All SAT II Math I Resources
Example Questions
Example Question #111 : Sat Subject Test In Math I
Multiply in modulo 6:
In modulo 6 arithmetic, a number is congruent to the reainder of its division by 6.
Therefore, since and
,
.
The correct response is 0.
Example Question #111 : Sat Subject Test In Math I
Which is an example of a set that is not closed under addition?
The set of all positive even integers
The set of all negative integers
The set
All of the sets given in the other responses are closed under addition.
The set of all integers between 1 and 10 inclusive
The set of all integers between 1 and 10 inclusive
A set is closed under addition if and only if the sum of any two (not necessarily distinct) elements of the set is also an element of the set.
is closed under addition, since
The set of all negative integers is closed under addition, since any two negative integers can be added to yield a third negative integer.
The set of all positive even integers is closed under addition, since any two positive even integers can be added to yield a third positive even integer.
The remaining set is the set of all integers between 1 and 10 inclusive. It is not closed under addition, as can be seen by this counterexample:
but
Example Question #111 : Sat Subject Test In Math I
varies directly as the square root of
.
If then
. To the nearest tenth, calculate
if
.
varies directly as
, which means that for some constant of variation
,
We can write this relationship alternatively as
where the initial conditions can be substituted on the left side and final conditions, on the right. We will be solving for in the equation
Example Question #71 : Mathematical Relationships
varies inversely as the square of
and directly as the cube of
.
If and
, then
. Calculate
if
.
varies inversely as
and directly as the cube of
. This means that for some constant of variation
,
We can write this relationship alternatively as
where the initial conditions can be substituted on the left side and final conditions, on the right. We will be solving for in the equation
Example Question #1 : Other Mathematical Relationships
Sarah notices her map has a scale of . She measures
between Beaver Falls and Chipmonk Cove. How far apart are the cities?
is the same as
So to find out the distance between the cities
Example Question #2 : Direct Proportionality
If an object is hung on a spring, the elongation of the spring varies directly as the mass of the object. A 20 kg object increases the length of a spring by exactly 7.2 cm. To the nearest tenth of a centimeter, by how much does a 32 kg object increase the length of the same spring?
Let be the mass of the weight and the elongation of the spring. Then for some constant of variation
,
We can find by setting
from the first situation:
so
In the second situation, we set and solve for
:
which rounds to 11.5 centimeters.
Example Question #1 : Other Mathematical Relationships
Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?
(1 gallon = 4 quarts)
First set up the proportion:
x =
Then convert this to gallons:
Example Question #1 : Other Mathematical Relationships
Sally currently has 192 books. Three months ago, she had 160 books. By what percentage did her book collection increase over the past three months?
To find the percentage increase, divide the number of new books by the original amount of books:
She has 32 additional new books; she originally had 160.
Example Question #1 : Proportionalities
Find for the proportion
.
To find x we need to find the direct proportion. In order to do this we need to cross multiply and divide.
From here we mulitply 100 and 1 together. This gets us 100 and now we divide 100 by 4 which results in
Example Question #1 : Basic Single Variable Algebra
On a map of the United States, Mark notices a scale of
. If the distance between New York City and Los Angeles in real life is
, how far would the two cities be on Mark's map?
If the real distance between the two cities is
, and
=
, then we can set up the proportional equation:
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