SAT II Math II : SAT Subject Test in Math II

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

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Example Questions

Example Question #11 : Real And Complex Numbers

 denotes the complex conjugate of .

If , then evaluate .

Possible Answers:

Correct answer:

Explanation:

Applying the Power of a Product Rule:

The complex conjugate of an imaginary number  is ; the product of the two is 

, so, setting  in the above pattern:

Consequently, 

Example Question #11 : Real And Complex Numbers

Let  and  be complex numbers.  and  denote their complex conjugates. 

Evaluate .

Possible Answers:

Correct answer:

Explanation:

Knowing the actual values of  and   is not necessary to solve this problem. The product of the complex conjugates of two numbers is equal to the complex conjugate of the product of the numbers; that is,

We are given that  is therefore the conjugate of , or .

 

Example Question #21 : Number Theory

 denotes the complex conjugate of .

If , then evaluate .

Possible Answers:

Correct answer:

Explanation:

By the difference of squares pattern, 

If , then .

Consequently:

Therefore, 

 

Example Question #21 : Number Theory

The fraction  is equivalent to which of the following?

Possible Answers:

Undefined

Correct answer:

Explanation:

Start by multiplying the fraction by .

Since , we can then simplify the fraction:

Thus, the fraction is equivalent to .

Example Question #12 : Real And Complex Numbers

The fraction  is equivalent to which of the following?

Possible Answers:

Correct answer:

Explanation:

Start by multiplying both the denominator and the numerator by the conjugate of , which is .

Next, recall , and combine like terms.

Finally, simplify the fraction.

Example Question #11 : Real And Complex Numbers

Evaluate 

Possible Answers:

Correct answer:

Explanation:

To evaluate a power of , divide the exponent by 4 and note the remainder.

The remainder is 3, so

Consequently, using the Product of Powers Rule:

Example Question #11 : Real And Complex Numbers

Let  be a complex number.  denotes the complex conjugate of 

 and .

How many of the following expressions could be equal to ?

(a) 

(b) 

(c) 

(d) 

Possible Answers:

None

Four

One 

Three

Two

Correct answer:

Two

Explanation:

 is a complex number, so  for some real ; also, .

Therefore, 

Substituting:

Therefore, we can eliminate choices (c) and (d).

Also, the product 

Setting  and substituting 10 for , we get

Therefore, either  or  - making two the correct response.

Example Question #1 : Elementary Operations

Add the following numbers:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits.

Add the tens digits with the two as the carryover.

Add the hundreds digits with the two as the carryover.

Combine this number with the ones digits of the previous calculations.

The answer is:  

Example Question #1 : Mathematical Relationships

Add the numbers:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits.

Carry the one, and add the tens digits.

Carry the two, and add the hundreds digits.

Combine this number with the ones digit of the other numbers.

The answer is:  

Example Question #1 : Mathematical Relationships

Add the numbers:  

Possible Answers:

Correct answer:

Explanation:

Add the ones digits.

Carry the two, and add the tens digits.

Carry the two, and add the hundreds places.

Combine all ones digits.

The answer is:  

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