SAT II Math I : Number Theory

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

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Example Question #1 : Sat Subject Test In Math I

Express 374 in base six.

Possible Answers:

Correct answer:

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 #1 : Sat Subject Test In Math I

Express   in base ten.

Possible Answers:

Correct answer:

Explanation:

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

Example Question #1 : Number Theory

Which of the following is the smallest prime number:?

Possible Answers:

Correct answer:

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 #2 : Sat Subject Test In Math I

Which of the following is a rational number?

Possible Answers:

None

Correct answer:

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 #1 : Understand The Difference Between Rational And Irrational Numbers: Ccss.Math.Content.8.Ns.A.1

Which of the following is not an irrational number?

Possible Answers:

Correct answer:

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:

Possible Answers:

Correct answer:

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:

Example Question #1 : Imaginary Numbers

Possible Answers:

Correct answer:

Explanation:

Example Question #1 : Imaginary Numbers

Multiply:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL technique:

Example Question #241 : Gre Subject Test: Math

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

We can set  in the cube of a binomial pattern:

Example Question #1 : Complex Imaginary Numbers

Evaluate 

Possible Answers:

You cannot divide by complex numbers

Correct answer:

Explanation:

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 

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