### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Solving Other Functions

Simplify:

You may assume that is a nonnegative real number.

**Possible Answers:**

**Correct answer:**

The best way to simplify a radical within a radical is to rewrite each root as a fractional exponent, then convert back.

First, rewrite the roots as exponents.

Multiply the exponents, per the power of a power rule:

### Example Question #2 : Solving Other Functions

Define functions and .

for exactly one value of on the interval .

Which of the following statements is correct about ?

**Possible Answers:**

**Correct answer:**

Define

Then if ,

it follows that

,

or, equivalently,

.

By the Intermediate Value Theorem (IVT), if is a continuous function, and and are of unlike sign, then for some . As a polynomial, is a continuous function, so the IVT applies here.

Evaluate for each of the following values: :

Only in the case of does it hold that assumes a different sign at both endpoints - . By the IVT, , and , for some .

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### All SAT II Math I Resources

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