Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

varsity tutors app store varsity tutors android store

Example Questions

Example Question #1 : Sigma Notation

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Rewrite the summation starting from 1 to 5 and add the terms.

Example Question #1 : Sigma Notation

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

The natural log domain is only valid for values greater than zero.  Therefore, the solution does not exist.

Example Question #1 : Sigma Notation

The Fibonacci sequence is given as

     .

     .

     .

Find      

.

Possible Answers:

Correct answer:

Explanation:

 is defined to be the sum of the  terms from  for .

In other words,

As such, the asnwer is .

Example Question #32 : Mathematical Relationships And Basic Graphs

Calculate:  

Possible Answers:

Correct answer:

Explanation:

The sigma notation indicates summation starting from 1 and ends at 4.

Substitute in order of the iteration.

The correct answer is .

Example Question #33 : Mathematical Relationships And Basic Graphs

Summation (Sigma) Notation

Rewrite the below series in summation or sigma notation: 

Possible Answers:

Correct answer:

Explanation:

First we must write an equation for the pattern in the series. We can see that this is an arithmetic pattern because the same number (4) is being added each time. 

The formula to write the rule or equation for an arithmetic pattern is: 

Where a1 is the first value in the sequence and d is the common difference, n is left as a variable. 

When we plug in the values we are given we get: 

Which simplifies to become: 

Which further simplifies to become: 

Now we must put this in the sigma or summation notation. 

We know that summation notation always involves the greek letter sigma 

The number on the bottom is the first number that is plugged in, first input or first domain number - in this case it is 1. 

The number on top is the last number that is plugged in, the last input or the number of numbers in the series - there are five numbers in this series, so it ends with 5. 

So the final summation will look like this: 

Example Question #34 : Mathematical Relationships And Basic Graphs

Solve:  

Possible Answers:

Correct answer:

Explanation:

Evaluate each summation term first.

The bottom number is the first term of the summation. Plug the number into the expression. Repeat the summation for every whole number until the summation reaches the top number.

Evaluate the next summation.

Subtract this value from the value of the first summation.

The answer is:  

Example Question #35 : Mathematical Relationships And Basic Graphs

Solve:  

Possible Answers:

Correct answer:

Explanation:

To evaluate this summation, first ignore the outside negative sign and substitute the bottom value into the quantity inside the summation.   Reiterate for every integer after zero until we reach the top integer.

Simplify.

Therefore:

The answer is .

Example Question #36 : Mathematical Relationships And Basic Graphs

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

The summation will loop from  to .

Rewrite the summation.

The answer is:  

Example Question #37 : Mathematical Relationships And Basic Graphs

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

In order to evaluate this summation, expand the terms.  Start by plugging in zero into , and repeat until we reach to two.

Simplify the terms by order of operations.

Evaluate the terms inside the parentheses first.

The answer is:  

Example Question #38 : Mathematical Relationships And Basic Graphs

Evaluate:   

Possible Answers:

Correct answer:

Explanation:

In order to solve the summation, expand the terms of the binomial.  Substitute two first, and add the quantities of each term for each integer repeating until the top integer is reached.

The answer is:  

Learning Tools by Varsity Tutors