxf xg xnaxmbx = = += +