Diploma Programme Mathematics SL formula booklet For use during the course and in the examinations First examinations 2014 Published March 2012 © International Baccalaureate Organization 2012 Mathematical studies SL: Formula booklet 1 5045 Contents Prior learning Topics Topic 1—Algebra Topic 2—Functions and equations Topic 3—Circular functions and trigonometry Topic 4—Vectors Topic 5—Statistics and probability Topic 6—Calculus 2 3 3 4 4 5 5 6 Mathematics SL formula booklet 1 Formulae
Prior learning Area of a parallelogram Area of a triangle A= b ? h = A 1 (b ? h) 2 1 ( a + b) h 2 Area of a trapezium = A Area of a circle Circumference of a circle Volume of a pyramid A = ? r 2 C = 2? r = V 1 (area of base ? vertical height) 3 Volume of a cuboid (rectangular prism) Volume of a cylinder Area of the curved surface of a cylinder Volume of a sphere V =l ? w ? h V = ? r 2 h A= 2? rh V= 4 3 ? r 3 Volume of a cone V= d= 1 2 ? r h 3 ( x1 ? x2 ) 2 + ( y1 ? y2 ) 2 + ( z1 ? z2 ) 2
Distance between two points ( x1 , y1 , z1 ) and ( x2 , y2 , z2 ) Coordinates of the midpoint of a line segment with endpoints ( x1 , y1 , z1 ) and ( x2 , y2 , z2 ) ? x1 + x2 y1 + y2 z1 + z2 ? , , ? ? 2 2 ? ? 2 Mathematics SL formula booklet 2 Topics Topic 1—Algebra 1.
1 The nth term of an arithmetic sequence The sum of n terms of an arithmetic sequence The nth term of a geometric sequence un = u1 + (n ? 1)d S n= n n (2u1 + (n ? 1)d ) = (u1 + un ) 2 2 un = u1r n ? 1 The sum of n terms of a u1 (r n ? 1) u (1 ? n ) , r ? 1 = = 1 Sn finite geometric sequence r ? 1 1? r The sum of an infinite geometric sequence 1.
2 Exponents and logarithms Laws of logarithms S? = u1 , r 0 ? cos ? sin x dx = x + C = ? cos x dx sin x + C ?e 6. 5 Area under a curve between x = a and x = b x d= e x + C x b A = ? y dx a b Volume of revolution V = ? ?y 2 dx a about the x-axis from x = a to x = b 6. 6 Total distance travelled from t1 to t 2 distance = ? t2 t1 v(t ) dt Mathematics SL formula booklet 6 Mathematics SL formula booklet 7
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