### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Analyzing Figures

The sides of a triangle have lengths 6 yards, 18 feet, and 216 inches. Which of the following is true about this triangle?

**Possible Answers:**

The triangle is acute and equilateral.

This triangle is right and isosceles, but not equilateral.

This triangle is right and scalene.

This triangle is acute and isosceles, but not equilateral.

This triangle is acute and scalene.

**Correct answer:**

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 #2 : Analyzing Figures

*Figures not drawn to scale*

**The triangles above are similar. Given the measurements above, what is the length of side c?**

**Possible Answers:**

inches

inches

inches

inches

inches

**Correct answer:**

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 #3 : Analyzing Figures

If line 2 and line 3 eventually intersect when extended to the left which of the following could be true?

**Possible Answers:**

I and III

I only

Cannot be determined

I, II, and III

I and II

**Correct answer:**

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 #71 : Geometry

What is the maximum number of distinct regions that can be created with 4 intersecting circles on a plane?

**Possible Answers:**

**Correct answer:**

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 #4 : 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 ?

**Possible Answers:**

cannot be determined

**Correct answer:**

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