Analysis and Approaches for IBDP Maths Ebook 2 | Page 64

Your Practice Set – Analysis and Approaches for IBDP Mathematics
Exercise 19
1. (a) If
N
2
�8N� 10 is an even number, prove that N is also an even number.
(b) By using a counter example, show that P �Q � P � Q is not always true, where
P , Q� .
2. (a) Prove that the equation
(b)
x .
By using a counter example, show that
b� and b � 0.
1 x � 4
� �0
has no real solution for all real values of
x � 2 2
a
b
e
a
e
b
e
� � is not always true, where a ,
1 1
3. (a) By using a counter example, show that � is not always true, where a ,
2 2
a b
b� and a , b � 0 .
(b) Prove that the sequence 2 x 2
� 1,
2 x � 1,
for all positive real values of x .
3
2 x � 1, … is not an arithmetic sequence
4. (a) By using a counter example, show that log2 x� log4
x is not always true for all
positive real values of x .
(b) Prove that the sequence log x ,
all positive real values of x .
2
log x ,
3
log x , … is not a geometric sequence for
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