All SAT II Math II Resources
Example Question #1 : Analyzing Figures
Refer to the above diagram. Which of the following is not a valid name for ?
All of the other choices give valid names for the angle.
is the correct choice. A single letter - the vertex - can be used for an angle if and only if that angle is the only one with that vertex. This is not the case here. The three-letter names in the other choices all follow the convention of the middle letter being vertex and each of the other two letters being points on a different side of the angle.
Example Question #2 : Analyzing Figures
Use the rules of triangles to solve for x and y.
Using the rules of triangles and lines we know that the degree of a straight line is 180. Knowing this we can find x by creating and solving the following equation:
Now using the fact that the interior angles of a triangle add to 180 we can create the following equation and solve for y:
Example Question #3 : Analyzing Figures
Use the facts of circles to solve for x and y.
x=11, y= 39.5
x=11, y= 39.5
In this question we use the rule that oppisite angles are congruent and a line is 180 degrees. Knowing these two facts we can first solve for x then solve for y.
Example Question #4 : Analyzing Figures
Solve for x and y using the rules of quadrilateral
By using the rules of quadrilaterals we know that oppisite sides are congruent on a rhombus. Therefore, we set up an equation to solve for x. Then we will use that number and substitute it in for x and solve for y.
Example Question #5 : Analyzing Figures
Chords and intersect at point . is twice as long as ; and .
Give the length of .
If we let , then .
The figure referenced is below (not drawn to scale):
If two chords intersect inside the circle, then the cut each other so that for each chord, the product of the lengths of the two parts is the same; in other words,
Setting , and solving for :
Taking the positive square root of both sides:
the correct length of .