Your Practice Paper – Analysis and Approaches 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
� Properties of the graphs of y� log a x:
a � 1 0�a
� 1
x -intercept � 1 y increases as x increases y decreases as x increases x tends to zero as y tends to x tends to zero as y tends to negative infinity positive infinity Vertical asymptote : x � 0
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Polynomials
� Number of roots of the polynomial The maximum number of roots of f( x) � 0 is n
n f ( x)
� a x � a x � � a x � a x � a : n n�1 2 n�1 2 1 0
� Sum and product of roots of
1 . r , 1 r
2
, …, r n
: Roots an�
1
2 . r1� r2 � � rn
� � a a0
3 . r1 r2 r3 r
1
( 1 ) n n� rn
� � a
n n n f ( x)
� a x � a x � � a x � a x � a : n n�1 2 n�1 2 1 0
� Factor theorem : ( x� a) is a factor of f( x ) if f( a) � 0 � q �
( px � q) is a factor of f( x ) if f � � � 0 � p �
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