1.
What is a conjecture?
A.
an educated guess that hasn't been proved yet
B.
a ''shot in the dark'' guess that hasn't been proved yet
C.
an educated guess that has been proved
D.
a ''shot in the dark'' guess that has been proved
Hint
2.
What is true of the second differences for the equation
x
2
– 6
x
+ 12?
A.
they decrease by 1
B.
they increase by 12
C.
they increase by 1
D.
they are constant
Hint
3.
What type of relationship does the equation have if its second differences are constant?
A.
cubic
B.
constant
C.
quadratic
D.
linear
Hint
4.
Consider the following conjecture. If an even number is written 2
k
, where
k
is a whole number, then 2
k
+ 1 must be an odd number. What can be your next course of action in dealing with this conjecture?
A.
test every possible case to prove the conjecture
B.
all answers are correct
C.
find a counterexample to disprove the conjecture
D.
develop an argument to prove the conjecture
Hint
5.
Find the values for
m
and
n
which the conjecture (
m – n
)
2
=
m
2
– n
2
is false.
A.
m
= 1,
n
= 0
B.
m
= 1,
n
= 1
C.
m
= 1,
n
= 2
D.
m
= –2,
n
= 0
Hint