All SAT II Math II Resources
Example Questions
Example Question #1 : Vectors
Add the vectors:
Combine the values as one vector.
Combine the terms.
The answer is:
Example Question #1 : Other Mathematical Relationships
Add in modulo 9:
In modulo 9 arithmetic, a number is congruent to the remainder of its division by 9.
Since
and
,
,
making "5" the correct response.
Example Question #1 : Other Mathematical Relationships
varies directly as
and inversely as
.
If and
, then
.
To the nearest whole number, evaluate if
and
.
Insufficient information is given to answer the question.
varies directly as
and inversely as
. This means that for some constant of variation
,
Alternatively,
We can substitute the initial conditions for thevariables on the left side and the final conditions for those on the right side, then solve for :
Example Question #2 : Other Mathematical Relationships
varies directly as both
and the square of
.
If and
, then
.
Evaluate if
and
.
varies directly as both
and the square of
. This means that for some constant of variation
,
.
Alternatively stated,
.
We can substitute the initial conditions for the variables on the left side and the final conditions for those on the right side, then solve for :
Example Question #1 : Other Mathematical Relationships
Evaluate .
The system has no solution.
Rewrite the two equations by setting and
and substituting:
The result is a two-by-two linear system in terms of and
:
This can be solved, among other ways, using Gaussian elimination on an augmented matrix:
Perform row operations until the left two columns show identity matrix . One possible sequence:
and
. In the former equation, substitute
back for
, and raise both sides to the power of 4:
All SAT II Math II Resources
