### All SAT II Math I Resources

## Example Questions

### Example Question #3 : The Number System

Which of the following is not an irrational number?

**Possible Answers:**

**Correct answer:**

A root of an integer is one of two things, an integer or an irrational number. By testing all five on a calculator, only comes up an exact integer - 5. This is the correct choice.

### Example Question #1 : Irrational Numbers

Simplify by rationalizing the denominator:

**Possible Answers:**

**Correct answer:**

Multiply the numerator and the denominator by the conjugate of the denominator, which is . Then take advantage of the distributive properties and the difference of squares pattern:

### Example Question #1 : Imaginary Numbers

**Possible Answers:**

**Correct answer:**

### Example Question #1 : Complex Imaginary Numbers

Multiply:

**Possible Answers:**

**Correct answer:**

Use the FOIL technique:

### Example Question #2 : Irrational Numbers

Evaluate:

**Possible Answers:**

**Correct answer:**

We can set in the cube of a binomial pattern:

### Example Question #3 : Irrational Numbers

Evaluate

**Possible Answers:**

You cannot divide by complex numbers

**Correct answer:**

To divide by a complex number, we must transform the expression by multiplying it by the complex conjugate of the denominator over itself. In the problem, is our denominator, so we will multiply the expression by to obtain:

.

We can then combine like terms and rewrite all terms as . Therefore, the expression becomes:

Our final answer is therefore

### Example Question #1 : Imaginary Numbers

Simplify the following product:

**Possible Answers:**

**Correct answer:**

Multiply these complex numbers out in the typical way:

and recall that by definition. Then, grouping like terms we get

which is our final answer.

### Example Question #2 : Imaginary Numbers

Identify the real part of

**Possible Answers:**

none of the above.

**Correct answer:**

A complex number in its standard form is of the form: , where stands for the real part and stands for the imaginary part. The symbol stands for .

The real part in this problem is 1.

### Example Question #1 : Irrational Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

### Example Question #2 : Imaginary Numbers & Complex Functions

Simplify:

**Possible Answers:**

**Correct answer:**

Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.

Remember that , so .

Substitute in for

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