### All SAT II Math II Resources

## Example Questions

### Example Question #1 : Simplifying Expressions

Decrease by 40%. Which of the following will this be equal to?

**Possible Answers:**

**Correct answer:**

A number decreased by 40% is equivalent to 100% of the number minus 40% of the number. This is taking 60% of the number, or, equivalently, multiplying it by 0.6.

Therefore, decreased by 40% is 0.6 times this, or

### Example Question #2 : Simplifying Expressions

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #3 : Simplifying Expressions

Assume all variables assume positive values.

Simplify:

**Possible Answers:**

**Correct answer:**

### Example Question #4 : Simplifying Expressions

Assume all variables assume positive values. Simplify:

**Possible Answers:**

The expression is already simplified.

The expression is undefined.

**Correct answer:**

Any nonzero expression raised to the power of 0 is equal to 1. Therefore,

### Example Question #5 : Simplifying Expressions

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

Distribute the outer term through both terms in the parentheses.

Multiply each term.

There are no like-terms.

The answer is:

### Example Question #6 : Simplifying Expressions

Simplify the expression:

**Possible Answers:**

**Correct answer:**

Distribute the integers through the binomials.

Combine like-terms.

The answer is:

### Example Question #7 : Simplifying Expressions

Simplify .

**Possible Answers:**

**Correct answer:**

We can start by distributing the negative sign in the parentheses term:

Now we can combine like terms. The constants go together, and the variables go together:

### Example Question #8 : Simplifying Expressions

Simplify .

**Possible Answers:**

**Correct answer:**

First, we can distribute the negative sign through the parentheses term:

Now we gather like terms. Remember, you can't gather different variables together. The 's and 's will still be separate terms:

### Example Question #9 : Simplifying Expressions

Simplify .

**Possible Answers:**

**Correct answer:**

Start by distributing the negative sign through the parentheses term:

Now combine like terms. Each variable can't be combined with different variables:

### Example Question #10 : Simplifying Expressions

Simplify

**Possible Answers:**

**Correct answer:**

A square root is the inverse of squaring a term, so they cancel each other out:

From there, there's nothing left to simplify.