### All SAT II Math I Resources

## Example Questions

### Example Question #1 : Sat Subject Test In Math I

Express 374 in base six.

**Possible Answers:**

**Correct answer:**

To convert a base ten number to base six, divide the number by six, with the remainder being the digit in the units place; continue, dividing each successive quotient by 6 and putting the remainder in the next position to the left until the final quotient is less than 6.

- the rightmost digit is 2

- the next digit to the left is 2

- the next digit to the left is 4, and the digit to the left of that is 1.

### Example Question #2 : Types Of Numbers

Express in base ten.

**Possible Answers:**

**Correct answer:**

Place values in the base five system are powers of five rather than powers of ten. is equal to

### Example Question #3 : Types Of Numbers

Which of the following is the smallest prime number:?

**Possible Answers:**

**Correct answer:**

A prime number has only two factor, and itself.

This is not true for or so they are not the answer.

are all prime numbers and is the smallest so it is your answer.

### Example Question #1 : Types Of Numbers

Which of the following is a rational number?

**Possible Answers:**

None

**Correct answer:**

A rational number is any number that can be expressed as an integer p or a fraction p/q. In the set of number given only fits into that category.

### Example Question #6 : Irrational Numbers

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 : Sat Subject Test In Math I

Multiply:

**Possible Answers:**

**Correct answer:**

Use the FOIL technique:

### Example Question #1 : Imaginary Numbers & Complex Functions

Evaluate:

**Possible Answers:**

**Correct answer:**

We can set in the cube of a binomial pattern:

### Example Question #1 : Complex Conjugates

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