n Algebra, a term, or monomial, is comprised of a combination of one to three of the following: numbers, variables, and exponents. In Algebraic expressions and equations, terms are separated by addition and subtraction signs.

* Numbers: Constant, known quantities that remain fixed.
Examples: 100, 23, -157, π
* Variables: Symbols that represent unknown quantities.
Examples: θ, x, y, and any other letter of the alphabet
* Exponents: A known or unknown quantity that raises a base to a given power. Examples: x2 (the 2 is the exponent, x is the base); abx(the x is the exponent, b is the base); eu (the u is the exponent) Each monomial has a coefficient, which is the number that is multiplied by the other elements of the term.

Quick tip for finding the coefficient: It’s usually the number at the beginning of the monomial. Examples of Monomials
1. 15xyz
Coefficient: 15
2. -b2
Coefficient: -1 because -b2 is the same as -1b2
3. 21pq3
Coefficient: 21
4. 4ac
Coefficient: 4
When monomials, or terms, share the same variable and same exponent, they are like terms. Note: Like terms don't have to share the same coefficient. Like Terms Practice #1
Find the like terms in the following expression:
x + 2y + 3y + 3x + 15y
Answers:
x and 3x are like terms.
2y, 3y, and 15y are like terms.
Like Terms Practice #2
Find the like terms in the following expression:
x + -x2 + - x3 + y2 - y + 4y4
None of these terms are alike because of different variables and exponents. Combining Like Terms
When combining like terms, or adding and subtracting monomials, remember that the variables and exponents must be the same. I love shopping at the grocery store in the summer because of the delectable fruit. Below is a depiction of how I tally the peaches and plums that I buy. * 6 peaches + 5 peaches = 11 peaches

* 16 plums + 5 plums = 21 plums
* 6 peaches + 5 plums = 6 peaches + 5 plums
Notice that 6 peaches plus 5 plums does not equal 11...

...Algebra is a way of working with numbers and signs to answer a mathematical problem (a question using numbers)
As a single word, "algebra" can mean[1]:
* Use of letters and symbols to represent values and their relations, especially for solving equations. This is also called "Elementary algebra". Historically, this was the meaning in pure mathematics too, like seen in "fundamental theorem of algebra", but not now.
* In modern pure mathematics,
* a major branch of mathematics which studies relations and operations. It's sometimes called abstract algebra, or "modern algebra" to distinguish it from elementary algebra.
* a mathematical structure as a "linear" ring, is also called "algebra," or sometimes "algebra over a field", to distinguish it from its generalizations.
A variable is a letter or symbol that takes place of a number in Algebra. Common symbols used are a, x, y, θ, and λ. The letters x and y are commonly used, but remember that any other symbols would work just as well.
Variables are used in algebra as placeholders for unknown numbers. If you see "3 + x", don't panic! All this means is that we are adding a number who's value we don't yet know.
Term: A term is a number or a variable or the product of a number and a variable(s).
An expression is two or more...

...Review of Algebra
2
s
REVIEW OF ALGEBRA
Review of Algebra
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Here we review the basic rules and procedures of algebra that you need to know in order to be successful in calculus.
Arithmetic Operations
The real numbers have the following properties: a b b a ab a b c a b ab c ab ac In particular, putting a b and so b c b c ba c (Commutative Law) (Associative Law) (Distributive law)
ab c
a bc
1 in the Distributive Law, we get c 1 b c 1b 1c
EXAMPLE 1
(a) 3xy 4x 3 4 x 2y 12x 2y (b) 2t 7x 2tx 11 14tx 4t 2x 22t (c) 4 3 x 2 4 3x 6 10 3x If we use the Distributive Law three times, we get a b c d a bc a bd ac bc ad bd
This says that we multiply two factors by multiplying each term in one factor by each term in the other factor and adding the products. Schematically, we have a In the case where c or
1
b c
d
a and d a b
b, we have
2
a2
ba
ab
b2
a
b
2
a2
2ab
b2
Similarly, we obtain
2
a
b
2
a2
2ab
b2
REVIEW OF ALGEBRA
x
3
EXAMPLE 2
6x 2 3x (a) 2x 1 3x 5 (b) x 6 2 x 2 12x 36 2x 6 (c) 3 x 1 4x 3
10x 3 4x 2 12x 2 12x 2
5 x 3x 5x
6x 2
7x
5 12 12
3 2x 9 2x 21
Fractions
To add two fractions with the same denominator, we use the Distributive Law: a b Thus, it is true that a b c a b c b...

...Cami Petrides
Mrs. Babich
Algebra Period 4
April 1, 2014
Extra Credit Project
12. When you flip a light switch, the light seems to come on almost immediately, giving the impression that the electrons in the wiring move very rapidly.
Part A: In reality, the individual electrons in a wire move very slowly through wires. A typical speed for an electron in a battery circuit is 5.0x10 to the -4th meters per second. How long does it take an electron moving at that speed to travel a wire 1.0 centimeter, or 1.0x10 to the -2nd?
Part B: Electrons move quickly through wires, but electric energy does. It moves at almost the speed of light, 3.0x10 to the 8th meters per second. How long would it take to travel 1.0 centimeters at the speed of light?
Part C: Electrons in an ordinary flashlight can travel a total distance of only several centimeters .suppose the distance an electron can travel in a flashlight circuit is 15 centimeters, or 1.5x10 to the -1st meter. The circumference of the earth is about 4.0x10 to the 7th meters. How many trips around the earth could a pulse of electric energy make at the speed of light in the same time an electron could travel through 15 centimeters of a battery circuit in 5.0x10 to the -4th meters per second?
For part A, the first step is to put (5.0) to the 10th to the -4th. The numerator would be (0.00050) if someone were trying to put 5.0x10 to the -4th in the form it’s supposed to be in. For the second scientific...

...Name/Student Number:
Algebra 2 Final Exam
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Simplify the trigonometric expression.
1.
a.
b.
c.
d.
Answer B
In , is a right angle. Find the remaining sides and angles. Round your answers to the nearest tenth.
2.
a = 3, c = 19
a.
= 9.1°, = 80.9°, b = 18.8
c.
= 14.5°, = 75.5°, b = 18.8
b.
= 80.9°, = 9.1°, b = 18.8
d.
= 75.5°, = 14.5°, b = 18.8
Answer A
3.
What is the simplified form of sin(x + p)?
a.
cos x
b.
sin x
c.
–sin x
d.
–cos x
Answer C
Rewrite the expression as a trigonometric function of a single angle measure.
4.
a.
b.
c.
d.
Answer A
Short Answer
5.
Consider the sequence 1, , , , ,...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
6.
Consider the sequence 16, –8, 4, –2, 1, ...
a.
Describe the pattern formed in the sequence.
b.
Find the next three terms.
7.
Consider the graph of the cosine function shown below.
a. Find the period and amplitude of the cosine function.
b. At what values of for do the maximum value(s), minimum values(s), and zeros occur?
Verify the identity. Justify each step.
8.
sinΘ/cosΘ+cosΘ/sinΘ
sin^20+cos^2Θ/sinΘcosΘ
1/sinΘcosΘ...

... a) b) c)
2) Determine the degree of each of the following polynomials.
a) b) c)
3) Remove the symbols of grouping and simplify the resulting expressions by combining like terms.
a) (x + 3y – z) – (2y – x +3z) + (4z – 3x +2y)
b)
c) 3 – {2x – [1 –(x +y)] + [x – 2y]}
4) Add the algebraic expressions in each of the following groups.
a)
b)
5) Subtract the algebraic expressions in each of the following groups.
a)
b)
6) Evaluate each algebraic expression, given that x= -1, y=3, z=2, a =1/2, b= -2/3.
b) b) c)
7) Determine the degree of each of the following polynomials.
b) b) c)
8) Remove the symbols of grouping and simplify the resulting expressions by combining like terms.
d) (x + 3y – z) – (2y – x +3z) + (4z – 3x +2y)
e)
f) 3 – {2x – [1 –(x +y)] + [x – 2y]}
9) Add the algebraic expressions in each of the following groups.
c)
d)
10) Subtract the algebraic expressions in each of the following groups.
c)
d)
11) Evaluate each algebraic expression, given that x= -1, y=3, z=2, a =1/2, b= -2/3.
c) b) c)
12) Determine the degree of each of the following polynomials.
c) b) c)
13) Remove the symbols of grouping and simplify the resulting expressions by combining like terms.
g) (x + 3y – z) – (2y – x +3z) + (4z – 3x +2y)
h)
i) 3 – {2x – [1 –(x +y)] + [x – 2y]}
14) Add the algebraic expressions in...

...ALGEBRA
In all three of these problems there is use of all of the terms required: simplify, like terms, coefficient, distribution, and removing parentheses. There is also use with the real number properties of the commutative property of addition and the commutative property of multiplication. In what ways are the properties of real numbers useful for simplifying algebraic expression? The properties are useful for identifying what should go where and with what, to make it simpler to understand and to solve the equation properly. When we break things down to a simplified process, it is much easier to see how the real numbers are placed and why they are placed that way. Real numbers do not actually show the value of something real in the “real world”. For example, in mathematics if we write 0.5 we mean exactly half, but in the real world half may not be exactly half. In all reality, we use mathematics every single day, whether we consciously realize it or not. Math is the key subject that applies to our everyday lives in the “real world”.
Expression number one like terms are combined by adding coefficients, the removal of parentheses, and the use of commutative property of addition and multiplication. Expression number two has the use of quite a bit of distribution, combining like terms, and removal of parentheses. Expression number three like terms are combined by adding...

...environment, and appropriate space. In accordance with these necessities, there are a number of survival techniques used by organisms in this kingdom. These techniques can fall within the category of adaptations, which help these organisms adapt to various habitats. This kingdom falls in the domain Eukaryota, and there are nearly 40 different phyla that can be classified under the Kingdom Anamalia. Besides that there are 5 other lower levels in which these organisms can be classified, called class, order, family, genus and species. .
Invertebrates
Invertebrates are apart of the Animal Kingdom and are characterized by their inability to possess or develop a vertebral column. In the world of taxonomy, the word invertebrate is merely a convenient term used to help with this characterization. A great majority of the animal kingdom are invertebrates due to the fact that only 4% of animal species even consist of a vertebral column in their composition. Invertebrates generally have bodies comprised of differentiated tissues that compensate for the lack of structural stability that is present in vertebrates. Some also have digestive chambers that have one or two openings to their exterior. Similar to vertebrates, invertebrates generally reproduce sexually and produce specialized reproductive cells that undergo meiosis. Those cells make smaller, motile spermatozoa or large, non-motile, ova. These form zygotes and finally develop into new individuals. Other...

...
Name: _________________________
Score: ______ / ______
Algebra I Quarter 1 Exam
Answer the questions below. Make sure to show your work when applicable.
Solve the absolute value equation. Check your solutions.
| 5x + 13| = –7
5x + 13 = -7
5x = -20
X = -4
Simplify the expression below.
6n2 - 5n2 + 7n2
6 – 5 + 7 = 8
=8n2
The total cost for 8 bracelets, including shipping was $54. The shipping charge was $6. Write an equation that models the cost of each bracelet.
8 x + 6 = 54 $8.00 each bracelets
The total cost for 8 bracelets, including shipping was $54. The shipping charge was $6. Determine the cost for each bracelet. Show your work
8x+6 =54
8x=54-6
8x = 48
X = 6
Solve the inequality. Show your work.
6y – 8 ≤ 10
5. 6y – 8 ≤ 10
6y ≤ 10 +8
6y ≤ 18
y ≤ 18/6
=y ≤ 3
The figures above are similar. Find the missing length. Show your work.
x = 1.8 in
What is 30% of 70? Show your work.
30 divied by100 = .30
70 times 0.3(30% as a decimal) which will be 21
=21
Simplify the expression below.
-5-8
(16x9)/(21x8)=144/168 divided by 12=12/14=6/7
8. 6/7
Which property is illustrated by 6 x 5 = 5 x 6?
commutative property of multiplication
Evaluate the expression for the given values of the variables. Show your work.
4t + 2u2 – u3; t = 2 and u = 1
4t + 2u2 – u3; t = 2 and u = 1
4 (2) + 2 (1) 2 – (1) 3
8 + 2 – 1 = 1
Solve the...