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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #11 : Sigma Notation

Evaluate: $2\sum_{i=2}^{5}2$

Possible Answers:

Correct answer:

Explanation:

Write out the terms of the sigma notation. This will repeat for the second to the fifth term. There is no variable to substitute, which means that after every iteration, the value that is summed is two.

$2\sum_{i=2}^{5}2 = 2[2+2+2+2] = 2[8] = 16$

The answer is:

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Example Question #40 : Mathematical Relationships And Basic Graphs

Evaluate: $\sum_{n=8}^{10} (10-n)$

Possible Answers:

Correct answer:

Explanation:

In order to evaluate the summation, substitute the bottom number into the quantity, and repeat for every integer after the eight and up to the top number, ten.

$\sum_{8}^{10} (10-n) = (10-8)+(10-9)+(10-10)$

Evaluate each term and simplify.

2+1+0 = 3

The answer is:

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Example Question #41 : Mathematical Relationships And Basic Graphs

Evaluate the summation: $\sum_{n=3}^{6} (1-6n)$

Possible Answers:

Correct answer:

Explanation:

This summation will repeat three times, for n=4,5,6 .

Substitute the first term into the parentheses, repeat, and sum the process for the next three terms.

$\sum_{n=3}^{6} (1-6n)$

=(1-6(3))+(1-6(4))+(1-6(5))+(1-6(6))

Simplify each term.

(-17)+(-23)+(-29)+(-35) =-104

The answer is:

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Example Question #42 : Mathematical Relationships And Basic Graphs

Determine the value of: $\sum_{0}^{2}2n^6$

Possible Answers:

128

130

$\textup{The answer is not given.}$

Correct answer:

130

Explanation:

Expand the summation sign. Start with zero as the first index, then one, and finally two. Since two is the top digit, the summation will stop.

$\sum_{0}^{2}2n^6=2(0)^6+2(1)^6+2(2)^6$

Simplify these terms.

0+2+2(64) = 2+128 = 130

The answer is: 130

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Example Question #2701 : Algebra Ii

$\sum_{k=1}^{4} k^2 - 7$

Possible Answers:

104

Correct answer:

Explanation:

This notation is asking us to add k^2 - 7 for all integer values of k between 1 and 4:

(1^2 - 7 ) + (2^2 - 7 ) + (3^2 - 7 ) + (4^2 - 7 )

(1-7) + (4-7) + (9-7) + (16-7 ) = -6 + -3 + 2 + 9 = 2

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Example Question #22 : Sigma Notation

$\sum_{n=0}^{4} \binom{4}{n}$

Possible Answers:

$8.\overline{3}$

Correct answer:

Explanation:

This expression is asking us to add the expressions $\binom{4}{n}$ for every integer value of n from 0 to 4:

$\binom{4}{0 } + \binom{4}{1} + \binom{4}{2} + \binom{4}{3} + \binom{4}{4}$

$\frac{4!}{0! \cdot 4!} + \frac{4!}{1!\cdot3! } + \frac{4!}{2! \cdot 2! } + \frac{4! } { 3! \cdot 1! } + \frac{4!}{4! \cdot 0!}$

1 + 4 + 6 + 4 + 1 = 16

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Example Question #23 : Sigma Notation

$\sum_{k=1}^{3} 20 \cdot (\frac{1}{2} ) ^k$

Possible Answers:

17.5

Correct answer:

17.5

Explanation:

$\sum_{k=1}^{3} 20 \cdot (\frac{1}{2} ) ^k$ means that we are adding half of 20, plus half of that, plus half of that.

1: $20 \cdot (\frac{1}{2} ) = 10$

2: $10(\frac{1}{2} ) = 5$

3: $5(\frac{1}{2} ) = 2.5$

10 + 5 + 2.5 = 17.5

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Example Question #2702 : Algebra Ii

$\sum_{n=3}^{5} \left (n-5 \right )$

Possible Answers:

Correct answer:

Explanation:

This is asking us to add n-5 for n = 3 and 4.

(3 -5 ) + (4 - 5 ) = -2 + -1 = -3

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Example Question #2703 : Algebra Ii

Calculate $\sum_{n=0}^{5} \frac{1}{2}n^2 +1$

Possible Answers:

33.5

32.5

27.5

Correct answer:

33.5

Explanation:

This is asking us to plug in the integers between 0 and 5, then add these numbers together.

$(\frac{1}{2} (0)^2 +1 ) + (\frac{1}{2} (1)^2 +1 ) + (\frac{1}{2} (2)^2 +1 ) + (\frac{1}{2} (3)^2 +1 ) + (\frac{1}{2} (4)^2 +1 ) +(\frac{1}{2} (5)^2 +1 )$

= (0+1) + (.5+1) + (2+1) + (4.5+1) + (8+1) + (12.5+1) = 33.5

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Example Question #2704 : Algebra Ii

Evaluate $\sum_{n=0}^{4} 6 \cdot(\frac{2}{3})^n$

Possible Answers:

$9.\overline{629}$

$1.\overline{185}$

$14.\overline{4}$

$15.\overline{629}$

Correct answer:

$15.\overline{629}$

Explanation:

This is asking us to add 6 plus two thirds of 6, plus two thirds of that, etc.

$6 + 6 \cdot \frac{2}{3} + 6 \cdot\left ( \frac{2}{3} \right )^2 + 6 \cdot \left (\frac{2}{3} \right ) ^3 + 6 \cdot \left (\frac{2}{3} \right )^4$

$= 6 + 4 + 2.\overline{6} + 1. \overline{7} + 1.\overline{185} = 15. \overline{629}$

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Algebra II : Algebra II

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #11 : Sigma Notation

Example Question #40 : Mathematical Relationships And Basic Graphs

Example Question #41 : Mathematical Relationships And Basic Graphs

Example Question #42 : Mathematical Relationships And Basic Graphs

Example Question #2701 : Algebra Ii

Example Question #22 : Sigma Notation

Example Question #23 : Sigma Notation

Example Question #2702 : Algebra Ii

Example Question #2703 : Algebra Ii

Example Question #2704 : Algebra Ii

All Algebra II Resources

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