下面为大家介绍的是7道SAT数学题及其解法的相关内容。这两道SAT数学题都是关于代数方面的，有一些难度，需要大家在解答的过程中适当的注意一下。下面是详细内容，大家一起来看看吧。
1.The length of a rectangle is increased by
, and the width of the rectangle is increased by
. By what percentage will the area of the rectangle be increased?
(A)
(B)
(C)
(D)
(E)
2.In an 
solution of water and alcohol, the ratio by mass of water to alcohol is 
to 
. If 
grams of a solution consisting of 
grams water for each gram of alcohol is added to the 
solution, what fraction by mass of the new solution is alcohol?
Answer Choices
(A) 
(B) 
(C) 
(D) 
(E) 
3.In the figure above, which quadrants contain pairs
that satisfy the condition
?
(A)
only
(B)
and
only
(C)
and
only
(D)
and
only
(E)
,
,
, and
4.In a class of
seniors, there are
boys for every
girls. In the junior class, there are
boys for every
girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?
(A)
(B)
(C)
(D)
(E)
5.Four distinct lines lie in a plane, and exactly two of them are parallel. Which of the following could be the number of points where at least two of the lines intersect?
. Three
. Four
. Five
Answer Choices
(A) 
only
(B)
only
(C) 
and 
only
(D) 
and 
only
(E) 
, 
, and 
6.If the graph of the function
in the
-plane contains the points
,
, and
, which of the following CANNOT be true?
(A) The graph of
has a maximum value.
(B)
for all points
on the graph of
.
(C) The graph of
is symmetric with respect to a line.
(D) The graph of
is a line.
(E) The graph of
is a parabola.
7.All numbers divisible by both 
and 
are also divisible by which of the following?
Answer Choices
(A) 
(B) 
(C) 
(D) 
(E) 
Explanation
1.The correct answer is D
Let
and
be the original length and width of the rectangle, respectively. If we denote by
and
the new length and width of the rectangle, respectively, then we have:
and
So, the new area will be:
where (
) is the original area of the rectangle.
So the area is increased by
.
2.The correct answer is B
To find what fraction by mass of the new solution is alcohol, you can find how many grams of alcohol are in the final solution of 
grams. Since the 
solution is 
part alcohol to 
parts water, it is 
alcohol. So it contains 
grams of alcohol. Similarly, the 
solution is 
alcohol by mass, so it contains 
grams of alcohol. Thus, the final 20-gram solution contains 
grams of alcohol, so 
, or 
, of it is alcohol.
3.The correct answer is C
In order for
to satisfy
, it must be true that
and
are equal to each other and not equal to zero. An example of such a pair is
, which is in quadrant
.
In quadrant
, all the
values are negative and all the
values are positive, so inquadrant
,
and
cannot be equal. For example, the pair
does not satisfy the condition, since
, not
.
In quadrant
, the
values and the
values are both negative, so it is possible for
and
to be equal. For example, the pair
is in quadrant
and
.
In quadrant
,
and
cannot be equal because the
values are positive and the
values are negative. For example, the pair
does not satisfy the condition, since
.
The quadrants that contain pairs
that satisfy the given condition are quadrants
and
only.
4.The correct answer is D
Among the
seniors, there are
boys for every
girls, so
of the seniors, or
, are boys and
, or
, are girls. Among the juniors,
are boys and
are girls. If
stands for the total number of juniors, then
are boys and
are girls. The total number of senior and junior boys is
. The total number of senior and junior girls is
. The question states that these quantities are equal, so
. Solving this gives
, or
5.The correct answer is D
Since exactly two of the four lines are parallel, the other two lines are not parallel. If the two non-parallel lines intersect at a point that is not on either one of the parallel lines, then the configuration of lines will give a total of 
points of intersection. (The best way to verify this is by drawing the two parallel lines and then putting in the other two lines.) If, on the other hand, the two non-parallel lines intersect at a point that is on one of the parallel lines, then there will be a total of 
points of intersection in the figure. (Again, a sketch is the best way to verify this.) Any arrangement of the four lines will again yield either 
or 
points of intersection. Since you can’t obtain four points of intersection, the correct answer is 
and 
only.
6.The correct answer is D
If the graph of the function
, which contains the points
,
, and
, were a line, then the slope of the segment connecting the points
and
would be the same as the slope of the segment connecting the points
and
. However, the slope of the segment connecting the points
and
is
, and the slope of the segment connecting the points
and
is
. Therefore, the graph of
cannot be a line.
The statements in the other four options could be true. For example, if the equation of
were
, then the graph of
would contain the points
,
, and
. The graph of
would be a parabola symmetric with respect to the line with equation
. The maximum value of
would occur at the point
, and
would be true for all points
on the graph of
.
7.The correct answer is A
All numbers divisible by both 
and 
are the multiples of 
and 
. Since 
and 
have no prime factor in common 
, then the least common multiple of 
and 
is equal to their product, namely 
. Every other multiple of 
and 
is divisible by 
. Thus, if 
is divisible by a number then all the multiples of 
and 
are divisible by that number. Therefore, it is enough to check by which number in the given options is 
divisible. Only 
divides
and none of the other do. The answer must be 
以上就是这7道SAT数学题的全部内容，后面的题目解答方法非常详细。大家可以在备考SAT数学考试的时候，利用题目对自己 掌握的知识点进行适当的检查和测试，以找出不足之处进行更改。
