Your Practice Paper – Analysis and Approaches HL for IBDP Mathematics

� Solving ^d y � f ( x) � y � g( x, y) by integrating factor : dx e ^� f ( x) dx

: Integrating factor dy f ( x) d x dy f ( x) d x f ( x) dx

� f ( x) � y � g( x, y) � e� � e� � f ( x) � y � e� � g( x, y) dx dx

� Solving ^d y f ( x, y) dx ^{� by Euler ’ s method , with} ( x0, y

0) and step length h :

�xn�1 � xn

�h

� � � � dy yn�

1

� yn �h d _x

( xn, yn)

� Developing a Maclaurin series from ^d y f ( x, y) dx ^{� :}

2 3 dy d y d d y d � d

2 3 d d d d d d

� � f ( x, y) � � f ( x, y) � � � f ( x, y)

� x x x x x � x �

� Relationship between frequencies and cumulative frequencies :

� Measures of central tendency for a data set { x1 , x2, x3, , x } arranged in ascending order : x1 � x2 � x3 � � xn 1 . x �

: Mean n 2 . The datum or the average value of two data at the middle : Median 3 . The datum appears the most : Mode n

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