Your Practice Paper – Applications and Interpretation HL for IBDP Mathematics
� Properties of the graphs of y x
� : a a � 1 0�a
� 1 y increases as x increases
y -intercept � 1 y decreases as x increases
y tends to zero as x tends to y tends to zero as x tends to negative infinity positive infinity Horizontal asymptote : y � 0
� Laws of logarithm , where a , b , c , p , q , x � 0 : y 1 . x � a � y � log x 2 . log a
1� 0
3 . log a � a
1 4 . log p �log q � log pq a a a
5 . log p�log q� log a a a
n
6 . log p � nlog p
7 . log a
b logc a a � log b c a a p q
L
� f( x)
� : Logistic function , where L , C and k are positive constants kx
1 � Ce �
� Semi-log model : x
1 . y � k �a � ln y � ( ln a) x � ln k : Semi-log model 2 . ln a : Gradient of the straight line graph on ln yx - plane 3 . ln k : Vertical intercept of the straight line graph on ln yx - plane
� Semi-log and log-log models : n
1 . y � k � x � ln y � nln x � ln k : Log-log model 2 . n : Gradient of the straight line graph on ln y-ln x plane 3 . ln k : Vertical intercept of the straight line graph on ln y-ln x plane
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