SAT II Math I : Number Theory

Example Questions

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Example Question #1 : Sat Subject Test In Math I

Express 374 in base six.

Explanation:

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.

Explanation:

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:?

Explanation:

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?

None

Explanation:

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?

Explanation:

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:

Explanation:

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:

Explanation:

Example Question #1 : Sat Subject Test In Math I

Multiply:

Explanation:

Use the FOIL technique:

Example Question #1 : Imaginary Numbers & Complex Functions

Evaluate:

Explanation:

We can set  in the cube of a binomial pattern:

Example Question #1 : Complex Conjugates

Evaluate

You cannot divide by complex numbers