All SAT II Math I Resources
Example Questions
Example Question #61 : 2 Dimensional Geometry
The sides of a triangle have lengths 6 yards, 18 feet, and 216 inches. Which of the following is true about this triangle?
This triangle is right and isosceles, but not equilateral.
This triangle is right and scalene.
This triangle is acute and scalene.
This triangle is acute and isosceles, but not equilateral.
The triangle is acute and equilateral.
The triangle is acute and equilateral.
One yard is equal to 3 feet; it is also equal to 36 inches. Therefore:
18 feet is equal to yards,
and
216 feet is equal to yards.
The three sides are congruent, making the triangle equilateral - and all equilateral triangles are acute.
Example Question #1 : Analyzing Figures
Figures not drawn to scale
The triangles above are similar. Given the measurements above, what is the length of side c?
inches
inches
inches
inches
inches
inches
You can find the length of c by first finding the length of the hypotenuse of the larger similar triangle and then setting up a ratio to find the hypotenuse of the smaller similar triangle.
You also could have found 10 by recognizing this triangle is a form of a 3-4-5 triangle.
The hypotenuse of the bigger triangle is 10 inches.
Now that we know the length of the hypotenuse for the larger triangle, we can set up a ratio equation to find the hypotenuse of the smaller triangle.
cross multiply
Example Question #1 : Analyzing Figures
If line 2 and line 3 eventually intersect when extended to the left which of the following could be true?
I and III
I only
Cannot be determined
I and II
I, II, and III
I only
Read the question carefully and notice that the image is deceptive: these lines are not parallel. So we cannot apply any of our rules about parallel lines. So we cannot infer II or III, those are only true if the lines are parallel. If we sketch line 2 and line 3 meeting we will form a triangle and it is possible to make a = e. One such solution is to make a and e 60 degrees.
Example Question #501 : Sat Subject Test In Math I
What is the maximum number of distinct regions that can be created with 4 intersecting circles on a plane?
Try sketching it out.
Start with one circle and then keep adding circles like a venn diagram and start counting. A region is any portion of the figure that can be defined and has a boundary with another portion. Don't forget that the exterior (labeled 14) is a region that does not have exterior boundaries.
Example Question #1 : Analyzing Figures
Note: Figure may not be drawn to scale
In rectangle has length and width
and
respectively. Point
lies on line segment
and point
lies on line segment
. Triangle
has area
, in terms of
and
what is the possible range of values for
?
cannot be determined
Notice that the figure may not be to scale, and points and
could lie anywhere on line segments
and
respectively.
Next, recall the formula for the area of a triangle:
To find the minimum area we need the smallest possible values for and
.
To make smaller we can shift points
and
all the way to point
. This will make triangle
have a height of
:
is the minimum possible value for the area.
To find the maximum value we need the largest possible values for and
. If we shift point
all the way to point
then the base of the triangle is
and the height is
, which we can plug into the formula for the area of a triangle:
which is the maximum possible area of triangle
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