All SAT II Math I Resources
Example Questions
Example Question #31 : Sat Subject Test In Math I
Evaulate:
Multiply both numerator and denominator by , then divide termwise:
Example Question #31 : Sat Subject Test In Math I
Which of the following is equal to ?
By the power of a product property,
Example Question #1 : Real And Complex Numbers
Multiply:
None of the other responses gives the correct answer.
Example Question #2 : Real And Complex Numbers
Which of the following is equal to ?
By the power of a product property,
Example Question #31 : Sat Subject Test In Math I
Which of the following is equal to ?
The expression is undefined.
To raise to a power, divide the exponent by 4, note its remainder, and raise
to the power of that remainder:
Therefore,
Example Question #1 : Real And Complex Numbers
What is the conjugate for the complex number
To find the conjugate of the complex number of the form , change the sign on the complex term. The complex part of the problem is
so changing the sign would make it a
. The sign in the real part of the number, the 3 in this case, does not change sign.
Example Question #1 : Real And Complex Numbers
denotes the complex conjugate of
.
If , then evaluate
.
By the difference of squares pattern,
If , then
. As a result:
Therefore,
Example Question #1 : Real And Complex Numbers
Which answer choice has the greatest real number value?
Recall the definition of and its exponents
because then
.
We can generalize this to say
Any time is a multiple of 4 then
. For any other value of
we get a smaller value.
For the correct answer each of the terms equal
So:
Because all the alternative answer choices have 4 terms, and each answer choice has at least one term that is not equal to they must all be less than the correct answer.
Example Question #1 : Real And Complex Numbers
Let and
be complex numbers.
and
denote their complex conjugates.
.
Evaluate .
Let , where all variables represent real quantities.
Then
Since
,
if follows that
and
Also, by definition,
It is known that and
, but without further information, nothing can be determined about
0r
. Therefore,
cannot be evaluated.
Example Question #31 : Sat Subject Test In Math I
Let be a complex number.
denotes the complex conjugate of
.
and
.
Evaluate .
None of these
is a complex number, so
for some real
; also,
.
Therefore,
Substituting:
Also,
Substituting:
Therefore,
Certified Tutor
All SAT II Math I Resources
![Learning Tools by Varsity Tutors](https://vt-vtwa-app-assets.varsitytutors.com/assets/problems/og_image_practice_problems-9cd7cd1b01009043c4576617bc620d0d5f9d58294f59b6d6556fd8365f7440cf.jpg)