1.
What is true of the second differences for the equation
x
2
– 6
x
+ 12?
A.
they increase by 12
B.
they are constant
C.
they decrease by 1
D.
they increase by 1
Hint
2.
What type of relationship does the equation have if its first differences are constant?
A.
linear
B.
cubic
C.
constant
D.
quadratic
Hint
3.
What is the relationship between constant second differences and the coefficient of the equation?
A.
the second difference is –2 times the coefficient
B.
the second difference is 2 times the coefficient
C.
the second difference is opposite the coefficient
D.
the second difference is the same as the coefficient
Hint
4.
How many counterexamples are needed to prove a conjecture wrong?
A.
4
B.
1
C.
3
D.
2
Hint
5.
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.
find a counterexample to disprove the conjecture
B.
all answers are correct
C.
develop an argument to prove the conjecture
D.
test every possible case to prove the conjecture
Hint